Mises1D

Uniaxial General Model Using von Mises Criterion

This is an abstract class that shall be overridden.

The Mises1D is a general model using von Mises yielding criterion and associated flow rule. The hardening rules can be customized.

Theory

Yield Function

A von Mises type yield function is used.

$$F=|\sigma-\beta|-k$$

Flow Rule

The associated plasticity is assumed.

$$\mathrm{d}\varepsilon^p=\gamma\dfrac{\partial{}F}{\partial\sigma}=\text{sign}(\sigma-\beta)~\gamma$$

Hardening

Both isotropic and kinematic hardening rules are employed.

Isotropic Hardening

A general function of accumulated plastic strain $p$ needs to be defined.

$$k=k(p),$$

where $p=\displaystyle\int|\mathrm{d}\varepsilon^p|~\mathrm{d}t$ is the accumulated plastic strain.

Kinematic Hardening

A general function of accumulated plastic strain $p$ needs to be defined.

$$\beta=h(p).$$

Implementation

The function $k(p)$ and $h(p)$ need to be defined in the derived classes.