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:
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.
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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.
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Hello Grant, links to formulas are broken for several problems in this series.
it's Ok now, thank you.
For a while, I thought that the stress-strain curve was linear up to the yield point and then given by the power law (suitably shifted). Now I realize that for strain hardening materials, the power law applies for strains between zero and the ultimate strain.
There's a somewhat confusing typo in your solution template - the fourth parameter passed is actually S_y, not S_u.
The typo has been fixed.
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