Bilinear1D

Uniaxial Bilinear Material Using J2 Plasticity

Syntax

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material Bilinear1D (1) (2) (3) [4] [5] [6]
# (1) int, unique material tag
# (2) double, elastic modulus
# (3) double, initial yield stress
# [4] double, hardening ratio, default: 0.0
# [5] double, beta, default: 1.0
# [6] double, density, default: 0.0

History Variable Layout

location	value
`initialize_history(0)`	back_stress
`initialize_history(1)`	equivalent_plastic_strain

Remarks

The parameter beta is employed for mixed hardening rule: zero $0.0$ for kinematic hardening and unity $1.0$ for isotropic hardening, anything falls in the range indicates a mixed hardening response.
Negative hardening ratio (softening) is supported. However, the yield surface will always be non-negative.

Usage

Isotropic Hardening

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1 2 3	`material Bilinear1D 1 1000.0 10.0 0.2 1.0 materialTest1D 1 0.001 20 40 60 80 100 100 exit`

Example 1

Isotropic Softening

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1 2 3	`material Bilinear1D 1 1000.0 10.0 -0.02 1.0 materialTest1D 1 0.001 20 40 60 80 100 100 exit`

Example 2

Kinematic Hardening

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1 2 3	`material Bilinear1D 1 1000.0 10.0 0.1 0.0 materialTest1D 1 0.001 20 40 60 80 100 100 exit`

Example 3

Combined Hardening

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1 2 3	`material Bilinear1D 1 1000.0 10.0 0.1 0.5 materialTest1D 1 0.001 20 40 60 80 100 100 exit`

Example 4