Problem 8053. Stress-Strain Properties - 6

Created by goc3

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The total energy absorbed by a material up to failure in a tensile test is termed the absorbed strain energy. With respect to the figure below, it is the total area of the elastic and plastic regions and can be calculated by integrating the stress-strain curve. As a first approximation, many stress-strain responses can be approximated by:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"center\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>where K is a strength coefficient, eps_p is the plastic strain, and n is the hardening exponent. Stress as a function of strain can be calculated by creating a strain vector from zero to the ultimate strain and integrating the stress values in that vector.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"center\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"397\"/><w:attr w:name=\"width\" w:val=\"600\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId2\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"center\"/></w:pPr><w:r><w:t>(from simsolid.com)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function to return the absorbed strain energy for a material provided K and n. If the material does not strain harden, then K and n will be set equal to zero. In these cases, the absorbed strain energy is equal to the resilience (triangular area up to yield point) and any absorbed plastic energy, if applicable, which can be approximated by a rectangle from the yield point to the failure point with those stresses being equal. If the ultimate strain equals the yield strain, that rectangular area is zero.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Previous problem: 5 -</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/8052-stress-strain-properties-5\"><w:r><w:t>stiffness-to-weight ratio</w:t></w:r></w:hyperlink><w:r><w:t>. Next problem: 7 -</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/8054-stress-strain-properties-7\"><w:r><w:t>toughness</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.png","relationshipId":"rId1"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.jpg","relationshipId":"rId2"}]},{"partUri":"/media/image1.png","contentType":"image/png","content":"data:image/png;base64,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","relationship":null},{"partUri":"/media/image1.jpg","contentType":"image/jpg","content":"https://www.simsolid.com/wp-content/uploads/2017/10/stress-strain-curve.jpg","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20px; 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: normal; text-decoration: none; white-space: normal; "><div style="display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 400.5px; vertical-align: baseline; perspective-origin: 332px 400.5px; "><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">The total energy absorbed by a material up to failure in a tensile test is termed the absorbed strain energy. With respect to the figure below, it is the total area of the elastic and plastic regions and can be calculated by integrating the stress-strain curve. As a first approximation, many stress-strain responses can be approximated by:</span></span></div><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: center; transform-origin: 309px 14.5px; white-space: pre-wrap; perspective-origin: 309px 14.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAXBAMAAAC12X9oAAAAMFBMVEX///8WFhZQUFBAQEAwMDBiYmLm5uZ0dHTMzMyKiooMDAyenp4EBAQiIiK2trYAAAARmbiRAAAAAXRSTlMAQObYZgAAAU9JREFUeNpjZiAAUsUCn31gwipV+8ebgfv/PRBTO7b7AgN2VRP/bmX4fVMJxCzz5tuAQ9X3vwwM9zXATOYHXxpwqOJYxcB5GsL81fD/KA4n8xswRECZLA1M0QzMDHw3JjQ4LkBV9YJR9d8FEGPrnccH/l8G2rhmZ8NzB6CAoSAIgOUYCu49CgDRDw+egmhj+8fAG4Buo9dsfpBGtpNQPtM/IwaGC+iqGp5+2Qak/l2HqeLewPC3AN2Lug2sf4A0d7FxA0SkH4gSGFDdxf6DgUEG5NUJMI8C8eJzINZ5MN8ARPw9wcDQ/LGA4S/cdMYGTgxn8QCdzi8ANNMAKsDM9sU8F00Rs8SU/9dczyVN+BtrW8q7nH35BEZCKWeCZCoTjpSDBArE/05gIKiKW+D7BAaCNjLJeX1bQEgRA6+6BQNhwAM2kJCqq8SoYvu5AUgCAMD/X3IO0icRAAAAAElFTkSuQmCC" data-image-state="image-loaded"></div><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; perspective-origin: 309px 31.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">where K is a strength coefficient, eps_p is the plastic strain, and n is the hardening exponent. Stress as a function of strain can be calculated by creating a strain vector from zero to the ultimate strain and integrating the stress values in that vector.</span></span></div><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: center; transform-origin: 309px 201.5px; white-space: pre-wrap; perspective-origin: 309px 201.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="https://www.simsolid.com/wp-content/uploads/2017/10/stress-strain-curve.jpg" data-image-state="image-loaded"></div><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: center; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">(from simsolid.com)</span></span></div><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 63px; white-space: pre-wrap; perspective-origin: 309px 63px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">Write a function to return the absorbed strain energy for a material provided K and n. If the material does not strain harden, then K and n will be set equal to zero. In these cases, the absorbed strain energy is equal to the resilience (triangular area up to yield point) and any absorbed plastic energy, if applicable, which can be approximated by a rectangle from the yield point to the failure point with those stresses being equal. If the ultimate strain equals the yield strain, that rectangular area is zero.</span></span></div><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">Previous problem: 5 -</span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style=""> </span></span><a target='_blank' href = "http://www.mathworks.com/matlabcentral/cody/problems/8052-stress-strain-properties-5"><span style=""><span style="">stiffness-to-weight ratio</span></span></a><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">. Next problem: 7 -</span></span><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style=""> </span></span><a target='_blank' href = "http://www.mathworks.com/matlabcentral/cody/problems/8054-stress-strain-properties-7"><span style=""><span style="">toughness</span></span></a><span style="display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; "><span style="">.</span></span></div></div></div>

Solve

Solution Stats

44 Solutions
8 Solvers

Last Solution submitted on Dec 17, 2020

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Jean-Marie Sainthillier on 5 Sep 2015

Hello Grant, links to formulas are broken for several problems in this series.

Jean-Marie Sainthillier on 5 Sep 2015

it's Ok now, thank you.

Problem Recent Solvers8

Problem Tags

absorbed elastic failure material property strain strain energy strength stress test ultimate yield

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 8053. Stress-Strain Properties - 6

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers8

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Problem 8053. Stress-Strain Properties - 6

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers8

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players