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E-raamat: Generalized Continua - from the Theory to Engineering Applications

Edited by Victor A. Eremeyev, Edited by Holm Altenbach

Formaat: PDF+DRM
Sari: CISM International Centre for Mechanical Sciences 541
Ilmumisaeg: 17-Oct-2012
Kirjastus: Springer Verlag GmbH
Keel: eng
ISBN-13: 9783709113714

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Formaat: PDF+DRM
Sari: CISM International Centre for Mechanical Sciences 541
Ilmumisaeg: 17-Oct-2012
Kirjastus: Springer Verlag GmbH
Keel: eng
ISBN-13: 9783709113714

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On the roots of continuum mechanics in differential geometry -- a review.- Cosserat media.- Cosserat-type shells.- Cosserat-type rods.- Micromorphic media.- Electromagnetism and generalized continua.- Computational methods for generalized continua.The need of generalized continua models is coming from practice. Complex material behavior sometimes cannot be presented by the classical Cauchy continua. At present the attention of the scientists in this field is focused on the most recent research items • new models, • application of well-known models to new problems, • micro-macro aspects, • computational effort, and • possibilities to identify the constitutive equations The new research directions are discussed in this volume - from the point of view of modeling and simulation, identification, and numerical methods.

This book presents new directions in research on generalized continua, from the point of view of modeling and simulation, identification and numerical methods. Covers micro-macro aspects, computational effort and much more.

Arvustused

From the reviews:

The book under review gathers the lecture notes of the Corse 541 held at CISM in Udine, Italy. The editors and organizers of the course have selected a very important topic which deserves attention and investment of young intellectual forces. The overall result is a textbook of very high quality and the volume will surely become a very important source of information and knowledge, as, together with basic concepts and ideas, it includes some interesting original results. (Francesco dellIsola, Mathematical Reviews, November, 2013)

On the Roots of Continuum Mechanics in Differential Geometry - A Review -

(64)

P. Steinmann

1 Introduction

(4)

2 Differential Geometry

(31)

2.1 Overview

(1)

2.2 Manifolds

(3)

2.3 Connection

(3)

2.4 Parallel Transport

(1)

2.5 Torsion

(5)

2.6 Curvature

(8)

2.7 Metric

(6)

2.8 Metric Curvature

(4)

3 Continuum Mechanics

(25)

3.1 Kinematics

(4)

3.2 Distortion

(1)

3.3 Integrability

(3)

3.4 Elasticity

(3)

3.5 Elastoplasticity

(14)

4 Summary

(4)

Bibliography

(4)

Cosserat Media

(66)

H. Altenbach

V.A. Eremeyev

1 Introduction

(13)

1.1 Elements of Rigid Body Dynamics

(7)

2.1 Elements of Mechanics of Elastic Rods

(4)

2 Kinematics of Cosserat Continuum

(2)

3 Forces and Couples, Stress and Couple Stress Tensors in Micropolar Continua

(13)

3.1 Forces and Couples

(2)

3.2 Eulers Laws of Motion

(1)

3.3 Stress Tensor and Couple Stress Tensor

(4)

3.4 Principal Stresses in Micropolar Continua

(2)

3.5 Equations of Motion

(1)

3.6 Boundary-Value Problems

(3)

4 Constitutive Equations of Cosserat Continua

(38)

4.1 General Principles Restricting the Constitutive Equations

(2)

4.2 Natural Lagrangian Strain Measures of Cosserat Continuum

(6)

4.3 Vectorial Parameterizations of Strain Measures

101

(1)

4.4 Kinetic Constitutive Equations

102

(2)

4.5 Material Symmetry Group

104

(4)

4.6 Non-Linear Micropolar Isotropic Solids

108

(2)

4.7 Physically Linear Micropolar Solids

110

(1)

4.8 Linear Micropolar Isotropic Solids

111

(2)

4.9 Constraints

113

(2)

4.10 Constitutive Inequalities

115

(4)

4.11 Micropolar Fluid

119

(1)

4.12 Some Sources of Cosserat's Constitutive Equations

120

(11)

Bibliography

122

(9)

Cosserat-Type Shells

131

(48)

H. Altenbach

Victor A. Eremeyev

1 Introduction

131

(6)

2 Cosserat Surface

137

(3)

2.1 Kinematics

137

(1)

2.2 Strain Energy Density of an Elastic Cosserat Surface

138

(1)

2.3 Principle of Virtual Work and the Equilibrium Conditions

139

(1)

3 Micropolar Shells

140

(18)

3.1 Kinematics

141

(2)

3.2 Principle of Virtual Work and Boundary-Value Problems

143

(2)

3.3 On the Constitutive Equations

145

(1)

3.4 Compatibility Conditions

146

(1)

3.5 Variational Statements

147

(2)

3.6 Linear Theory of Micropolar Shells

149

(3)

3.7 Constitutive Restrictions for Micropolar Shells

152

(3)

3.8 Strong Ellipticity Condition and Acceleration Waves

155

(2)

3.9 Principle Peculiarities of the Micropolar Shell Theory

157

(1)

4 Theories of Shells and Plates by Reduction of the Three-Dimensional Micropolar Continuum

158

(5)

4.1 Basic Equations of Three-Dimensional Linear Cosserat Continuum

158

(2)

4.2 Transition to the Two-Dimensional Equilibrium Equations: Eringen's Approach

160

(2)

4.3 Transition to the Two-Dimensional Equilibrium Equations: Other Reduction Procedures

162

(1)

5 Conclusions and Discussion

163

(16)

Bibliography

165

(14)

Cosserat-Type Rods

179

(70)

H. Altenbach

M. Birsan

Victor A. Eremeyev

1 Introduction

179

(2)

2 Kinematical Model of Directed Curves

181

(3)

3 Governing Equations of the Non-Linear Theory

184

(5)

4 Constitutive Equations for Thermoelastic Porous Rods

189

(3)

4.1 Free Energy Function

190

(1)

4.2 Structure of Constitutive Tensors

190

(2)

5 Linearized Equations of Directed Rods

192

(8)

5.1 Boundary-Initial-Value Problems

193

(1)

5.2 Uniqueness of Solution

194

(2)

5.3 Existence Results in the Dynamical Theory

196

(4)

6 Statical Theory for Rods

200

(8)

6.1 Inequalities of Korn-Type for Cosserat Rods

201

(3)

6.2 Existence of Solution

204

(2)

6.3 Analysis of Pure Traction Problems

206

(2)

7 Equations for Straight Rods

208

(5)

7.1 Decoupling of the Problem

209

(1)

7.2 Solution of Simple Problems

210

(3)

8 Derivation of Rods Equations from the Three-Dimensional Equations

213

(3)

9 Identification of Constitutive Coefficients for Thermo-Elastic Porous Orthotropic Rods

216

(9)

9.1 Bending and Extension of Orthotropic Rods

217

(1)

9.2 Torsion of Orthotropic Rods

218

(1)

9.3 Shear Vibrations of an Orthotropic Rod

219

(2)

9.4 Problem of Thermal Deformation

221

(1)

9.5 Extension of Porous Thermo-Elastic Rods

222

(3)

10 Extended Thermodynamic Theory for Rods with Two Temperature Fields

225

(7)

10.1 Basic Laws

225

(2)

10.2 Constitutive Equations

227

(5)

11 Non-Homogeneous Rods and Composite Beams Analyzed by the Direct Approach

232

(12)

11.1 Constitutive Coefficients for Non-Homogeneous Rods

235

(5)

11.2 Effective Stiffness Properties of Composite Beams

240

(4)

12 Conclusions

244

(5)

Bibliography

244

(5)

Micromorphic Media

249

(52)

S. Forest

1 Introduction

249

(2)

1.1 Scope of this chapter

249

(1)

1.2 Notations

250

(1)

2 Micromorphic Continua

251

(7)

2.1 Kinematics of Micromorphic Media

251

(2)

2.2 Principle of Virtual Power

253

(2)

2.3 Elastoviscoplasticity of Micromorphic Media

255

(3)

3 From a Heterogeneous Cauchy Material to a Homogeneous Equivalent Micromorphic Medium

258

(16)

3.1 Definition of the Micromorphic Degrees of Freedom

260

(2)

3.2 Higher Order Strain Measures

262

(1)

3.3 Polynomial Ansatz

263

(2)

3.4 Identification of Generalised Effective Elastic Moduli

265

(8)

3.5 Validation of the Extended Homogenisation Method

273

(1)

4 Homogenization of Micromorphic Media

274

(27)

4.1 Multiscale Asymptotic Expansion Method

274

(16)

4.2 Application to Polycrystalline Plasticity

290

(11)

Bibliography

296

(5)

Electromagnetism and Generalized Continua

301

(60)

G.A. Maugin

1 Introduction and Historical Perspective

301

(5)

2 Electromagnetic Sources in Galilean Invariant Continuum Physics

306

(6)

2.1 Maxwell's Equations

306

(3)

2.2 Ponderomotive Force and Couple in a Continuum

309

(3)

3 Deformable Magnetized Bodies with Magnetic Microstructure

312

(14)

3.1 Model of Interactions

312

(3)

3.2 Statement of Global Balance Laws

315

(4)

3.3 Approach via the Principle of Virtual Power

319

(2)

3.4 Hamiltonian Variational Formulation

321

(2)

3.5 Ferrimagnetic and Antiferromagnetic Materials

323

(2)

3.6 Analogy with Cosserat Continua

325

(1)

3.7 Reduction to a Model without Microstructure (Paramagnetic and Soft-Ferromagnetic Bodies)

325

(1)

4 Deformable Dielectrics with Electric-Polarization Microstructure

326

(6)

4.1 Model of Interactions

326

(2)

4.2 Approach via the Principle of Virtual Power

328

(1)

4.3 Hamiltonian Variational Principle

329

(1)

4.4 Antiferroelectric Materials

330

(1)

4.5 Analogy with Cosserat Continua

330

(1)

4.6 Reduction to a Model without Microstructure

331

(1)

4.7 Remark on Electric Quadrupoles

331

(1)

5 Dynamical Couplings between Deformation and Electromagnetic Microstructure

332

(13)

5.1 Introductory Note: Resonance Coupling between Wave Modes

332

(3)

5.2 The Case of Magnetoelasticity in Ferromagnets

335

(8)

5.3 The Case of Electroelasticity in Ferroelectrics

343

(2)

6 Configurational Forces in Presence of an Electromagnetic Microstructure

345

(8)

6.1 Definition

345

(1)

6.2 Reminder of a Purely Mechanical Case

346

(3)

6.3 The Ferroelectric Case

349

(2)

6.4 The Ferromagnetic Case

351

(2)

7 Conclusive Remark

353

(8)

A Reminder of Basic Equations of Generalized Mechanical Continua

353

(2)

Bibliography

355

(6)

Computational Methods for Generalised Continua

361

R. deBorst

1 Introduction

361

(1)

2 Isotropic Elasticity-Based Damage

362

(4)

3 Stability, Ellipticity, and Mesh Sensitivity

366

(6)

3.1 Stability and Ellipticity

366

(4)

3.2 Mesh Sensitivity

370

(2)

4 Non-Local and Gradient Damage Models

372

(5)

4.1 Non-local Damage Models

372

(1)

4.2 Gradient Damage Models

373

(4)

5 Cosserat Elasto-Plasticity

377

(6)

5.1 Cosserat Elasticity

377

(2)

5.2 Cosserat Plasticity

379

(3)

5.3 A Return-Mapping Algorithm

382

(1)

5.4 Consistent Tangent Operator

383

(1)

6 Non-Local and Gradient Plasticity

383

6.1 Non-Local Plasticity

383

(2)

6.2 Gradient Plasticity

385

Bibliography

387

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Continuum mechanics - Mathematical models

E-raamat: Generalized Continua - from the Theory to Engineering Applications

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