Plasticity corrections

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

Elements tested
Problem description
Results and discussion
Input files

Elements tested

C3D8
CPE4

T3D2

Problem description

The tests are used to verify the correctness of the equivalent stresses and strains computed using the Neuber and Glinka rules in Abaqus/Standard.

All tests consist of four elements subjected to uniaxial tension. The same isotropic linearly elastic material definition is used in all cases, and three different methods are used to specify the plastic material properties used for the evaluation of the plasticity corrections: Ramberg-Osgood, tabular, and Mises yield surface. When the Ramberg-Osgood or the tabular method is used, Abaqus evaluates plasticity corrections in both general and static perturbation procedures. However, if an elastic-plastic material with Mises yield surface is used, the plasticity corrections are evaluated only in static perturbation procedures.

Material:

Elasticity
Young's modulus: $E = 3.0 \times 10^{6}$
Poisson's ratio: $ν = 0.3$

Plasticity

Hardening


Yield stress	Plastic strain
$10^{6}$	$0.0$
$2 \times 10^{6}$	$1.0$

Plasticity corrections

Ramberg-Osgood model


K	$10^{6}$
n	$3.0$

Tabular form


Yield stress	Plastic strain
$10^{6}$	$0.0$
$2 \times 10^{6}$	$1.0$

Results and discussion

The numerically computed values of Neuber and Glinka equivalent stresses and strains agree well with the results obtained analytically.

Input files

: C3D8, CPE4, S4, T3D2 elements; Ramberg-Osgood model; static procedure.
: C3D8, CPE4, S4, T3D2 elements; tabular form; static procedure.
: C3D8, CPE4, S4, T3D2 elements; Ramberg-Osgood model; static perturbation procedure.
: C3D8, CPE4, S4, T3D2 elements; tabular form; static perturbation procedure.
: C3D8, CPE4, S4, T3D2 elements; Mises yield surface; static perturbation procedure.
: C3D8, CPE4, S4, T3D2 elements; Ramberg-Osgood model; static procedure followed by static perturbation procedure.
: C3D8, CPE4, S4, T3D2 elements; tabular form; static procedure followed by static perturbation procedure.
: C3D8, CPE4, S4, T3D2 elements; Mises yield surface; static procedure followed by static perturbation procedure.