NLE3D01

Nonlinear Elastic 3D Model

Syntax

material NLE3D01 (1) (2) (3) (4) (5) [6]
# (1) int, unique material tag
# (2) double, bulk modulus
# (3) double, reference strain
# (4) double, reference stress
# (5) double, m
# [6] double, density, default: 0.0

Theory

The strain energy potential is expressed as

$$W={\displaystyle \frac{9}{2}}K{\epsilon }_v^2+{\displaystyle \frac{{\epsilon }_0{\sigma }_0}{1-m}}{\left({\displaystyle \frac{{\epsilon }_p}{{\epsilon }_0}}\right)}^{(1-m)},$$

where $K$ is the bulk modulus, ${\epsilon }_0$ is the reference strain, ${\sigma }_0$ is the reference stress and $m\in [0,1]$ is an exponent controls nonlinearity. The volumetric strain ${\epsilon }_v$ and equivalent strain ${\epsilon }_p$ are expressed as

$${\epsilon }_v=\text{trace}\left(\epsilon \right),{\epsilon }_p=\sqrt{{\displaystyle \frac{2}{3}}{\epsilon }_d:{\epsilon }_d}.$$