Micromechanics of fracture and damage / Luc Dormieux, Djimedo Kondo.

Format:

Book

Author/Creator:

Dormieux, Luc, author.

Kondo, Djimédo, author.

Series:

Mechanical engineering and solid mechanics series.

Mechanical Engineering and Solid Mechanics Series

Language:

English

Subjects (All):

Micromechanics.

Fracture mechanics.

Physical Description:

1 online resource (251 p.)

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : iSTE : Wiley, 2016.

Summary:

This book deals with the mechanics and physics of fractures at various scales. Based on advanced continuum mechanics of heterogeneous media, it develops a rigorous mathematical framework for single macrocrack problems as well as for the effective properties of microcracked materials. In both cases, two geometrical models of cracks are examined and discussed: the idealized representation of the crack as two parallel faces (the Griffith crack model), and the representation of a crack as a flat elliptic or ellipsoidal cavity (the Eshelby inhomogeneity problem). The book is composed of two parts: * The first part deals with solutions to 2D and 3D problems involving a single crack in linear elasticity. Elementary solutions of cracks problems in the different modes are fully worked. Various mathematical techniques are presented, including Neuber-Papkovitch displacement potentials, complex analysis with conformal mapping and Eshelby-based solutions. * The second part is devoted to continuum micromechanics approaches of microcracked materials in relation to methods and results presented in the first part. Various estimates and bounds of the effective elastic properties are presented. They are considered for the formulation and application of continuum micromechanics-based damage models.

Contents:

2.2. Green's function in two-dimensional conditions2.3. Green's function in three-dimensional conditions; 2.4. Eshelby's problems in linear microelasticity; 2.5. Hill tensor for the elliptic inclusion; 2.6. Hill's tensor for the spheroidal inclusion; 2.7. Appendix; 2.8. Appendix: derivation of the χij; 3 Two-dimensional Griffith Crack; 3.1. Stress singularity at crack tip; 3.2. Solution to mode I problem; 3.3. Solution to mode II problem; 3.4. Appendix: Abel's integral equation; 3.5. Appendix: Neuber-Papkovitch displacement potentials; 4 The Elliptic Crack Model in Plane Strains

4.1. The infinite plane with elliptic hole4.2. Infinite plane with elliptic hole: the anisotropic case; 4.3. Eshelby approach; 5 Griffith Crack in 3D; 5.1. Griffith circular (penny-shaped) crack in mode I; 5.2. Griffith circular (penny-shaped) crack under shear loading; 6 Ellipsoidal Crack Model: the Eshelby Approach; 6.1. Mode I; 6.2. Mode II; 7 Energy Release Rate and Conditions for Crack Propagation; 7.1. Driving force of crack propagation; 7.2. Stress intensity factor and energy release rate; PART 2: Homogenization of Microcracked Materials; 8 Fundamentals of Continuum Micromechanics

8.1. Scale separation8.2. Inhomogeneity model for cracks; 8.3. General results on homogenization with Griffith cracks; 9 Homogenization of Materials Containing Griffith Cracks; 9.1. Dilute estimates in isotropic conditions; 9.2. A refined strain-based scheme; 9.3. Homogenization in plane strain conditions for anisotropic materials; 10 Eshelby-based Estimates of Strain Concentration and Stiffness; 10.1. Dilute estimate of the strain concentration tensor: general features; 10.2. The particular case of opened cracks; 10.3. Dilute estimates of the effective stiffness for opened cracks

10.4. Dilute estimates of the effective stiffness for closed cracks10.5. Mori-Tanaka estimate of the effective stiffness; 11 Stress-based Estimates of Stress Concentration and Compliance; 11.1. Dilute estimate of the stress concentration tensor; 11.2. Dilute estimates of the effective compliance for opened cracks; 11.3. Dilute estimate of the effective compliance for closed cracks; 11.4. Mori-Tanaka estimates of effective compliance; 11.5. Appendix: algebra for transverse isotropy and applications; 12 Bounds; 12.1. The energy definition of the homogenized stiffness

12.2. Hashin-Shtrikman's bound

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781119292180

1119292182

9781119292173

1119292174

OCLC:

945979063