Trends in Computational Contact Mechanics (Lecture Notes in Applied and Computational Mechanics, 58)

✍ Scribed by Giorgio Zavarise (editor), Peter Wriggers (editor)

• Publisher: Springer
• Year: 2011
• Tongue: English
• Leaves: 363
• Edition: 2011
• Category: Library

✦ Synopsis

The subject of Computational Contact Mechanics  has many facets. Its main impact lies in the transfer of knowledge form theoretical research to applied sciences, and from there to industry. The application fields are literally countless, ranging from classical engineering to biomechanics and nano-sciences.

The remarkable increase of computer power in recent years has been instrumental in enabling the development of simulation-based analysis in current design activity. This still involves tremendous effort in research,  which focuses on, for example, multi-field and multi-scale problems, algorithmic robustness, and geometrical accuracy. Moreover, several aspects of Contact Mechanics, Debonding and Fracture Mechanics,  have been combined to offer new enhanced possibilities to the computer simulation of complex phenomena.

With these contributions of prominent scientists, this book offers a wide overview on the ongoing research at the highest level in the field.

✦ Table of Contents

Cover
Lecture Notes in Applied
and Computational Mechanics
58
Trends in Computational
Contact Mechanics
ISBN: 9783642221668
Preface
Table of Contents
Contact Modelling in Entangled Fibrous Materials
Introduction
Mechanical Equilibrium of an Assembly of Entangled Fibers
Principle of Virtual Work
3D Beam Model
Geometrical Handling of Contacts within an Assembly of Fibers
Continuous Geometrical Approach of Contact between Fibers
Proximity Zones
Intermediate Geometries
Discretization by Contact Elements
Kinematical Contact Conditions
Mechanical Models for Contact and Friction
Quadratic Regularization of the Penalty Method for Contact
Local Adjustment of the Penalty Parameter
Regularized Coulomb’s Law for Friction
Algorithmic Aspects
Applications
Test of Alternate Sliding between Two Beams
Modeling of Woven Fabrics
Identification of the Transverse Mechanical Behaviour of a Twisted Textile Yarn
Conclusion
References
3D Contact Smoothing Method Based on Quasi-C1 Interpolation
Introduction
Finite Element Formulation
Constitutive Equation and Integral Formulation
Finite Element Formulation
Discrete Contact Treatment
Friction
Smoothing Technique
Nagata’s Method
Validation
Normal Vector Calculation
Contact Algorithm for the Smoothed Surface
Applications
Hertz’s Contact: Indenting a Bulk Parallelepiped
Wire Drawing
Conclusions
References
On a Geometrically Exact Theory for Contact Interactions
On Geometrical Approaches in Contact Mechanics
Bottleneck: Consistent Linearization
Development of a Geometrically Exact Theory
Goals of a Geometrically Exact Theory
Overview of the Developments
Selection of a Coordinate System
Applicability to a Majority of Problems – FE Approximation
Contact Interface Law – Anisotropic Adhesion-Friction
Curve-to-Curve Contact
Conclusions
References
Finite Deformation Contact Based on a 3D Dual Mortar and Semi-Smooth Newton Approach
Introduction
General Formulation of the Finite Deformation Contact Problem
Dual Mortar Finite Element Discretization
Semi-Smooth Newton Method and Consistent Linearization
Solution Algorithm
Implementation Details and Extensions
Evaluation of Mortar Integrals
Quadratic Interpolation
Conservation of Linear and Angular Momentum
Efficient Parallel Contact Search
Treatment of Self Contact
Treatment of Friction
Examples
Hertzian Contact
Two Torus Impact
Sphere in Sphere
Conclusions
References
The Contact Patch Test for Linear Contact Pressure Distributions in 2D Frictionless Contact
Introduction
NTS Formulation
The Basis for an Enhanced NTS Formulation
The Contact Element Passing the Uniform Contact Patch Test
A New Contact Element Passing the Linear Contact Patch Test
Step 1: Slave Nodal Force Computation (VTS-MEL)
Step 2: Slave Nodal Force Transmission (VTS-PPTL)
The VTS-MEL Algorithm
Computation of the Residual Vector
Consistent Linearization
The VTS-PPTL Algorithm
Contact Contribution to the Residual Vector
Contact Contribution to the Tangent Stiffness Matrix
Conclusions
References
Finite Deformation Thermomechanical Contact Homogenization Framework
Introduction
Thermomechanical Contact Formulation
Thermal Contact Homogenization Methodology
Interface Testing Procedure
Macro-to-Micro Transition
Boundary Conditions
Averaging Theorems
Micro-to-Macro Transition
Representative Contact Element
Numerical Investigations
Modeling Aspects
Dependence on Primary Macroscopic Variables
Conclusion
References
Analysis of Granular Chute Flow Based on a Particle Model Including Uncertainties
Introduction
Classification, Representation and Propagation of Uncertainty
Uncertainty Classification and Representation
Uncertainty Propagation Based on the Transformation Method
Chute Flow Studies Using Particle Methods
Laboratory Model
Numerical Simulations
Uncertainty and Sensitivity Analysis
Results
Conclusions
References
Soft Soil Contact Modeling Technique for Multi-Body System Simulation
Introduction and Motivation
MBS Based Soil Contact Modeling Technique
Details of SCM Implementation
Contact Force Computation
Plastic Soil Deformation
Verification of SCM
Profiling of SCM Code
Conclusion
References
A Semi-Explicit Modified Mass Method for Dynamic Frictionless Contact Problems
Introduction
Space Semi-Discretization by the Modified Mass Method
Governing Equations
Space Semi-Discrete Formulation
Semi-Explicit Time Schemes
The Semi-Explicit Scheme with Modified Mass
The Semi-Explicit Scheme with Implicit Contact
Energy Balance
Stability
Gibbs Phenomenon
Numerical Simulations
1D Simulations
2D Simulations
References
An Explicit Asynchronous Contact Algorithm for Elastic-Rigid Body Interaction
Introduction
Frictionless Contact Mechanics for Finite Dimensional Mechanical Systems
Symplectic Algorithms and Energy Conservation
Asynchronous Variational Integrators (AVI)
Explicit Asynchronous Contact Algorithm
Construction of the Admissible Region
Time Step Refinement Zone
Contact Detection and Momentum Reflection
Performance
AVI’s Computational Efficiency
Energy Conservation
Numerical Examples
Multiple Impacts
Impact of a Rigid Body on an Elastic Block
References
Dynamics of a Soft Contractile Body on a Hard Support
Introduction
Affine Contractile Body
Dissipation Inequality and Material Characterization
Surface Energy and Contact Force Characterization
Contact Constitutive Laws
Contact Force Distributions
Numerical Simulations
Parameter Choice and Computational Details
Sliding, Bouncing and Rocking
Bouncing and Rolling
Adhesion and Detachment
Bouncing and Vibrations of a Soft Body
Driven Motion of a Soft Contractile Body
Conclusions
References
Two-Level Block Preconditioners for Contact Problems
Introduction
Mixed Constraint Preconditioner
Multi-Level Incomplete Factorization
Positive Definiteness of S$_i,11$
Positive Definiteness of S$_i+1$
Numerical Results
Concluding Remarks
References
A Local Contact Detection Technique for Very Large Contact and Self-Contact Problems: Sequential and Parallel Implementations
Introduction
Method Description
Preliminary Stage of Contact Detection
Contact Detection
Validation and Performance
Self-Contact Detection
Parallelization
Conclusion
References
Cauchy and Cosserat Equivalent Continua for the Multiscale Analysis of Periodic Masonry Walls
Introduction
Micropolar Masonry Model for Periodic Masonry
Numerical Applications
Conclusions
References
Coupled Friction and Roughness Surface Effects in Shallow Spherical Nanoindentation
Introduction
Numerical Indentation Setups
Sliding Velocity Dependent Friction
Geometrical and Material Parameters
Post-Treatment of the Data
Slip Rate Dependent Friction in Flat Surface Indentation
Friction Induced Variation in the Evaluated Elastic Modulus
Influence of the Loading Rate
Influence of the Friction Law Parameters
Slip Rate Dependent Friction in Rough Surface Nanoindentation
Influence of the Frictionless Surface Roughness
Coupled Influence of Friction and Surface Roughness
Discussion
Concluding Remarks
References
Application of the Strain Rate Intensity Factor to Modeling Material Behavior in the Vicinity of Frictional Interfaces
Introduction
Strain Rate Intensity Factor
Basic Relations for Plane Strain Deformation
Rigid Perfectly Plastic Material
Double Shearing Model
Thickness of the Layer of Intensive Plastic Deformation
General Approach
Plane Strain Drawing/Extrusion
Ductile Fracture near Frictional Interfaces
General Approach
Plane Strain Drawing/Extrusion
Computational Aspects
Conclusions
References
Unilateral Problems for Laminates: A Variational Formulation with Constraints in Dual Spaces
Introduction
Unilateral Problems for a Laminated Plate
Laminated Models by Using Constraints in Dual Spaces: A Single-Layer Approach
First-Order Shear-Deformable Laminated-Plate Model
Lo–Christensen–Wu-Type Laminate Model: An Outline
Concluding Remarks
References
Contact Modelling in Structural Simulation – Approaches, Problems and Chances
Contact in Structural Problems
Boundary Conditions or Contact?
Contact as Part of Manufacturing Processes
Numerical Contact Studies
Terms and Definitions
Real Contact
Numerical Contact
Parameters Used in Contact Studies
Some Problems and Some Proposals
Element Types and Contact Definition
Contact State
Friction
Time History Integration
Time Integration Schemes
Reliability of Codes
Scatter and Robustness
Scatter in Contact Studies
Parameter Sensitivity
Conclusions
References