Preface |
Introduction / 1: |
Scope of this Monograph / 1.1: |
Useful Background for this Presentation / 1.2: |
Overview / 1.3: |
Finite Element Formulations in Nonlinear Solid Mechanics / 2: |
Initial/Boundary Value Problems in the Kinematically Lin-ear Regime / 2.1: |
Strong Form of the EBVP / 2.1.1: |
Weak Form of the IBVP / 2.1.2: |
The IBVP in the Finite Strain Case / 2.2: |
Notation and Problem Formulation / 2.2.1: |
Finite Strain Kinematics / 2.2.2: |
Stress Definitions Appropriate for Large Deformations / 2.2.3: |
Frame Indifference / 2.2.4: |
The Strong Form in Finite Strains / 2.2.5: |
The Weak Form in Finite Strains / 2.2.6: |
Finite Element Discretization / 2.3: |
Discretized Weak Form; Generation of Discrete Non-linear Equations / 2.3.1: |
Discrete Nonlinear Equations for the Kinematically Linear Case / 2.3.2: |
Solution Strategies for Spatially Discrete Systems / 2.4: |
Quasistatics and Incremental Load Methods / 2.4.1: |
Dynamics and Global Time Stepping Procedures / 2.4.2: |
Local (Constitutive) Time Stepping Procedures / 2.4.3: |
Nonlinear Equation Solving / 2.4.4: |
Consistent Algorithmic Linearization of Material Re-sponse / 2.4.5: |
The Kinematically Linear Contact Problem / 3: |
Strong Forms in Linearized Frictionless Contact / 3.1: |
The Signorini Problem: Contact with a Rigid Obstacle / 3.1.1: |
The Two Body Contact Problem / 3.1.2: |
Weak Statements of the Contact Problem / 3.2: |
Variational Inequalities / 3.2.1: |
The Quasistatic Elastic Case: Contact as a Problem of Constrained Optimization / 3.2.2: |
Methods of Constraint Enforcement / 3.3: |
Classical Lagrange Multiplier Methods / 3.3.1: |
Penalty Methods / 3.3.2: |
Augmented Lagrangian Methods / 3.3.3: |
Inclusion of Friction into the Problem Description / 3.4: |
Friction Kinematics and Traction Measures / 3.4.1: |
Unregularized Coulomb Friction Laws / 3.4.2: |
Regularization of Friction / 3.4.3: |
Variational Statements Including Friction / 3.4.4: |
Nonlocal Frictional Descriptions / 3.4.5: |
Continuum Mechanics of Large Deformation Contact / 4: |
Two Body Contact Problem Definition / 4.1: |
Local Momentum Balances / 4.1.1: |
Initial and Boundary Conditions / 4.1.2: |
Contact Constraints in Large Deformations / 4.2: |
The Gap Function as Defined by Closest Point Projection / 4.2.1: |
Frictional Kinematics on Interfaces / 4.2.2: |
Frame Indifference of Contact Rate Variables / 4.2.3: |
Coulomb Friction in Large Sliding / 4.2.4: |
Summary: Strong Form of the Large Deformation Contact Problem / 4.3: |
Virtual Work Expressions Incorporating Contact / 4.4: |
Contact Virtual Work: The Contact Integral / 4.4.1: |
Linearization of Contact Virtual Work / 4.4.2: |
Summary: Weak Form of the Large Deformation Con-tact Problem / 4.4.3: |
Finite Element Implementation of Contact Interaction / 5: |
Finite Dimensional Representation of Contact Interaction / 5.1: |
Contact Surface Discretization / 5.1.1: |
Numerical Integration of the Contact Integral / 5.1.2: |
Contact Detection (Searching) / 5.1.3: |
Time Discretization / 5.2: |
Global time integration schemes / 5.2.1: |
Temporally Discrete Frictional Laws for the Penalty Regularized Case / 5.2.2: |
Contact Stiffness and Residual: Penalty Regularized Case / 5.3: |
Three dimensional matrix expressions / 5.3.1: |
Two dimensional matrix expressions / 5.3.2: |
Augmented Lagrangian Constraint Enforcement Algorithms / 5.4: |
Uzawa's Method (Method of Multipliers) / 5.4.1: |
Algorithmic Symmetrization Using Augmented La-grangians / 5.4.2: |
Augmented Lagrangian Discrete Force and Stiffness Expressions / 5.4.3: |
Numerical Examples / 5.5: |
General Demonstrations of the Computational Frame-work / 5.5.1: |
Demonstrations of Augmented Lagrangian Algorith-mic Performance / 5.5.2: |
Tribological Complexity in Interface Constitutive Models / 6: |
Rate and State Dependent Friction / 6.1: |
Motivation / 6.1.1: |
One Dimensional Model Development / 6.1.2: |
Model Incorporation into Convective Slip Advected Frame / 6.1.3: |
Local Time Stepping Algorithm / 6.1.4: |
Contact Force Vector and Stiffness Matrix / 6.1.5: |
Thermomechanically Coupled Friction on Interfaces / 6.1.6: |
Thermally Coupled Problem Definition / 6.2.1: |
A Thermodynamically Consistent Friction Model / 6.2.3: |
Variational Principle and Finite Element Implemen-tation / 6.2.4: |
Thermodynamical Algorithmic Consistency / 6.2.5: |
Constitutive Framework for Bulk Continua / 6.3.1: |
Thermomechanical Interface Model Framework / 6.3.2: |
A Priori Stability Estimates for Dynamic Frictional Contact / 6.3.3: |
A New Partitioned Scheme for Thermomechanical Contact / 6.3.4: |
Algorithmic Treatment of Contact Conditions According to the Adiabatic Split / 6.3.5: |
Energy-Momentum Approaches to Impact Mechanics / 7: |
Energy Stability of Traditional Schemes / 7.1: |
A Model System / 7.1.1: |
The Concept of Energy Stability / 7.1.2: |
Influence of Contact Constraints on System Energy / 7.1.3: |
Energy-Momentum Methods for Elastodynamics / 7.2: |
Conservation Laws / 7.2.1: |
Conservative Discretization Schemes / 7.2.2: |
Energy-Momentum Algorithmic Treatment of Prictionless Impact / 7.3: |
Discrete Contact Constraints / 7.3.1: |
Spatial Discretization and Implementation / 7.3.2: |
Introduction of Frictional and Bulk Dissipation: Energy Con-sistency / 7.3.3: |
Coulomb Friction Model Formulation / 7.4.1: |
Local Split of the Coulomb Model / 7.4.2: |
Algorithmic Formulation / 7.4.3: |
Energy Consistent Treatment of Bulk Inelasticity / 7.4.4: |
Numerical Examples With Friction and Inelasticity / 7.4.5: |
EM Algorithms Involving a Discontinuous Velocity Update / 7.5: |
Temporally Discontinuous Velocity Update / 7.5.1: |
Reexamination of Conservation Conditions / 7.5.2: |
Contact Constraints / 7.5.3: |
Summary of the Algorithm / 7.5.4: |
Emerging Paradigms for Contact Surface Discretization / 7.5.5: |
Contact Smoothing / 8.1: |
An Alternative Variational Framework / 8.1.1: |
Smoothing Strategies in Two Dimensions / 8.1.2: |
Smoothing Strategies in Three Dimensions / 8.1.3: |
Mortar-Finite Element Methods for Contact Description / 8.1.4: |
Tied Contact and the Role of Mortar Formulations in Convergence / 8.2.1: |
A Mortar-Finite Element Formulation of Frictional Contact / 8.2.2: |
Numerical Examples of Mortar Treatment of Frictional Contact / 8.2.3: |
References |
Index |
Preface |
Introduction / 1: |
Scope of this Monograph / 1.1: |