PolyJ2

Polynomial Hardening J2 Model

The PolyJ2 defines a J2 material with isotropic hardening. The isotropic hardening is controlled by a polynomial. The kinematic hardening is disabled.

Syntax

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material PolyJ2 (1) (2) (3) (4) [(5)...]
# (1) int, unique material tag
# (2) double, elastic modulus
# (3) double, poisson's ratio
# (4) double, density
# [(5)...] double, parameters in polynomial

Example

The isotropic hardening function is defined to be a polynomial function of equivalent plastic strain.

σ_{y} ({\bar{ε}}_{p}) = a_{0} + a_{1} {\bar{ε}}_{p} + a_{2} {\bar{ε}}_{p}^{2} + \dots + a_{n} {\bar{ε}}_{p}^{n} .

Clearly, $a_{0}$ is the initial yielding stress.

To define for example the following hardening

σ_{y} ({\bar{ε}}_{p}) = 100 + 4000 {\bar{ε}}_{p} + 80000 {\bar{ε}}_{p}^{3}

with $E = 200000$ and $ν = 0.3$ , the following command can be used.

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1	`material PolyJ2 1 2E5 .3 .0 1E2 4E3 0. 8E4`