RambergOsgood

Ramberg-Osgood Steel Model

Syntax

material RambergOsgood (1) (2) (3) [4] [5] [6]
# (1) int, unique material tag
# (2) double, elastic modulus
# (3) double, initial yield stress
# [4] double, offset alpha, default: 1.0
# [5] double, n, default: 4.0
# [6] double, density, default: 0.0

History Variable Layout

location
value

initialize_history(0)

load_sign

initialize_history(1)

reverse_strain

initialize_history(2)

reverse_stress

initialize_history(3)

previous_reverse_strain

initialize_history(4)

previous_reverse_stress

Remarks

  1. Local iterations are required to obtain the stress value.

Theory

The Ramberg-Osgood relationship is defined as

ε=σE+ασE(σσ0)n1\varepsilon=\dfrac{\sigma}{E}+\alpha\dfrac{\sigma}{E}(\dfrac{\sigma}{\sigma_0})^{n-1}

where α\alpha is the offset and nn is the material constant controls hardening. Noting that ε=εe+εp=σE+εp\varepsilon=\varepsilon_e+\varepsilon_p=\dfrac{\sigma}{E}+\varepsilon_p, hence

σE+εp=σE+ασE(σσ0)n1\dfrac{\sigma}{E}+\varepsilon_p=\dfrac{\sigma}{E}+\alpha\dfrac{\sigma}{E}(\dfrac{\sigma}{\sigma_0})^{n-1}

so

εp=ασE(σσ0)n1.\varepsilon_p=\alpha\dfrac{\sigma}{E}(\dfrac{\sigma}{\sigma_0})^{n-1}.

At the yield stress, viz., σ=σ0\sigma=\sigma_0, then

εp=αεe.\varepsilon_p=\alpha\varepsilon_e.

So the offset α\alpha indicates the magnitude of plastic strain at yield stress.

The cyclic response uses the difference between current reverse stress and previous reverse stress as "yield stress".

Examples

material RambergOsgood 1 100.0 8.0 1 10.0
materialTest1D 1 1E-2 20 20 30 20 30 20 30 20 30 20 30 20
exit
material RambergOsgood 1 100.0 8.0 1 10.0
materialTest1D 1 1E-2 20 40 40 40 40 40 40
exit
material RambergOsgood 1 100.0 8.0 1 10.0
materialTest1D 1 1E-2 20 20 30 15 20 40 15 25 15 20 30
exit

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