The use of computational techniques, like the finite element method, is increasingly becoming popular in engineering companies involved in the design and analysis of engineering components and structures made from a variety of materials. An important aspect of FE analysis is modelling of the material behaviour.

The aim of the book is to offer physical understanding of the material modelling features. This book is aimed at engineering students and professional engineers who are familiar with the finite element method and its terminology. It will be assumed that the reader’s experience is limited to carrying out linear stress analysis. A non-specialist reader will be able to follow the booklet and understand the important modelling issues, techniques and assumptions.

Examples have been used to illustrate the modelling techniques and also show the sensitivity of the results to the input data used to describe the material behaviour. The book will be useful to practising engineers as it will explain the physical significance of the various input data that has been used to describe the material behaviour.

A range of constitutive models typically used in an FE analysis is described in the book and where appropriate, material failure under severe loading is also covered. However, analysis of failure due to fracture, fatigue and buckling which require different procedures is not covered in this book.

NAFEMS has already produced a series of book which give guidance on how to create finite element models, select analysis codes and perform stress analysis. This book goes a step further and provides practical guidance on how to model material behaviour in a finite element analysis.

Contents

1. Introduction

2. Classes of Materials

3. Linear Elastic

3.1 Isotropic
3.2 Orthotropic
3.3 Anisotropic

4. Linear vs Non-linear

5. Plasticity

5.1 Yield Function
5.2 Flow Rules
5.3 Metal Plasticity

5.3.1 Perfectly Plastic Material
5.3.2 Isotropic Hardening
5.3.3 Kinematic Hardening
5.3.4 Non linear kinematic hardening
5.4 Models for cyclic loading

6. Concrete

6.1 Modelling of Plain Concrete
6.2 Modelling of Reinforced Concrete
6.3 Post-Tensioned Concrete
6.4 Concrete Cracking

6.4.1 The Discrete Crack Approach
6.4.2 The Smeared Crack Approach

7. Foam and Wood

7.1 Physical considerations
7.2 Material Models for Crushable Foam

8. Composites

8.1 Material Classification
8.2 Advantages and Disadvantages of Composites
8.3 Fibres and Matrices 
8.4 Micromechanics and Macromechanics of Composites
8.5 Generation of Material Design Data

8.5.1 Material Constants

8.6 Modelling of Composites

8.6.1 Layered
8.6.2 Equivalent Lamina Properties

9. Rubber

9.1 Physical Behaviour and FE Formulations
9.2 Types of Hyperelastic Material Models

10. Soils

10.1 Physical considerations
10.2 Mohr-Coulomb Model
10.3 Drucker-Prager Model
10.4 Matching Soil Parameters
10.5 Cap Hardening
10.6 Analysis Assumptions

11. Creep

11.1 Time Hardening
11.2 Strain Hardening
11.3 Creep Laws
11.4 Analysis Procedures

12. Applications of Material Models

12.1 Aircraft Engineering

12.1.1 Conventional aluminium alloy
12.1.2 Aluminium-lithium
12.1.3 Magnesium alloy
12.1.4 Titanium
12.1.5 Steel
12.1.6 Carbon Fibre Composite
12.1.7 Woven Cloth

12.2 Medical Engineering
12.3 Automotive Engineering
12.4 Verification of Material Models

13. Concluding Remarks

14. References