计算接触力学 扫描版

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中文名: 计算接触力学

原名: Computational Contact Mechanics

作者: Peter Wriggers

图书分类: 科技

资源格式: PDF

版本: 扫描版

出版社: Peter Wriggers

书号: ISBN-10 3-540-32608

发行时间: 2006年01月01日

地区: 美国

语言: 英文

简介: 

目录:

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Introduction to Contact Mechanics . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 Contact in a Mass Spring System. . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.1 General formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.2 Lagrange multiplier method . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.3 Penalty method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Finite Element Analysis of the Contact of Two Bars . . . . . . . . . 18

2.3 Thermo-mechanical Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Continuum Solid Mechanics and Weak Forms. . . . . . . . . . . . . . 31

3.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1.1 Motion and deformation gradient . . . . . . . . . . . . . . . . . . . . 31

3.1.2 Strain measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.1.3 Transformation of vectors and tensors . . . . . . . . . . . . . . . . 36

3.1.4 Time derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2 Balance Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2.1 Balance of mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2.2 Local balance of momentum and moments of momentum 38

3.2.3 First law of thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2.4 Transformation to the initial configuration, different

stress tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3 Weak Form of Balance of Momentum, Variational Principles . . 41

3.3.1 Weak form of balance of momentum in the initial

configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.3.2 Spatial form of the weak formulation . . . . . . . . . . . . . . . . . 42

3.3.3 Minimum of total potential energy . . . . . . . . . . . . . . . . . . . 43

3.4 Constitutive Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4.1 Hyperelastic response function . . . . . . . . . . . . . . . . . . . . . . 44

3.5 Linearizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.5.1 Linearization of kinematical quantities . . . . . . . . . . . . . . . 51

3.5.2 Linearization of constitutive equations . . . . . . . . . . . . . . . 52

3.5.3 Linearization of the weak form . . . . . . . . . . . . . . . . . . . . . . 53

3.5.4 Linearization of a deformation dependent load . . . . . . . . 55

4 Contact Kinematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.1 Normal Contact of Three-dimensional Bodies . . . . . . . . . . . . . . . 58

4.2 Tangential Contact of Three-dimensional Bodies . . . . . . . . . . . . . 62

4.2.1 Stick condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.2.2 Slip condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.3 Variation of the Normal and Tangential Gap . . . . . . . . . . . . . . . . 66

4.3.1 Variation of normal gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3.2 Variation of tangential gap . . . . . . . . . . . . . . . . . . . . . . . . . 67

5 Constitutive Equations for Contact Interfaces . . . . . . . . . . . . . 69

5.1 Normal Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.1.1 Constraint formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.1.2 Constitutive equations for normal contact . . . . . . . . . . . . 72

5.2 Tangential Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.2.1 Stick as a constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.2.2 Coulomb law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.2.3 Regularization of the Coulomb law . . . . . . . . . . . . . . . . . . 79

5.2.4 Elasto-plastic analogy for friction . . . . . . . . . . . . . . . . . . . . 80

5.2.5 Friction laws for metal forming . . . . . . . . . . . . . . . . . . . . . . 86

5.2.6 Friction laws for rubber and polymers . . . . . . . . . . . . . . . . 88

5.2.7 Friction laws for concrete structures on soil . . . . . . . . . . . 90

5.2.8 Friction laws from computational homogenization

procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.3 Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.4 Adhesion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.5 Decohesion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.6 Wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.7 Fractal Contact Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6 Contact Boundary Value Problem and Weak Form . . . . . . . . 109

6.1 Frictionless Contact in Linear Elasticity . . . . . . . . . . . . . . . . . . . . 109

6.2 Frictionless Contact in Finite Deformations Problems . . . . . . . . 113

6.3 Treatment of Contact Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.3.1 Lagrange multiplier method . . . . . . . . . . . . . . . . . . . . . . . . 117

6.3.2 Penalty method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.3.3 Direct constraint elimination . . . . . . . . . . . . . . . . . . . . . . . . 120

6.3.4 Constitutive equation in the interface . . . . . . . . . . . . . . . . 121

6.3.5 Nitsche method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Contact mechanics has its application in many engineering problems. No one

can walk without frictional contact, and no car would move for the same reason.

Hence contact mechanics has, from an engineering point of view, a long

history, beginning in ancient Egypt with the movement of large stone blocks,

over first experimental contributions from leading scientists like Leonardo

da Vinci and Coulomb, to today’s computational methods. In the past contact

conditions were often modelled in engineering analysis by more simple

boundary conditions since analytical solutions were not present for real world

applications. In such cases, one investigated contact as a local problem using

the stress and strain fields stemming from the analysis which was performed

for the entire structure. With the rapidly increasing power of modern computers,

more and more numerical simulations in engineering can include contact

constraints directly, which make the problems nonlinear.

This book is an account of the modern theory of nonlinear continuum

mechanics and its application to contact problems, as well as of modern simulation

techniques for contact problems using the finite element method. The

latter includes a variety of discretization techniques for small and large deformation

contact. Algorithms play another prominent role when robust and efficient

techniques have to be designed for contact simulations. Finally, adaptive

methods based on error controlled finite element analysis and mesh adaption

techniques are of great interest for the reliable numerical solution of contact

problems. Nevertheless, all numerical models need a strong backup provided

by modern continuum mechanics and its constitutive theory, which is applied

in this book to the development of interface laws for normal and frictional

contact.

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