Advanced Theories for Deformation, Damage and Failure in Materials

Preface
Contents
1 Creep and Damage of Materials at Elevated Temperatures
	1.1 Motivation and Some Historical Remarks
		1.1.1 Motivation
		1.1.2 Creep
		1.1.3 Brief Historical Overview
	1.2 Creep Model
		1.2.1 Basic Model
		1.2.2 Continuum Damage Mechanics
	1.3 Continuum Mechanics
		1.3.1 Preliminary Remarks
		1.3.2 Brief Historical Outline
		1.3.3 One-Dimensional Case
		1.3.4 Three-Dimensional Case
		1.3.5 Latest Developments
		1.3.6 Conclusions
	1.4 Rheological Models
		1.4.1 Some Remarks
		1.4.2 Simplest Three-dimensional Rheological Models
		1.4.3 Simplest Two-dimensional Rheological Models
		1.4.4 Advanced Rheological Models
	References
2 Anisotropic Plasticity During Non-proportional Loading
	2.1 Introduction
	2.2 Stress States
		2.2.1 Uniaxial
		2.2.2 Multiaxial
	2.3 Elasto-Plasticity
		2.3.1 Elasticity
		2.3.2 Plasticity
		2.3.3 Yield Condition
		2.3.4 Flow Rule
		2.3.5 Hardening
	2.4 Anisotropy
		2.4.1 Elasticity
		2.4.2 Plasticity
		2.4.3 Hill's Yield Condition
		2.4.4 Application
	2.5 Non-linear Strain Path
		2.5.1 Deformation History
		2.5.2 Experimental
		2.5.3 Interpretation
		2.5.4 Discussion
	2.6 Anisotropic Hardening
		2.6.1 Kinematic Hardening
		2.6.2 Mutli-surface Kinematic Hardening
		2.6.3 Distortional Hardening
	2.7 Homogeneous Anisotropic Hardening Model
		2.7.1 Background
		2.7.2 Yield Condition
		2.7.3 Calibration
	2.8 Finite Element Implementation
		2.8.1 Stress Integration Algorithm
		2.8.2 Elasto-Plastic Tangent Modulus
		2.8.3 FE-Application: Non-proportional Loading
	References
3 Anisotropy of Yield/Failure Criteria—Comparison of Explicit and Implicit Formulations
	3.1 Lecture—Preliminaries
		3.1.1 Even Order Tensors—Invariants and Matrix Representations
		3.1.2 Fourth-Order Tensors
		3.1.3 Positive Definiteness of Quadratic Form {t}T[B]{t} in Sylvester's Sense
	3.2 Lecture—General Concept of Limit Surfaces
		3.2.1 Pressure Sensitive or Insensitive Yield Criteria
		3.2.2 Survey of Symmetry Groups
		3.2.3 Drucker's Postulate of Stability
	3.3 Lecture – Initial Yield Criteria of Pressure Insensitive Materials
		3.3.1 von Mises Anisotropic Criterion
		3.3.2 von Mises Orthotropic Criterion, the Hill Deviatoric Criterion
		3.3.3 Comparison of Hill's Criterion Versus Hu–Marin's Concept
		3.3.4 Transverse Isotropy of Hill's Type Tetragonal Symmetry Versus Hu–Marin's Type Hexagonal Symmetry
	3.4 Lecture—Implicit Formulation of Pressure Insensitive Yield Criteria
	3.5 Lecture–Yield/Failure Criteria for Hydrostatic Pressure Sensitive Materials
		3.5.1 von Mises–Tsai–Wu Type Criteria
		3.5.2 Transversely Isotropic Case of Tsai–Wu Type Criteria
	3.6 Lecture—Implicit Formulation of Pressure Sensitive Anisotropic Initial Failure Criteria
	References
4 Time-dependent and Time-independent Models of Cyclic Plasticity for Low-cycle and Thermomechanical Fatigue Life Assessment
	4.1 Introduction
		4.1.1 Motivation
		4.1.2 Aims of This Work
		4.1.3 Structure of This Work
	4.2 Concept of Internal Variables and Normality Rules
		4.2.1 Helmholtz Free Energy and Internal Variables
		4.2.2 Flow Potential and Normality Rule
	4.3 Time-independent Cyclic Plasticity
		4.3.1 Isotropic Hardening
		4.3.2 Kinematic Hardening
		4.3.3 Combined Hardening
	4.4 Time-dependent Cyclic Plasticity
		4.4.1 Rate-dependent Yielding: Unified Models
		4.4.2 Rate-dependent Yielding: Non-unified Models
		4.4.3 Static Recovery of Hardening
	4.5 Thermomechanical Loadings
		4.5.1 Temperature-dependent Material Properties
		4.5.2 Temperature Rate Terms
	4.6 Conclusion
	References
5 Damage and Failure of Composite Materials
	5.1 Introduction
	5.2 Failure Modes in UD Composites
		5.2.1 Fiber Failure Mode in Axial Tension
		5.2.2 Fiber Failure Mode in Axial Compression
		5.2.3 Matrix and Fiber/Matrix Interface Failure Mode in Transverse Tension
		5.2.4 Matrix and Fiber/Matrix Interface Failure Mode in Transverse Compression
		5.2.5 Matrix and Fiber/Matrix Interface Failure Mode in In-plane Shear
		5.2.6 Failure in Combined Loading
	5.3 Failure Modes in Laminates
		5.3.1 Cross Ply Laminates
		5.3.2 General Laminates
	5.4 Damage and Failure
		5.4.1 Damage Mechanics
		5.4.2 Damage Characterization
		5.4.3 CDM Framework for Materials Response
		5.4.4 Synergistic Damage Mechanics (SDM)
		5.4.5 Remarks on Characterization of Damage
		5.4.6 Evolution of Damage
	5.5 Modeling of Failure
		5.5.1 Phenomenological Failure Theories for UD Composites
		5.5.2 Physical Modeling of Failure
	5.6 Future Directions for Research
	5.7 Concluding Remarks
	References