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Fundamental Tests for Two and Three-Dimensional, Elastoplastic Small Strain Finite Element Analysis

This report describes a set of fundamental benchmark tests concerning finite element software for elastoplastic, stress analysis of planar and three—dimensional structures. In particular, it is assumed that the plastic behaviour is described by the von Mises yield criterion with an associated flow rule. Geometric nonlinearities, rate and temperature effects are excluded. 

The report focuses mainly on constitutive model tests. Some nonlinear equation solution and incompressibility tests are also presented. 
In the constitutive model tests, three classes of plastic behaviour are considered : perfect plasticity, isotropic and kinematic hardening.


Introduction to tests

  • Background to tests
  • Organisation of Report
  • Fundamentals of Elastoplastic Models
    • Observed One-Dimensional Elastoplastic Behaviour
    • Generalisation to multiaxial stress states
    • Plane Problems

Constitutive  Model Benchmark tests

  • Introduction

  • Plane Stain Tests
    • Plane Strain with perfect plasticity
    • Plane Strain with isotropic hardening

  • Three Dimensional tests
    • Perfect Plasticity
    • Isotropic Hardening

  • Axisymmetric Tests
    • Axisymmetric with Perfect Plasticity
    • Axisymmetric with Isotropic Hardening

  • Comparison of Kinematic and Isotropic Hardening for Plane Strain Conditions
    • Introduction
    • Kinematic versus Isotropic Hardening Benchmark tests for Plane Strain Conditions

Nonlinear Equation Solutions Tests 

  • Introduction
  • Input Data
  • Reference Solution
  • Finite Element Target Solution

Incompressibility Tests

  • Introduction
  • Cylinder 'locking' problem


Appendix A

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E. Hinton & M.H. Ezzat

First Published - May 1987

Softback, 148 Pages