- #1
FQVBSina_Jesse
- 15
- 1
- TL;DR Summary
- Calculating full displacement tensor from strain tensor using Hencky (true) strain definition.
The Hencky strain, AKA true strain, logarithmic strain, can be related to displacement tensor as follows:
$$
E = ln(U)
$$
However, Hencky strain is typically done only for principal strains. This can be easily shown by actually trying to calculate the full displacement tensor using the above definition:
$$
U = e^E
$$
Typically we have E<1, and if I am looking at a strain rate, then it is E<<1, the above equation will return a displacement tensor with a value around 1 in all components when only the principal components should be close to 1. I haven't found any literature discussing the proper correction to calculate the shear terms, specifically the Hencky definition of strain and displacement. Does anyone know more about this topic?
$$
E = ln(U)
$$
However, Hencky strain is typically done only for principal strains. This can be easily shown by actually trying to calculate the full displacement tensor using the above definition:
$$
U = e^E
$$
Typically we have E<1, and if I am looking at a strain rate, then it is E<<1, the above equation will return a displacement tensor with a value around 1 in all components when only the principal components should be close to 1. I haven't found any literature discussing the proper correction to calculate the shear terms, specifically the Hencky definition of strain and displacement. Does anyone know more about this topic?