Bilinear1D

Uniaxial Bilinear Material Using J2 Plasticity

Syntax

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

1. 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.

2. Negative hardening ratio (softening) is supported. However, the yield surface will always be non-negative.

Usage

Isotropic Hardening

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

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

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

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

Example 4