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

$$W=\dfrac{9}{2}K\varepsilon_v^2+\dfrac{\varepsilon_0\sigma_0}{1-m}\left(\dfrac{\varepsilon_p}{\varepsilon_0}\right)^{( 1-m)},$$

where $K$ is the bulk modulus, $\varepsilon_0$ is the reference strain, $\sigma_0$ is the reference stress and $m\in[0,1]$ is an exponent controls nonlinearity. The volumetric strain $\varepsilon_v$ and equivalent strain $\varepsilon_p$ are expressed as

$$\varepsilon_v=\text{trace}\left(\varepsilon\right),\qquad\varepsilon_p=\sqrt{\dfrac{2}{3}\varepsilon_d: \varepsilon_d}.$$