This document provides details of 10 benchmark tests for finite element assemblies modelling non-linear material behaviour with small deformations. Its aim is to provide a compendium of simple, authoritatively documented tests covering the more common types of material non-linear phenomena encountered in industrial practise. Emphasis is on quasi-static small-displacement small-strain continuum behaviour of ductile metals.

Collectively the tests may be used for a number purposes including:

• To check the ability of a finite element program to produce acceptable solutions to problems involving material non-linearity.
  
• To exercise a program’s ability to model physical behaviour.

• To educate inexperienced users about the potential pitfalls and difficulties that may arise when modelling non-linear phenomena.

The overall philosophy has been to select problems with a clear industrial relevance, which can be modelled satisfactorily with the capabilities of robust general purpose commercial codes ad which, moreover, are both physically simple and computationally undemanding. The problems have been drawn from an earlier survey [Ref. 1.2], but in most instances have been “tuned” to make them more discriminating or to improve their clarity and ease of interpretation.

Full details of each test are provided in the Appendices. A companion volume to this report [Ref. 1.1] gives a summary of each test in a standard form.

NL7B Corrigendum

Work carried out by Dr Angus Ramsay of Ramsay Maunder Associates has identified that the published target solution for problem NL7B is mesh dependent. The published unconservative target solution is 17% higher than the true collapse load of 0.03303.

NAFEMS would like to thank Angus for identifying this error.

Contents

ACKNOWLEDGEMENTS

SUMMARY

TABLE OF CONTENTS

INTRODUCTION

SCOPE OF TESTS

• Criteria for Benchmarks
• Overview of Tests
• Reporting Format

REFERENCES

APPENDICES

• NL1. TORSIONAL CREEP OF CIRCULAR SHAFT
• NL2. CYCLIC THERMAL LODING OF TWO-BAR ASSEMBLY
• NL3. THERMAL RATCHETING OF TWO-BAR ASSEMLY
• NL4. THERMAL RATCHETING OF UNIFORM BEAM
• NL5. PLANE STRAIN RIGID PUNCH
• NL6. TORSIONAL CREEP OF SQUARE SHAFT
• NL7. SQUARE PLATE UNDER UNIFORMLY DISTRIBUTED LOAD
• NL8. NON-PROPORTIONAL LOADING OF THICK CYLINDER
• NL9. THERMAL RAT CHETING OF ECCENTRIC TUBE
• NL10. THERMALLY INDUCED CREEP OF INTERNALLY PRESSURISED SPHERE.