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This model combines a plastic yield surface (J2) with a visco-plastic creep law. All inelastic flow follows a simple radial return law. The total strain is assumed additive:

$\varepsilon = \varepsilon^e + \varepsilon^p + \varepsilon^c$

where $e$ stands for elastic, $p$ plastic and $c$ for creep. The effective plastic flow stress is:

$\sigma_y = A(T) + B(T) \left[ \varepsilon_{eff}^p \right]^{n(T)}$

The creep strain rate is:

$\displaystyle{\dot\varepsilon_{eff}^c = \left[ \frac{\sigma_{eff}}{c_1(T) + c_2(T) \varepsilon_{eff}^c + c_3(T) ( \varepsilon_{eff}^c )^2} \right]^{c_0(T)}}$

The hydrostatic pressure $p$ is defined as:

$p = -K \varepsilon_v + 3K \alpha_T (T-T_{ref})$

where $K$ is the bulk modulus, $\varepsilon_v$ is the volumetric strain. $\alpha_T$ is the thermal expansion coefficient and $T_{ref}$ is the reference temperature (see PROP_THERMAL).

Temperature dependent hardening and creep behavior

Typical (but not real) properties for a generic aluminum alloy. Note the use of both constants and curves (see CURVE or FUNCTION).