{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":8050,"title":"Stress-Strain Properties - 3","description":"A brittle material will not exhibit a yield point. In other words, the yield point and failure point coincide. In such cases, the yield strain and failure strain (also known as ultimate strain or elongation) are the same value. On the other hand, ductile materials have a failure strain that is significantly greater than the elastic strain, as shown in the figure below.\r\n\r\n(from quora.com)\r\nWrite a function to determine the qualitative brittleness of the material by calculating the ratio of elastic strain to failure strain. A ratio of one indicates complete brittleness, whereas a ratio close to zero indicates essentially no brittleness.\r\nPrevious problem: 2 - resilience. Next problem: 4 - strength-to-weight ratio.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 529px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 264.5px; transform-origin: 332px 264.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 42px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA brittle material will not exhibit a yield point. In other words, the yield point and failure point coincide. In such cases, the yield strain and failure strain (also known as ultimate strain or elongation) are the same value. On the other hand, ductile materials have a failure strain that is significantly greater than the elastic strain, as shown in the figure below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 304px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 152px; text-align: center; transform-origin: 309px 152px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://qph.cf2.quoracdn.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: center; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(from quora.com)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 31.5px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the qualitative brittleness of the material by calculating the ratio of elastic strain to failure strain. A ratio of one indicates complete brittleness, whereas a ratio close to zero indicates essentially no brittleness.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePrevious problem: 2 -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eresilience\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Next problem: 4 -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003estrength-to-weight ratio\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [BR] = stress_strain3(e_y,e_u)\r\n\r\nBR = 1;\r\n\r\nend\r\n","test_suite":"%% Note\r\n% The following properties are measured at room temperature and are tensile\r\n% in a single direction. Some materials, such as metals are generally\r\n% isotropic, whereas others, like composite are highly anisotropic\r\n% (different properties in different directions). Also, property values can\r\n% range depending on the material grade. Finally, thermal or environmental\r\n% changes can alter these properties, sometimes drastically.\r\n\r\n%% steel alloy (ASTM A36)\r\nS_y = 250e6; %Pa\r\nS_u = 400e6; %Pa\r\ne_y = 0.00125;\r\ne_u = 0.35;\r\nnu = 0.26;\r\nG = 79.3e9; %Pa\r\nE = 200e9; %Pa\r\ndensity = 7.85; %g/cm^3\r\nsh_exp = 0.14; %strain-hardening exponent\r\nsh_coeff = 0.463; %strain-hardening coefficient\r\nBR_corr = 0.003571;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% titanium (Ti-6Al-4V)\r\nS_y = 830e6; %Pa\r\nS_u = 900e6; %Pa\r\ne_y = 0.00728;\r\ne_u = 0.14;\r\nnu = 0.342;\r\nG = 44e9; %Pa\r\nE = 114e9; %Pa\r\ndensity = 4.51; %g/cm^3\r\nsh_exp = 0.04; %strain-hardening exponent\r\nsh_coeff = 0.974; %strain-hardening coefficient\r\nBR_corr = 0.052;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% Inconel 718\r\nS_y = 1172e6; %Pa\r\nS_u = 1407e6; %Pa\r\ne_y = 0.00563;\r\ne_u = 0.027;\r\nnu = 0.29;\r\nG = 11.6e9; %Pa\r\nE = 208e9; %Pa\r\ndensity = 8.19; %g/cm^3\r\nsh_exp = 0.075; %strain-hardening exponent\r\nsh_coeff = 1.845; %strain-hardening coefficient\r\nBR_corr = 0.2085;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% aluminum alloy (6061-T6)%^\u0026\r\nS_y = 241e6; %Pa\r\nS_u = 300e6; %Pa\r\ne_y = 0.0035;\r\ne_u = 0.15;\r\nnu = 0.33;\r\nG = 26e9; %Pa\r\nE = 68.9e9; %Pa\r\ndensity = 2.7; %g/cm^3\r\nsh_exp = 0.042; %strain-hardening exponent\r\nsh_coeff = 0.325; %strain-hardening coefficient\r\nBR_corr = 0.02333;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% copper\r\nS_y = 70e6; %Pa\r\nS_u = 220e6; %Pa\r\ne_y = 0.00054;\r\ne_u = 0.48;\r\nnu = 0.34;\r\nG = 48e9; %Pa\r\nE = 130e9; %Pa\r\ndensity = 8.92; %g/cm^3\r\nsh_exp = 0.44; %strain-hardening exponent\r\nsh_coeff = 0.304; %strain-hardening coefficient\r\nBR_corr = 0.001125;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% rhenium\r\nS_y = 317e6; %Pa\r\nS_u = 1130e6; %Pa\r\ne_y = 0.000685;\r\ne_u = 0.24;\r\nnu = 0.3;\r\nG = 178e9; %Pa\r\nE = 463e9; %Pa\r\ndensity = 21.02; %g/cm^3\r\nsh_exp = 0.353; %strain-hardening exponent\r\nsh_coeff = 1.870; %strain-hardening coefficient\r\nBR_corr = 0.002854;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6)\r\nS_y = 82e6; %Pa\r\nS_u = 82e6; %Pa\r\ne_y = 0.0265;\r\ne_u = 0.45;\r\nnu = 0.41;\r\nG = 2.8e9; %Pa\r\nE = 3.1e-2; %Pa\r\ndensity = 1.14; %g/cm^3\r\nBR_corr = 0.058889;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6) reinforced with 45wt.% glass fiber\r\nS_y = 230e6; %Pa\r\nS_u = 230e6; %Pa\r\ne_y = 0.016;\r\ne_u = 0.016;\r\nnu = 0.35;\r\nG = 13.0e9; %Pa\r\nE = 14.5e9; %Pa\r\ndensity = 1.51; %g/cm^3\r\nBR_corr = 1.0;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% diamond\r\nS_y = 1200e6; %Pa\r\nS_u = 1200e6; %Pa\r\ne_y = 0.001;\r\ne_u = 0.001;\r\nnu = 0.20;\r\nG = 478e9; %Pa\r\nE = 1200e9; %Pa\r\ndensity = 3.51; %g/cm^3\r\nBR_corr = 1.0;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\te_y = 0.00125;\r\n\t\te_u = 0.35;\r\n\t\tBR_corr = 0.003571;\r\n\tcase 2\r\n\t\te_y = 0.00054;\r\n\t\te_u = 0.48;\r\n\t\tBR_corr = 0.001125;\r\n\tcase 3\r\n\t\te_y = 0.0035;\r\n\t\te_u = 0.15;\r\n\t\tBR_corr = 0.02333;\r\n\tcase 4\r\n\t\te_y = 0.00054;\r\n\t\te_u = 0.48;\r\n\t\tBR_corr = 0.001125;\r\nend\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\te_y = 0.0265;\r\n\t\te_u = 0.45;\r\n\t\tBR_corr = 0.058889;\r\n\tcase 2\r\n\t\te_y = 0.00728;\r\n\t\te_u = 0.14;\r\n\t\tBR_corr = 0.052;\r\n\tcase 3\r\n\t\te_y = 0.00563;\r\n\t\te_u = 0.027;\r\n\t\tBR_corr = 0.2085;\r\n\tcase 4\r\n\t\te_y = 0.016;\r\n\t\te_u = 0.016;\r\n\t\tBR_corr = 1.0;\r\nend\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\te_y = 0.00125;\r\n\t\te_u = 0.35;\r\n\t\tBR_corr = 0.003571;\r\n\tcase 2\r\n\t\te_y = 0.00563;\r\n\t\te_u = 0.027;\r\n\t\tBR_corr = 0.2085;\r\n\tcase 3\r\n\t\te_y = 0.00728;\r\n\t\te_u = 0.14;\r\n\t\tBR_corr = 0.052;\r\n\tcase 4\r\n\t\te_y = 0.00054;\r\n\t\te_u = 0.48;\r\n\t\tBR_corr = 0.001125;\r\nend\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":26769,"edited_by":26769,"edited_at":"2024-03-27T17:42:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":241,"test_suite_updated_at":"2015-03-30T18:54:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-03-30T18:53:23.000Z","updated_at":"2026-03-31T10:56:32.000Z","published_at":"2015-03-30T18:53:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA brittle material will not exhibit a yield point. In other words, the yield point and failure point coincide. In such cases, the yield strain and failure strain (also known as ultimate strain or elongation) are the same value. On the other hand, ductile materials have a failure strain that is significantly greater than the elastic strain, as shown in the figure below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(from quora.com)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine the qualitative brittleness of the material by calculating the ratio of elastic strain to failure strain. A ratio of one indicates complete brittleness, whereas a ratio close to zero indicates essentially no brittleness.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 2 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eresilience\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Next problem: 4 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003estrength-to-weight ratio\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"contentType\":\"image/net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"content\":\"https://qph.cf2.quoracdn.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":8054,"title":"Stress-Strain Properties - 7","description":"The toughness of a material is technically defined as the plastic strain energy absorbed by the material (the plastic region in the figure below). Practically speaking, it's a measure of how much deformation a material can undergo (or energy it can absorb) before failure.\r\n\r\nWrite a function to calculate the toughness of a material—the absorbed strain energy minus the resilience. This can be accomplished by combining the code written in problem 2 (resilience) and problem 6 (absorbed strain energy). Also, return the fraction of absorbed strain energy that the toughness represents.\r\nPrevious problem: 6 - absorbed strain energy. Next problem: 8 - material properties list.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 499px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 249.5px; transform-origin: 332px 249.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 31.5px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe toughness of a material is technically defined as the plastic strain energy absorbed by the material (the plastic region in the figure below). Practically speaking, it's a measure of how much deformation a material can undergo (or energy it can absorb) before failure.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 304px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 152px; text-align: center; transform-origin: 309px 152px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://qph.cf2.quoracdn.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 42px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to calculate the toughness of a material—the absorbed strain energy minus the resilience. This can be accomplished by combining the code written in\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eproblem 2\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (resilience) and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eproblem 6\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (absorbed strain energy). Also, return the fraction of absorbed strain energy that the toughness represents.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePrevious problem: 6 -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eabsorbed strain energy\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Next problem: 8 -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ematerial properties list\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff)\r\n\r\nT = 1;\r\n\r\nfrac = 0.5;\r\n\r\nend\r\n","test_suite":"%% Note\r\n% The following properties are measured at room temperature and are tensile\r\n% in a single direction. Some materials, such as metals, are generally\r\n% isotropic, whereas others, like composites, are highly anisotropic\r\n% (different properties in different directions). Also, property values can\r\n% range depending on the material grade. Finally, thermal or environmental\r\n% changes can alter these properties, sometimes drastically.\r\n\r\n%% steel alloy (ASTM A36)\r\nS_y = 250e6; %Pa\r\nS_u = 400e6; %Pa\r\ne_y = 0.00125;\r\ne_u = 0.35;\r\nnu = 0.26;\r\nG = 79.3e9; %Pa\r\nE = 200e9; %Pa\r\ndensity = 7.85; %g/cm^3\r\nsh_exp = 0.14; %strain-hardening exponent\r\nsh_coeff = 463e6; %strain-hardening coefficient\r\nT_corr = 12.26e7;\r\nfrac_corr = 0.9987;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% titanium (Ti-6Al-4V)\r\nS_y = 830e6; %Pa\r\nS_u = 900e6; %Pa\r\ne_y = 0.00728;\r\ne_u = 0.14;\r\nnu = 0.342;\r\nG = 44e9; %Pa\r\nE = 114e9; %Pa\r\ndensity = 4.51; %g/cm^3\r\nsh_exp = 0.04; %strain-hardening exponent\r\nsh_coeff = 974e6; %strain-hardening coefficient\r\nT_corr = 11.82e7;\r\nfrac_corr = 0.9751;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% Inconel 718\r\nS_y = 1172e6; %Pa\r\nS_u = 1407e6; %Pa\r\ne_y = 0.00563;\r\ne_u = 0.027;\r\nnu = 0.29;\r\nG = 11.6e9; %Pa\r\nE = 208e9; %Pa\r\ndensity = 8.19; %g/cm^3\r\nsh_exp = 0.075; %strain-hardening exponent\r\nsh_coeff = 1845e6; %strain-hardening coefficient\r\nT_corr = 3.205e7;\r\nfrac_corr = 0.9067;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% aluminum alloy (6061-T6)\r\nS_y = 241e6; %Pa\r\nS_u = 300e6; %Pa\r\ne_y = 0.0035;\r\ne_u = 0.15;\r\nnu = 0.33;\r\nG = 26e9; %Pa\r\nE = 68.9e9; %Pa\r\ndensity = 2.7; %g/cm^3\r\nsh_exp = 0.042; %strain-hardening exponent\r\nsh_coeff = 325e6; %strain-hardening coefficient\r\nT_corr = 4.279e7;\r\nfrac_corr = 0.9902;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% copper\r\nS_y = 70e6; %Pa\r\nS_u = 220e6; %Pa\r\ne_y = 0.00054;\r\ne_u = 0.48;\r\nnu = 0.34;\r\nG = 48e9; %Pa\r\nE = 130e9; %Pa\r\ndensity = 8.92; %g/cm^3\r\nsh_exp = 0.44; %strain-hardening exponent\r\nsh_coeff = 304e6; %strain-hardening coefficient\r\nT_corr = 7.340e7;\r\nfrac_corr = 0.9997;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% rhenium\r\nS_y = 317e6; %Pa\r\nS_u = 1130e6; %Pa\r\ne_y = 0.000685;\r\ne_u = 0.24;\r\nnu = 0.3;\r\nG = 178e9; %Pa\r\nE = 463e9; %Pa\r\ndensity = 21.02; %g/cm^3\r\nsh_exp = 0.353; %strain-hardening exponent\r\nsh_coeff = 1870e6; %strain-hardening coefficient\r\nT_corr = 20.05e7;\r\nfrac_corr = 0.9995;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6)\r\nS_y = 82e6; %Pa\r\nS_u = 82e6; %Pa\r\ne_y = 0.0265;\r\ne_u = 0.45;\r\nnu = 0.41;\r\nG = 2.8e9; %Pa\r\nE = 3.1e9; %Pa\r\ndensity = 1.14; %g/cm^3\r\nsh_exp = 0; %strain-hardening exponent\r\nsh_coeff = 0; %strain-hardening coefficient\r\nT_corr = 3.473e7;\r\nfrac_corr = 0.9697;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6) reinforced with 45wt.% glass fiber\r\nS_y = 230e6; %Pa\r\nS_u = 230e6; %Pa\r\ne_y = 0.016;\r\ne_u = 0.016;\r\nnu = 0.35;\r\nG = 13.0e9; %Pa\r\nE = 14.5e9; %Pa\r\ndensity = 1.51; %g/cm^3\r\nsh_exp = 0; %strain-hardening exponent\r\nsh_coeff = 0; %strain-hardening coefficient\r\nT_corr = 0;\r\nfrac_corr = 0;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(isequal(T,T_corr))\r\nassert(isequal(frac,frac_corr))\r\n\r\n%% diamond\r\nS_y = 1200e6; %Pa\r\nS_u = 1200e6; %Pa\r\ne_y = 0.001;\r\ne_u = 0.001;\r\nnu = 0.20;\r\nG = 478e9; %Pa\r\nE = 1200e9; %Pa\r\ndensity = 3.51; %g/cm^3\r\nsh_exp = 0; %strain-hardening exponent\r\nsh_coeff = 0; %strain-hardening coefficient\r\nT_corr = 0;\r\nfrac_corr = 0;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(isequal(T,T_corr))\r\nassert(isequal(frac,frac_corr))\r\n\r\n%%\r\nfor i = 1:30\r\nind = randi(8);\r\nswitch ind\r\n\tcase 1\r\n\t\tS_y = 250e6; %Pa\r\n\t\te_y = 0.00125;\r\n\t\te_u = 0.35;\r\n\t\tsh_exp = 0.14; %strain-hardening exponent\r\n\t\tsh_coeff = 463e6; %strain-hardening coefficient\r\n\t\tT_corr = 12.26e7;\r\n\t\tfrac_corr = 0.9987;\r\n\t\t[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\n\t\tassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\n\t\tassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\tcase 2\r\n\t\tS_y = 830e6; %Pa\r\n\t\te_y = 0.00728;\r\n\t\te_u = 0.14;\r\n\t\tsh_exp = 0.04; %strain-hardening exponent\r\n\t\tsh_coeff = 974e6; %strain-hardening coefficient\r\n\t\tT_corr = 11.82e7;\r\n\t\tfrac_corr = 0.9751;\r\n\t\t[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\n\t\tassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\n\t\tassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\tcase 3\r\n\t\tS_y = 230e6; %Pa\r\n\t\te_y = 0.016;\r\n\t\te_u = 0.016;\r\n\t\tsh_exp = 0; %strain-hardening exponent\r\n\t\tsh_coeff = 0; %strain-hardening coefficient\r\n\t\tT_corr = 0;\r\n\t\tfrac_corr = 0;\r\n\t\t[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\n\t\tassert(isequal(T,T_corr))\r\n\t\tassert(isequal(frac,frac_corr))\r\n\tcase 4\r\n\t\tS_y = 317e6; %Pa\r\n\t\te_y = 0.000685;\r\n\t\te_u = 0.24;\r\n\t\tsh_exp = 0.353; %strain-hardening exponent\r\n\t\tsh_coeff = 1870e6; %strain-hardening coefficient\r\n\t\tT_corr = 20.05e7;\r\n\t\tfrac_corr = 0.9995;\r\n\t\t[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\n\t\tassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\n\t\tassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\tcase 5\r\n\t\tS_y = 70e6; %Pa\r\n\t\te_y = 0.00054;\r\n\t\te_u = 0.48;\r\n\t\tsh_exp = 0.44; %strain-hardening exponent\r\n\t\tsh_coeff = 304e6; %strain-hardening coefficient\r\n\t\tT_corr = 7.340e7;\r\n\t\tfrac_corr = 0.9997;\r\n\tcase 6\r\n\t\tS_y = 1172e6; %Pa\r\n\t\te_y = 0.00563;\r\n\t\te_u = 0.027;\r\n\t\tsh_exp = 0.075; %strain-hardening exponent\r\n\t\tsh_coeff = 1845e6; %strain-hardening coefficient\r\n\t\tT_corr = 3.205e7;\r\n\t\tfrac_corr = 0.9067;\r\n\tcase 7\r\n\t\tS_y = 82e6; %Pa\r\n\t\te_y = 0.0265;\r\n\t\te_u = 0.45;\r\n\t\tsh_exp = 0; %strain-hardening exponent\r\n\t\tsh_coeff = 0; %strain-hardening coefficient\r\n\t\tT_corr = 3.473e7;\r\n\t\tfrac_corr = 0.9697;\r\n\tcase 8\r\n\t\tS_y = 241e6; %Pa\r\n\t\te_y = 0.0035;\r\n\t\te_u = 0.15;\r\n\t\tsh_exp = 0.042; %strain-hardening exponent\r\n\t\tsh_coeff = 325e6; %strain-hardening coefficient\r\n\t\tT_corr = 4.279e7;\r\n\t\tfrac_corr = 0.9902;\r\nend\r\nend % for i = 1:30\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":26769,"edited_by":26769,"edited_at":"2024-03-27T17:44:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":88,"test_suite_updated_at":"2021-08-03T17:04:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-03-30T22:03:11.000Z","updated_at":"2026-02-19T09:46:19.000Z","published_at":"2015-03-30T22:03:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe toughness of a material is technically defined as the plastic strain energy absorbed by the material (the plastic region in the figure below). Practically speaking, it's a measure of how much deformation a material can undergo (or energy it can absorb) before failure.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"298\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to calculate the toughness of a material—the absorbed strain energy minus the resilience. This can be accomplished by combining the code written in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproblem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (resilience) and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproblem 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (absorbed strain energy). Also, return the fraction of absorbed strain energy that the toughness represents.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 6 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eabsorbed strain energy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Next problem: 8 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ematerial properties list\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"contentType\":\"image/net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"content\":\"https://qph.cf2.quoracdn.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":8050,"title":"Stress-Strain Properties - 3","description":"A brittle material will not exhibit a yield point. In other words, the yield point and failure point coincide. In such cases, the yield strain and failure strain (also known as ultimate strain or elongation) are the same value. On the other hand, ductile materials have a failure strain that is significantly greater than the elastic strain, as shown in the figure below.\r\n\r\n(from quora.com)\r\nWrite a function to determine the qualitative brittleness of the material by calculating the ratio of elastic strain to failure strain. A ratio of one indicates complete brittleness, whereas a ratio close to zero indicates essentially no brittleness.\r\nPrevious problem: 2 - resilience. Next problem: 4 - strength-to-weight ratio.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 529px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 264.5px; transform-origin: 332px 264.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 42px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA brittle material will not exhibit a yield point. In other words, the yield point and failure point coincide. In such cases, the yield strain and failure strain (also known as ultimate strain or elongation) are the same value. On the other hand, ductile materials have a failure strain that is significantly greater than the elastic strain, as shown in the figure below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 304px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 152px; text-align: center; transform-origin: 309px 152px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://qph.cf2.quoracdn.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: center; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(from quora.com)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 31.5px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the qualitative brittleness of the material by calculating the ratio of elastic strain to failure strain. A ratio of one indicates complete brittleness, whereas a ratio close to zero indicates essentially no brittleness.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePrevious problem: 2 -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eresilience\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Next problem: 4 -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003estrength-to-weight ratio\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [BR] = stress_strain3(e_y,e_u)\r\n\r\nBR = 1;\r\n\r\nend\r\n","test_suite":"%% Note\r\n% The following properties are measured at room temperature and are tensile\r\n% in a single direction. Some materials, such as metals are generally\r\n% isotropic, whereas others, like composite are highly anisotropic\r\n% (different properties in different directions). Also, property values can\r\n% range depending on the material grade. Finally, thermal or environmental\r\n% changes can alter these properties, sometimes drastically.\r\n\r\n%% steel alloy (ASTM A36)\r\nS_y = 250e6; %Pa\r\nS_u = 400e6; %Pa\r\ne_y = 0.00125;\r\ne_u = 0.35;\r\nnu = 0.26;\r\nG = 79.3e9; %Pa\r\nE = 200e9; %Pa\r\ndensity = 7.85; %g/cm^3\r\nsh_exp = 0.14; %strain-hardening exponent\r\nsh_coeff = 0.463; %strain-hardening coefficient\r\nBR_corr = 0.003571;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% titanium (Ti-6Al-4V)\r\nS_y = 830e6; %Pa\r\nS_u = 900e6; %Pa\r\ne_y = 0.00728;\r\ne_u = 0.14;\r\nnu = 0.342;\r\nG = 44e9; %Pa\r\nE = 114e9; %Pa\r\ndensity = 4.51; %g/cm^3\r\nsh_exp = 0.04; %strain-hardening exponent\r\nsh_coeff = 0.974; %strain-hardening coefficient\r\nBR_corr = 0.052;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% Inconel 718\r\nS_y = 1172e6; %Pa\r\nS_u = 1407e6; %Pa\r\ne_y = 0.00563;\r\ne_u = 0.027;\r\nnu = 0.29;\r\nG = 11.6e9; %Pa\r\nE = 208e9; %Pa\r\ndensity = 8.19; %g/cm^3\r\nsh_exp = 0.075; %strain-hardening exponent\r\nsh_coeff = 1.845; %strain-hardening coefficient\r\nBR_corr = 0.2085;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% aluminum alloy (6061-T6)%^\u0026\r\nS_y = 241e6; %Pa\r\nS_u = 300e6; %Pa\r\ne_y = 0.0035;\r\ne_u = 0.15;\r\nnu = 0.33;\r\nG = 26e9; %Pa\r\nE = 68.9e9; %Pa\r\ndensity = 2.7; %g/cm^3\r\nsh_exp = 0.042; %strain-hardening exponent\r\nsh_coeff = 0.325; %strain-hardening coefficient\r\nBR_corr = 0.02333;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% copper\r\nS_y = 70e6; %Pa\r\nS_u = 220e6; %Pa\r\ne_y = 0.00054;\r\ne_u = 0.48;\r\nnu = 0.34;\r\nG = 48e9; %Pa\r\nE = 130e9; %Pa\r\ndensity = 8.92; %g/cm^3\r\nsh_exp = 0.44; %strain-hardening exponent\r\nsh_coeff = 0.304; %strain-hardening coefficient\r\nBR_corr = 0.001125;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% rhenium\r\nS_y = 317e6; %Pa\r\nS_u = 1130e6; %Pa\r\ne_y = 0.000685;\r\ne_u = 0.24;\r\nnu = 0.3;\r\nG = 178e9; %Pa\r\nE = 463e9; %Pa\r\ndensity = 21.02; %g/cm^3\r\nsh_exp = 0.353; %strain-hardening exponent\r\nsh_coeff = 1.870; %strain-hardening coefficient\r\nBR_corr = 0.002854;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6)\r\nS_y = 82e6; %Pa\r\nS_u = 82e6; %Pa\r\ne_y = 0.0265;\r\ne_u = 0.45;\r\nnu = 0.41;\r\nG = 2.8e9; %Pa\r\nE = 3.1e-2; %Pa\r\ndensity = 1.14; %g/cm^3\r\nBR_corr = 0.058889;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6) reinforced with 45wt.% glass fiber\r\nS_y = 230e6; %Pa\r\nS_u = 230e6; %Pa\r\ne_y = 0.016;\r\ne_u = 0.016;\r\nnu = 0.35;\r\nG = 13.0e9; %Pa\r\nE = 14.5e9; %Pa\r\ndensity = 1.51; %g/cm^3\r\nBR_corr = 1.0;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%% diamond\r\nS_y = 1200e6; %Pa\r\nS_u = 1200e6; %Pa\r\ne_y = 0.001;\r\ne_u = 0.001;\r\nnu = 0.20;\r\nG = 478e9; %Pa\r\nE = 1200e9; %Pa\r\ndensity = 3.51; %g/cm^3\r\nBR_corr = 1.0;\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\te_y = 0.00125;\r\n\t\te_u = 0.35;\r\n\t\tBR_corr = 0.003571;\r\n\tcase 2\r\n\t\te_y = 0.00054;\r\n\t\te_u = 0.48;\r\n\t\tBR_corr = 0.001125;\r\n\tcase 3\r\n\t\te_y = 0.0035;\r\n\t\te_u = 0.15;\r\n\t\tBR_corr = 0.02333;\r\n\tcase 4\r\n\t\te_y = 0.00054;\r\n\t\te_u = 0.48;\r\n\t\tBR_corr = 0.001125;\r\nend\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\te_y = 0.0265;\r\n\t\te_u = 0.45;\r\n\t\tBR_corr = 0.058889;\r\n\tcase 2\r\n\t\te_y = 0.00728;\r\n\t\te_u = 0.14;\r\n\t\tBR_corr = 0.052;\r\n\tcase 3\r\n\t\te_y = 0.00563;\r\n\t\te_u = 0.027;\r\n\t\tBR_corr = 0.2085;\r\n\tcase 4\r\n\t\te_y = 0.016;\r\n\t\te_u = 0.016;\r\n\t\tBR_corr = 1.0;\r\nend\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\te_y = 0.00125;\r\n\t\te_u = 0.35;\r\n\t\tBR_corr = 0.003571;\r\n\tcase 2\r\n\t\te_y = 0.00563;\r\n\t\te_u = 0.027;\r\n\t\tBR_corr = 0.2085;\r\n\tcase 3\r\n\t\te_y = 0.00728;\r\n\t\te_u = 0.14;\r\n\t\tBR_corr = 0.052;\r\n\tcase 4\r\n\t\te_y = 0.00054;\r\n\t\te_u = 0.48;\r\n\t\tBR_corr = 0.001125;\r\nend\r\nassert(abs(stress_strain3(e_y,e_u)-BR_corr)/BR_corr\u003c1e-2)\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":26769,"edited_by":26769,"edited_at":"2024-03-27T17:42:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":241,"test_suite_updated_at":"2015-03-30T18:54:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-03-30T18:53:23.000Z","updated_at":"2026-03-31T10:56:32.000Z","published_at":"2015-03-30T18:53:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA brittle material will not exhibit a yield point. In other words, the yield point and failure point coincide. In such cases, the yield strain and failure strain (also known as ultimate strain or elongation) are the same value. On the other hand, ductile materials have a failure strain that is significantly greater than the elastic strain, as shown in the figure below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(from quora.com)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine the qualitative brittleness of the material by calculating the ratio of elastic strain to failure strain. A ratio of one indicates complete brittleness, whereas a ratio close to zero indicates essentially no brittleness.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 2 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eresilience\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Next problem: 4 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003estrength-to-weight ratio\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"contentType\":\"image/net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"content\":\"https://qph.cf2.quoracdn.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":8054,"title":"Stress-Strain Properties - 7","description":"The toughness of a material is technically defined as the plastic strain energy absorbed by the material (the plastic region in the figure below). Practically speaking, it's a measure of how much deformation a material can undergo (or energy it can absorb) before failure.\r\n\r\nWrite a function to calculate the toughness of a material—the absorbed strain energy minus the resilience. This can be accomplished by combining the code written in problem 2 (resilience) and problem 6 (absorbed strain energy). Also, return the fraction of absorbed strain energy that the toughness represents.\r\nPrevious problem: 6 - absorbed strain energy. Next problem: 8 - material properties list.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 499px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 249.5px; transform-origin: 332px 249.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 31.5px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe toughness of a material is technically defined as the plastic strain energy absorbed by the material (the plastic region in the figure below). Practically speaking, it's a measure of how much deformation a material can undergo (or energy it can absorb) before failure.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 304px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 152px; text-align: center; transform-origin: 309px 152px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://qph.cf2.quoracdn.net/main-qimg-b2693f4b9ea8430af25df920757e0b29-lq\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 42px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to calculate the toughness of a material—the absorbed strain energy minus the resilience. This can be accomplished by combining the code written in\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eproblem 2\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (resilience) and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eproblem 6\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (absorbed strain energy). Also, return the fraction of absorbed strain energy that the toughness represents.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePrevious problem: 6 -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eabsorbed strain energy\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Next problem: 8 -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ematerial properties list\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff)\r\n\r\nT = 1;\r\n\r\nfrac = 0.5;\r\n\r\nend\r\n","test_suite":"%% Note\r\n% The following properties are measured at room temperature and are tensile\r\n% in a single direction. Some materials, such as metals, are generally\r\n% isotropic, whereas others, like composites, are highly anisotropic\r\n% (different properties in different directions). Also, property values can\r\n% range depending on the material grade. Finally, thermal or environmental\r\n% changes can alter these properties, sometimes drastically.\r\n\r\n%% steel alloy (ASTM A36)\r\nS_y = 250e6; %Pa\r\nS_u = 400e6; %Pa\r\ne_y = 0.00125;\r\ne_u = 0.35;\r\nnu = 0.26;\r\nG = 79.3e9; %Pa\r\nE = 200e9; %Pa\r\ndensity = 7.85; %g/cm^3\r\nsh_exp = 0.14; %strain-hardening exponent\r\nsh_coeff = 463e6; %strain-hardening coefficient\r\nT_corr = 12.26e7;\r\nfrac_corr = 0.9987;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% titanium (Ti-6Al-4V)\r\nS_y = 830e6; %Pa\r\nS_u = 900e6; %Pa\r\ne_y = 0.00728;\r\ne_u = 0.14;\r\nnu = 0.342;\r\nG = 44e9; %Pa\r\nE = 114e9; %Pa\r\ndensity = 4.51; %g/cm^3\r\nsh_exp = 0.04; %strain-hardening exponent\r\nsh_coeff = 974e6; %strain-hardening coefficient\r\nT_corr = 11.82e7;\r\nfrac_corr = 0.9751;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% Inconel 718\r\nS_y = 1172e6; %Pa\r\nS_u = 1407e6; %Pa\r\ne_y = 0.00563;\r\ne_u = 0.027;\r\nnu = 0.29;\r\nG = 11.6e9; %Pa\r\nE = 208e9; %Pa\r\ndensity = 8.19; %g/cm^3\r\nsh_exp = 0.075; %strain-hardening exponent\r\nsh_coeff = 1845e6; %strain-hardening coefficient\r\nT_corr = 3.205e7;\r\nfrac_corr = 0.9067;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% aluminum alloy (6061-T6)\r\nS_y = 241e6; %Pa\r\nS_u = 300e6; %Pa\r\ne_y = 0.0035;\r\ne_u = 0.15;\r\nnu = 0.33;\r\nG = 26e9; %Pa\r\nE = 68.9e9; %Pa\r\ndensity = 2.7; %g/cm^3\r\nsh_exp = 0.042; %strain-hardening exponent\r\nsh_coeff = 325e6; %strain-hardening coefficient\r\nT_corr = 4.279e7;\r\nfrac_corr = 0.9902;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% copper\r\nS_y = 70e6; %Pa\r\nS_u = 220e6; %Pa\r\ne_y = 0.00054;\r\ne_u = 0.48;\r\nnu = 0.34;\r\nG = 48e9; %Pa\r\nE = 130e9; %Pa\r\ndensity = 8.92; %g/cm^3\r\nsh_exp = 0.44; %strain-hardening exponent\r\nsh_coeff = 304e6; %strain-hardening coefficient\r\nT_corr = 7.340e7;\r\nfrac_corr = 0.9997;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% rhenium\r\nS_y = 317e6; %Pa\r\nS_u = 1130e6; %Pa\r\ne_y = 0.000685;\r\ne_u = 0.24;\r\nnu = 0.3;\r\nG = 178e9; %Pa\r\nE = 463e9; %Pa\r\ndensity = 21.02; %g/cm^3\r\nsh_exp = 0.353; %strain-hardening exponent\r\nsh_coeff = 1870e6; %strain-hardening coefficient\r\nT_corr = 20.05e7;\r\nfrac_corr = 0.9995;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6)\r\nS_y = 82e6; %Pa\r\nS_u = 82e6; %Pa\r\ne_y = 0.0265;\r\ne_u = 0.45;\r\nnu = 0.41;\r\nG = 2.8e9; %Pa\r\nE = 3.1e9; %Pa\r\ndensity = 1.14; %g/cm^3\r\nsh_exp = 0; %strain-hardening exponent\r\nsh_coeff = 0; %strain-hardening coefficient\r\nT_corr = 3.473e7;\r\nfrac_corr = 0.9697;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\nassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6) reinforced with 45wt.% glass fiber\r\nS_y = 230e6; %Pa\r\nS_u = 230e6; %Pa\r\ne_y = 0.016;\r\ne_u = 0.016;\r\nnu = 0.35;\r\nG = 13.0e9; %Pa\r\nE = 14.5e9; %Pa\r\ndensity = 1.51; %g/cm^3\r\nsh_exp = 0; %strain-hardening exponent\r\nsh_coeff = 0; %strain-hardening coefficient\r\nT_corr = 0;\r\nfrac_corr = 0;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(isequal(T,T_corr))\r\nassert(isequal(frac,frac_corr))\r\n\r\n%% diamond\r\nS_y = 1200e6; %Pa\r\nS_u = 1200e6; %Pa\r\ne_y = 0.001;\r\ne_u = 0.001;\r\nnu = 0.20;\r\nG = 478e9; %Pa\r\nE = 1200e9; %Pa\r\ndensity = 3.51; %g/cm^3\r\nsh_exp = 0; %strain-hardening exponent\r\nsh_coeff = 0; %strain-hardening coefficient\r\nT_corr = 0;\r\nfrac_corr = 0;\r\n[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\nassert(isequal(T,T_corr))\r\nassert(isequal(frac,frac_corr))\r\n\r\n%%\r\nfor i = 1:30\r\nind = randi(8);\r\nswitch ind\r\n\tcase 1\r\n\t\tS_y = 250e6; %Pa\r\n\t\te_y = 0.00125;\r\n\t\te_u = 0.35;\r\n\t\tsh_exp = 0.14; %strain-hardening exponent\r\n\t\tsh_coeff = 463e6; %strain-hardening coefficient\r\n\t\tT_corr = 12.26e7;\r\n\t\tfrac_corr = 0.9987;\r\n\t\t[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\n\t\tassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\n\t\tassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\tcase 2\r\n\t\tS_y = 830e6; %Pa\r\n\t\te_y = 0.00728;\r\n\t\te_u = 0.14;\r\n\t\tsh_exp = 0.04; %strain-hardening exponent\r\n\t\tsh_coeff = 974e6; %strain-hardening coefficient\r\n\t\tT_corr = 11.82e7;\r\n\t\tfrac_corr = 0.9751;\r\n\t\t[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\n\t\tassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\n\t\tassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\tcase 3\r\n\t\tS_y = 230e6; %Pa\r\n\t\te_y = 0.016;\r\n\t\te_u = 0.016;\r\n\t\tsh_exp = 0; %strain-hardening exponent\r\n\t\tsh_coeff = 0; %strain-hardening coefficient\r\n\t\tT_corr = 0;\r\n\t\tfrac_corr = 0;\r\n\t\t[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\n\t\tassert(isequal(T,T_corr))\r\n\t\tassert(isequal(frac,frac_corr))\r\n\tcase 4\r\n\t\tS_y = 317e6; %Pa\r\n\t\te_y = 0.000685;\r\n\t\te_u = 0.24;\r\n\t\tsh_exp = 0.353; %strain-hardening exponent\r\n\t\tsh_coeff = 1870e6; %strain-hardening coefficient\r\n\t\tT_corr = 20.05e7;\r\n\t\tfrac_corr = 0.9995;\r\n\t\t[T,frac] = stress_strain7(e_y,e_u,S_y,sh_exp,sh_coeff);\r\n\t\tassert(abs(T-T_corr)/T_corr\u003c1e-2)\r\n\t\tassert(abs(frac-frac_corr)/frac_corr\u003c1e-2)\r\n\tcase 5\r\n\t\tS_y = 70e6; %Pa\r\n\t\te_y = 0.00054;\r\n\t\te_u = 0.48;\r\n\t\tsh_exp = 0.44; %strain-hardening exponent\r\n\t\tsh_coeff = 304e6; %strain-hardening coefficient\r\n\t\tT_corr = 7.340e7;\r\n\t\tfrac_corr = 0.9997;\r\n\tcase 6\r\n\t\tS_y = 1172e6; %Pa\r\n\t\te_y = 0.00563;\r\n\t\te_u = 0.027;\r\n\t\tsh_exp = 0.075; %strain-hardening exponent\r\n\t\tsh_coeff = 1845e6; %strain-hardening coefficient\r\n\t\tT_corr = 3.205e7;\r\n\t\tfrac_corr = 0.9067;\r\n\tcase 7\r\n\t\tS_y = 82e6; %Pa\r\n\t\te_y = 0.0265;\r\n\t\te_u = 0.45;\r\n\t\tsh_exp = 0; %strain-hardening exponent\r\n\t\tsh_coeff = 0; %strain-hardening coefficient\r\n\t\tT_corr = 3.473e7;\r\n\t\tfrac_corr = 0.9697;\r\n\tcase 8\r\n\t\tS_y = 241e6; %Pa\r\n\t\te_y = 0.0035;\r\n\t\te_u = 0.15;\r\n\t\tsh_exp = 0.042; %strain-hardening exponent\r\n\t\tsh_coeff = 325e6; %strain-hardening coefficient\r\n\t\tT_corr = 4.279e7;\r\n\t\tfrac_corr = 0.9902;\r\nend\r\nend % for i = 1:30\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":26769,"edited_by":26769,"edited_at":"2024-03-27T17:44:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":88,"test_suite_updated_at":"2021-08-03T17:04:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-03-30T22:03:11.000Z","updated_at":"2026-02-19T09:46:19.000Z","published_at":"2015-03-30T22:03:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe toughness of a material is technically defined as the plastic strain energy absorbed by the material (the plastic region in the figure below). Practically speaking, it's a measure of how much deformation a material can undergo (or energy it can absorb) before failure.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"298\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to calculate the toughness of a material—the absorbed strain energy minus the resilience. This can be accomplished by combining the code written in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproblem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (resilience) and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproblem 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (absorbed strain energy). Also, return the fraction of absorbed strain energy that the toughness represents.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 6 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eabsorbed strain energy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Next problem: 8 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ematerial properties 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