Model: Elastic Isotropic Pressure Dependent


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}


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.


A typical Constititutive block will look like: