INTRODUCTION TO COMPUTATIONAL PLASTICITY

By A. JOZIS

CONTENTS PART I MICROPLASTICITY AND CONTINUUM PLASTICITY 1 MICROPLASTICITY INTRODUCTION CRYSTAL SLIP CRITICAL RESOLVED SHEAR STRESS DISLOCATIONS FURTHER READING 2 CONTINUUM PLASTICITY SOME PRELIMINARIES YIELD CRITERION ISOTROPIC HARDENING KINEMATIC HARDENING COMBINED ISOTROPIC AND KINEMATIC HARDENING VISCOPLASTICITY AND CREEP 3 KINEMATICS OF LARGE DEFORMATIONS AND CONTINUUM MECHANICS THE DEFORMATION GRADIENT MEASURES OF STRAIN INTERPRETATION OF STRAIN MEASURES POLAR DECOMPOSITION VELOCITY GRADIENT, RATE OF DEFORMATION, AND CONTINUUM SPIN ELASTIC–PLASTIC COUPLING OBJECTIVE STRESS RATES SUMMARY 4 THE ?NITE ELEMENT METHOD FOR STATIC AND DYNAMIC PLASTICITY HAMILTON’S PRINCIPLE INTRODUCTION TO THE ?NITE ELEMENT METHOD FINITE ELEMENT EQUILIBRIUM EQUATIONS INTEGRATION OF MOMENTUM BALANCE AND EQUILIBRIUM EQUATIONS 5 IMPLICIT AND EXPLICIT INTEGRATION OF VON MISES PLASTICITY IMPLICIT AND EXPLICIT INTEGRATION OF CONSTITUTIVE EQUATIONS MATERIAL JACOBIAN IMPLICIT INTEGRATION IN VISCOPLASTICITY INCREMENTALLY OBJECTIVE INTEGRATION FOR LARGE DEFORMATIONS 6 IMPLEMENTATION OF PLASTICITY MODELS INTO ?NITE ELEMENT CODE ELASTICITY IMPLEMENTATION VERI?CATION OF IMPLEMENTATIONS ISOTROPIC HARDENING PLASTICITY IMPLEMENTATION LARGE DEFORMATION IMPLEMENTATIONS ELASTO-VISCOPLASTICITY IMPLEMENTATION PART II PLASTICITY MODELS 7 SUPERPLASTICITY SOME PROPERTIES OF SUPERPLASTIC ALLOYS CONSTITUTIVE EQUATIONS FOR SUPERPLASTICITY MULTIAXIAL CONSTITUTIVE EQUATIONS AND APPLICATIONS REFERENCES 8 POROUS PLASTICITY FINITE ELEMENT IMPLEMENTATION OF THE POROUS MATERIAL CONSTITUTIVE EQUATIONS APPLICATION TO CONSOLIDATION OF TI–MMCS 9 CREEP IN AN AERO-ENGINE COMBUSTOR MATERIAL PHYSICALLY BASED CONSTITUTIVE EQUATIONS MULTIAXIAL IMPLEMENTATION INTO ABAQUS 10 CYCLIC PLASTICITY, CREEP, AND TMF CONSTITUTIVE EQUATIONS FOR CYCLIC PLASTICITY CONSTITUTIVE EQUATIONS FOR C263 UNDERGOING TMF