Problem 8048. Stress-Strain Properties - 1

Created by goc3

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<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 320px; vertical-align: baseline; perspective-origin: 332px 320px; "><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="">This is the first in a series of problems regarding mechanics of materials, in particular, material properties drawn from stress-strain responses. A simplified typical stress-strain response is illustrated below (from</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=""> 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: 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 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="">The yield stress is the pressure required to start deformation of the material being tested. The yield point is the point along the response indicated by the yield stress (vertical axis) and the yield strain (horizontal axis). The response of the material up to this point is elastic, meaning that all deformation is reversible. The elastic modulus (E, also known as modulus of elasticity or Young's modulus) is the slope of this line. Write a function to calculate the elastic modulus for a material, provided the elastic strain and yield stress (yield point).</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="">Next problem: 2 -</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 = "https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2"><span style=""><span style="">resilience</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>

This is the first in a series of problems regarding mechanics of materials, in particular, material properties drawn from stress-strain responses. A simplified typical stress-strain response is illustrated below (figure from <http://www.pt.ntu.edu.tw/hmchai/ here>):

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

The yield stress is the pressure required to start deformation of the material being tested. The yield point is the point along the response indicated by the yield stress (vertical axis) and the yield strain (horizontal axis). The response of the material up to this point is elastic, meaning that all deformation is reversible. The elastic modulus (also known as modulus of elasticity or Young's modulus) is the slope of this line. Write a function to calculate the elastic modulus for a material, provided the elastic strain and yield stress (yield point).

Next problem: 2 - <https://www.mathworks.com/matlabcentral/cody/problems/8049-stress-strain-properties-2 resilience>.

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Last Solution submitted on May 19, 2022

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Rafael S.T. Vieira on 5 Sep 2020

The figure is missing.

goc3 on 29 Sep 2020

@Rafael S.T. Vieiera: thanks for pointing that out. The image has been updated.

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characterization elastic material modulus property strain strength stress test ultimate yield young

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Problem 8048. Stress-Strain Properties - 1

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