> 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/material1d/elastic/polyelastic1d.md).

# PolyElastic1D

Polynomial Based Uniaxial Nonlinear Elastic

## Syntax

```
material PolyElastic1D (1) [(2)...]
# (1) int, unique material tag
# (2) double, polynomial parameters, a_n
```

## Theory

The stress response is defined as a polynomial function of strain on the positive strain ($$\varepsilon>0$$).

$$
\sigma=a\_1\varepsilon+a\_2\varepsilon^2+a\_3\varepsilon^3\cdots
$$

The response is always an odd function so that

$$
\sigma\left(\varepsilon\right)=-\sigma\left(-\varepsilon\right)
$$

For example, if one wants to define

$$
\sigma=4\varepsilon+6\varepsilon^2+2\varepsilon^3,
$$

the following command shall be used.

```
material PolyElastic1D 1 4. 6. 2.
```

Please note density is not supported in this model.


---

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