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.

$$\mathrm{d}{\epsilon }^p=\gamma {\displaystyle \frac{\partial F}{\partial \sigma }}=\text{sign}(\sigma -\beta )\gamma$$

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 $p={\displaystyle \int |\mathrm{d}{\epsilon }^p|\mathrm{d}t}$ 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.