Command manual

Command list

MAT_ELASTIC

Material properties
*MAT_ELASTIC
"Optional title"
mid, $\rho$, $E$, $\nu$, did, tid
$a$, $b$, $c$, $c_{dec}$

Parameter definition

VariableDescription
mid Unique material identification number
$\rho$ Density
$E$ Young's modulus
$\nu$ Poisson's ratio
did Damage property command ID
tid Thermal property command ID
$a$, $b$ Non-linear elasticity parameters
$c$ Damping coefficient
$c_{dec}$ Damping decay coefficient

Description

A non-linear elastic constitutive model with damping. The stress is defined as:

$\mathbf{\sigma} = -p \mathbf{I} + 2G \cdot [1 + a \epsilon_{dev}^{geo} + b (\epsilon_{dev}^{geo})^2] \cdot \mathbf{\epsilon}_{dev} + \displaystyle{ \frac{c}{c_{dec}} \int_0^t \dot{\mathbf{\epsilon}}(\tau) \cdot \mathrm{e}^{(\tau-t)/c_{dec}} \mathrm{d}\tau }$

$G$ is the shear modulus, $\mathbf{\epsilon}_{dev}$ is the deviatoric strain and $\epsilon_{dev}^{geo}$ is the effective deviatoric geometric strain.

$\epsilon_{dev}^{geo} = \displaystyle{ \sqrt{ \frac{2}{3} \mathbf{\epsilon}_{dev} : \mathbf{\epsilon}_{dev} } }$

The hydrostatic pressure $p$ is defined as:

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

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