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.
1. Fundamentals of Plane Elasticity.
2. Fundamentals of Elasticity in View of Homogenization Theory.
3. Two-dimensional Griffith Crack.
4. The Elliptic Crack Model in Plane Strains.
5. Griffith Crack in 3D.
6. Ellipsoidal Crack Model: the Eshel by Approach.
7. Energy Release Rate and Conditions for Crack Propagation.
8. Fundamentals of Continuum Micromechanics.
9. Homogenization of Materials Containing Griffith Cracks.
10. Eshel by-based Estimates of Strain Concentration and Stiffness.
11. Stress-based Estimates of Stress Concentration and Compliance.
13. Micromechanics-based Damage Constitutive Law and Application.
Luc Dormieux is Professor at Ecole Nationale des Ponts et Chaussées (Laboratoire NAVIER) in Marne-la-Vallée, France.
Djimédo Kondo is Professor at Sorbonne University (UPMC, Institut D'Alembert) in Paris, France
Table of Contents
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