3D Stress-Strain Tensor Relations

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.


Contributed by: Richard Jerue, Leon Tran, Daniel Balerite, Mark Michael, Tanraj Shergill and Joshua Steimel (August 2022)
Open content licensed under CC BY-NC-SA




[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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.