3.3.1.1. Plasticity Model

Refer to the Ansys Mechanical APDL Material Reference for a general background.

The constitutive models for elastic-plastic behavior start with a decomposition of the total strain into elastic and plastic parts (ignoring thermal strains)

(3–55)

The stress is proportional to the elastic strain

(3–56)

and the evolution of plastic strain is a result of the plasticity model. The essential characteristics of the plastic constitutive models are:

  1. The yield criterion that defines the material state at the transition from elastic to elastic-plastic behavior

    (3–57)

  2. The hardening rule that gives the evolution in the yield criterion during plastic deformation

  3. The flow rule that determines the increment in plastic strain from the increment in load

    (3–58)

    where is the plastic multiplier and is the plastic potential.

Next under consideration is an anisotropic Hill yield criterion combined with an isotropic hardening law and an associative flow rule– that is, we assume the plastic potential coincides with the yield function .