Model: Elastic Isotropic Pressure Dependent

Overview

This model may be used for solid materials with a pressure-dependent elastic isotropic behavior. The relationship between stress and strain is given by a hyperelastic law. The elastic constitutive equations for the volumetric and deviatoric stresses and strain are expressed as:

$p = p_0 \exp{\left(\frac{\epsilon_{v0}-\epsilon_v^e}{c_r}\right)} \, , \quad q = 3 \mu \epsilon_s^e$

where $p$ and $q$ are the volumetric and deviatoric components of the Cauchy stress tensor. $\epsilon_{v}^e$ and $\epsilon_{s}^e$ are the volumetric and deviatoric components of the strain tensor. $\epsilon_{v0}$ and $p_0$ are the initial volumetric strain and initial pressure. $C_r$ denotes the elastic compressibility index, and $\mu$ is the elastic shear modulus. In this model, the shear modulus is constant and the bulk modulus, $K$ , varies linearly with pressure as follows:

$K = -\frac{p}{c_r}$

Parameters

The following attributes are supported. Note that two elastic constants $c_r$ and $\mu$ , as well as the initial volumetric strain and initial pressure need to be provided. The “default” keyword in front of certain properties indicates that this is the default value adopted for a region unless the user separately specifies a heterogeneous field via the FieldSpecification mechanism.

Example

A typical Constititutive block will look like:

<Constitutive>
  <ElasticIsotropicPressureDependent
    name="elasticPressure"
    defaultDensity="2700"
    defaultRefPressure="-1.0"
    defaultRefStrainVol="1"
    defaultRecompressionIndex="0.003"
    defaultShearModulus="200"/>
</Constitutive>