Problem 8054. Stress-Strain Properties - 7

Created by goc3

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{"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 toughness of a material is technically defined as the plastic strain energy absorbed by the material (the olive 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.</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>Write 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</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2\"><w:r><w:t>problem 2</w:t></w:r></w:hyperlink><w:r><w:t> (resilience) and</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6\"><w:r><w:t>problem 6</w:t></w:r></w:hyperlink><w:r><w:t> (absorbed strain energy). Also, return the fraction of absorbed strain energy that the toughness represents.</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: 6 -</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6\"><w:r><w:t>absorbed strain energy</w:t></w:r></w:hyperlink><w:r><w:t>. Next problem: 8 -</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/8055-stress-strain-properties-8\"><w:r><w:t>material properties list</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.jpg","relationshipId":"rId1"}]},{"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 299px; vertical-align: baseline; perspective-origin: 332px 299px; "><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; ">The toughness of a material is technically defined as the plastic strain energy absorbed by the material (the olive 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.</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: 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; ">Write 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 <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2">problem 2</a> (resilience) and <a target='_blank' href = "http://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6">problem 6</a> (absorbed strain energy). Also, return the fraction of absorbed strain energy that the toughness represents.</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; ">Previous problem: 6 - <a target='_blank' href = "http://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6">absorbed strain energy</a>. Next problem: 8 - <a target='_blank' href = "http://www.mathworks.com/matlabcentral/cody/problems/8055-stress-strain-properties-8">material properties list</a>.</div></div></div>

The toughness of a material is technically defined as the plastic strain energy absorbed by the material (the olive 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.

<<http://www.pt.ntu.edu.tw/hmchai/Biomechanics/BMmeasure/StressMeasure.files/StressStrainCurve.jpg>>

Write 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 <https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2 problem 2> (resilience) and <http://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6 problem 6> (absorbed strain energy). Also, return the fraction of absorbed strain energy that the toughness represents.

Previous problem: 6 - <http://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6 absorbed strain energy>. Next problem: 8 - <http://www.mathworks.com/matlabcentral/cody/problems/8055-stress-strain-properties-8 material properties list>.

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43 Solutions
12 Solvers

Last Solution submitted on Jul 31, 2021

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Problem Comments

1 Comment

1 Comment

Aarón Rivas Menchi on 31 Jul 2021 at 19:35

For test 4, I had to calculate the fraction as follows:
frac = (T-R)/T +.001 where R is the resilience of the material

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Problem Tags

absorbed deformation ductile energy material property resilience strain strain energy strength stress test toughness yield

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