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.