2nd Edition

Material Modeling in Finite Element Analysis

By Zhaochun Yang Copyright 2024
    320 Pages 283 Color & 1 B/W Illustrations
    by CRC Press

    320 Pages 283 Color & 1 B/W Illustrations
    by CRC Press

    Finite element analysis has been widely applied in mechanical, civil, and biomedical designs. This new edition provides the readers with comprehensive views of various material models through practical examples, which will help them better understand various materials and build appropriate material models in finite element analysis. Material Modeling in Finite Element Analysis, Second Edition, consists of four main parts: (1) metals, (2) polymers, (3) soils, and (4) modern materials. Each part starts with the structure and function of different materials and then follows the corresponding material models and the temperature and time effects on the material models. The final part focuses on user subroutines such as UserMat and UserHyper. This book presents some specific problems including the metal-forming process, combustion room, Mullins effect of rubber tires, viscoelasticity of liver soft tissues, small punch test, tunnel excavation, slope stability, concrete slump test, orthodontic wire, and piezoelectric microaccelerometer. All modeling files are provided in the appendices of this book. This book would be helpful for graduate students and researchers in the mechanical, civil, and biomedical fields who conduct finite element analysis. This book provides all readers with a comprehensive understanding of modeling various materials.


    Chapter 1 Introduction

    Part 1 METAL

    Chapter 2 Structure and Material Properties of Metal

                   2.1 Structure of Metal

                   2.2 Elasticity and Plasticity of Metal


    Chapter 3 Some Plastic Material Models of Metals

                   3.1 Introduction of Plasticity

                   3.2 Nonlinear Kinematic Hardening


    Chapter 4 Material Properties as Function of Time

                   4.1 Viscoplasticity

                   4.2 Creep

                   4.3 Discussion of Viscoplasticity and Creep


    Chapter 5 Influence of Temperature on Material Properties

                   5.1 Temperature Dependency of Material Properties

                   5.2 Simulation of Combustion Chamber under Different



    Chapter 6 Subroutine UserMat

                   6.1 UserMat Development

                   6.2 UserMat of Strain-Hardening Material Model


    Part 2 POLYMERS

    Chapter 7 Structure and Features of Polymer

                   7.1 Structure of Polymer

                   7.2 Features of Polymer


    Chapter 8 Hyperelasticity

                   8.1 Some Widely Used Hyperelastic Models

                   8.2 Stability Discussion

                   8.3 Curve-Fitting of Material Parameters from Experimental Data


    Chapter 9 Viscoelasticity of Polymers

                   9.1 Viscoelasticity of Polymers

                   9.2 Shift Functions


    Chapter 10 Eight-Chain-Based Viscoplasticity Models

                   10.1 Bergstrom-Boyce Model

                   10.2 Simulation of Small Punch Test


    Chapter 11 Mullins Effect

                   11.1 Introduction of Mullins Effect

                   11.2 Ogden-Roxburgh Mullins Effect Model

                   11.3 Simulation of a Rubber Tire with the Mullins Effect


    Chapter 12 UserHyper for Modeling Hyperelastic Materials

                   12.1 Introduction of Subroutine UserHyper

                   12.2 Simulation of Veronda-Westman Model


    Part 3 SOIL

    Chapter 13 Soil Introduction

                   13.1 Soil Structure

                   13.2 Soil Parameters


    Chapter 14 Cam Clay Model

                   14.1 Introduction of Modified Cam Clay Model

                   14.2 Modified Cam Clay Model in ANSYS

                   14.3 Simulation of Soil Excavation

                   14.4 Simulation of a Tower on the Ground by Modified Cam Clay Model


    Chapter 15 Drucker-Prager Model

                   15.1 Introduction of Drucker-Prager Model

                   15.2 Simulation of Concrete Slump Test

                   15.3 Study of a Soil-Arch Interaction


    Chapter 16 Mohr-Coulomb Model

                   16.1 Introduction of Mohr-Coulomb Model

                   16.2 Mohr-Coulomb Model in ANSYS

                   16.3 Concrete Slump Test

                   16.4 Study of Slope Stability


    Chapter 17 Jointed Rock Model

                   17.1 Jointed Rock Model

                   17.2 Definition of the Jointed Rock Model in ANSYS

                   17.3 Simulation of Tunnel Excavation


    Chapter 18 Consolidation of Soils

                   18.1 Consolidation of Soils

                   18.2 Modeling Porous Media in ANSYS

                   18.3 Simulation of Terzaghi’s Problem

                   18.4 Simulation of Consolidation of Three-Well Zone



    Chapter 19 Composite Materials

                   19.1 Introduction of Composite Materials

                   19.2 Modeling Composite in ANSYS

                   19.3 Simulation of Composite Structure in Failure Test

                   19.4 Simulation of Crack Growth in Single Leg Bending Problem


    Chapter 20 Functionally Graded Material

                   20.1 Introduction of Functionally Graded Material

                   20.2 Material Model of Functionally Graded Material

                   20.3 Simulation of a Spur Gear with Functionally Graded Materials


    Chapter 21 Shape Memory Alloys

                   21.1 Structure of SMA and Various Material Models

                   21.2 Simulation of Orthodontic Wire

                   21.3 Simulation of a Vacuum-Tight Shape Memory Flange


    Chapter 22 Simulation of Piezoelectricity

                   22.1 Introduction to Piezoelectricity

                   22.2 Structures and Mechanical Behaviors of Piezoelectric Materials

                   22.3 Constitutive Equation of Piezoelectricity

                   22.4 Simulation of Piezoelectric Accelerometer


    Chapter 23 Nano Materials

                   23.1 Introduction of Nano

                   23.2 Determination of Young’s Modulus of Fe Particles



    Chapter 24 Retrospective

                   24.1 Close Association of Material Properties with the Structure

                   24.2 Significant Influences of Temperature on Material Properties

                   24.3 Various Materials with Different Solution Controls

                   24.4 Various Fields with Different Units

                   24.5 Anisotropic Material with Symmetrical Conditions

                   24.6 Application of Four Soil Models

                   24.7 Definition of Material Parameters

                   24.8 User Subroutine

    Appendix 1 Input File of Curve-Fitting of the Chaboche Model in Section 3.2

    Appendix 2 Input File of the Ratcheting Model in Section 3.2

    Appendix 3 Input File of the Forming Process Model in Section 4.1

    Appendix 4 Input File of the Bolt Model under Pretension in Section 4.2

    Appendix 5 Input File of the Combustion Chamber Model in Section 5.2

    Appendix 6 UserMat of Strain-Hardening Model in Section 6.2

    Appendix 7 Input File of the Forming Process Model in Section 4.1

    Appendix 8 Input File of Curve-Fitting of the Ogden Model in Section 8.3

    Appendix 9 Input File of the Liver Soft Tissue Model in Section 9.1

    Appendix 10 Input File of the Stress Evolution of Glass Tube in Section 9.2

    Appendix 11 Input File of the Small Punch Test in Section 10.2

    Appendix 12 Input File of the Rubber Tire Damage Model in Section 11.3

    Appendix 13 Input File of the Breast Tumor Model in Section 12.2

    Appendix 14 Input File of the Soil Excavation in Section 14.3

    Appendix 15 Input File of the Tower Subsidence Model in Section 14.4

    Appendix 16 Input File of the Concrete Slump Test in Section 15.2

    Appendix 17 Input File of the Soil-Arch Interaction Model in Section 15.3

    Appendix 18 Input File of the Concrete Slump Test in Section 16.3

    Appendix 19 Input File of the Slope Stability Model in Section 16.4

    Appendix 20 Input File of the Tunnel Excavation Model in Section 17.3

    Appendix 21 Input File of One-Dimensional Terzaghi’s Problem in Section 18.3

    Appendix 22 Input File of the Settlement Model in Section 18.4

    Appendix 23 Input File of the Composite Damage Model in Section 19.3

    Appendix 24 Input File of the SLB Model in Section 19.4

    Appendix 25 Input File of the Spur Gear Model with FGM in Section 20.3

    Appendix 26 Input File of the Orthodontic Wire Model in Section 21.2

    Appendix 27 Input File of the Vacuum Tight Shape Memory Flange Model in Section 21.3

    Appendix 28 Input File of the Piezoelectric Microaccelerometer Model in Section 22.4

    Appendix 29 Input File of the Contact Model in Section 23.2



    Zhaochun Yang received his PhD in Mechanical Engineering from the University of Pittsburgh in 2004. Since 2005, he has worked for big companies and national labs such as Nation Energy Technology Laboratory. He has been in the field of finite element analysis for over 20 years and has gained much experience, especially in material modeling. Up to now, he has published 12 journal papers and 3 books.