Nonlinear finite elements/Homework 11/Solutions

  • Problem 1: Small Strain Elastic-Plastic Behavior
For small strains, the strain tensor is given by
In classical (small strain) rate-independent plasticity we start off with an additive decomposition :of the strain tensor
Assuming linear elasticity, we have the following elastic stress-strain law
Let us assume that the theory applies during plastic deformation of the material. :Hence, the material obeys an associated flow rule
where is the plastic flow rate, is the yield function, is the temperature, and is an internal variable.