Hooke’s Law Using Stress and Strain Invariants
Description:
The stress and strain invariants for an elastic material are related as follows:
is the effective bulk modulus and the superscript e denotes elastic.
is called the shear modulus. Hooke’s law in terms of the stress and strain invariants is
Equation reveals that for a linear, isotropic, elastic material, shear stresses do not cause volume changes and mean effective stresses do not cause shear deformation.
We can generate a generalized Poisson’s ratio by eliminating E9 from Equations , as follows:
THE ESSENTIAL POINTS ARE:
1. Stress and strain invariants are independent of the chosen axis system.
2. Stress and strain invariants are convenient measures to determine the effects of a general state of stresses and strains on soils.
3. Mean stress represents the average stress on a soil, while deviatoric stress represents the average shear or distortional stress.