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 ($\epsilon >0$).

$$\sigma =a_1\epsilon +a_2{\epsilon }^2+a_3{\epsilon }^3\cdots$$

The response is always an odd function so that

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

For example, if one wants to define

$$\sigma =4\epsilon +6{\epsilon }^2+2{\epsilon }^3,$$

the following command shall be used.

material PolyElastic1D 1 4. 6. 2.

Please note density is not supported in this model.