3D Stress-Strain Tensor Relations

This Demonstration considers stress-strain relationships in the mechanical behavior of materials. Stress is represented by a second-rank tensor with nine components. However, only six components are independent, since the tensor is symmetrical. We calculate the relationship between uniaxial stress/strain in 3D space. You can select values of Young's modulus and Poisson's ratio , which determine the strain state, represented by the strain tensor .
As well, consider rotation about the three Cartesian axes through selected angles. The stress and strain tensors are correspondingly transformed to and (not shown), while the physical situation is not changed.


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[1] J. P. Steimel. "Materials Science and Engineering." Pacific Open Texts. (May 11, 2022) scholarlycommons.pacific.edu/open-textbooks/8.
[2] Mathematica Stack Exchange. "Resize a Manipulate by Grabbing a Corner." (May 11, 2022) mathematica.stackexchange.com/questions/199234/resize-a-manipulate-by-grabbing-a-corner.
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