> For the complete documentation index, see [llms.txt](https://tlcfem.gitbook.io/suanpan-manual/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://tlcfem.gitbook.io/suanpan-manual/material/material3d/elastic/nle3d01.md).

# 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]$$ is an exponent that controls nonlinearity. The volumetric strain $$\varepsilon\_v$$ and equivalent strain $$\varepsilon\_p$$ are expressed as

$$
\varepsilon\_v=\text{trace}\left(\varepsilon\right),\qquad\varepsilon\_p=\sqrt{\dfrac{2}{3}\varepsilon\_d:
\varepsilon\_d}.
$$


---

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