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.
Author(s): Dormieux, Luc; Kondo, Djimédo
Series: Micromechanics set volume 1
Edition: 1
Publisher: Wiley-ISTE
Year: 2016
Language: English
Pages: 332
Tags: Механика;Механика деформируемого твердого тела;Механика разрушения;
Content: Elastic Solutions to Single Crack Problems. Fundamentals of Plane Elasticity / Luc Dormieux, Djimédo Kondo --
Fundamentals of Elasticity in View of Homogenization Theory / Luc Dormieux, Djimédo Kondo --
Two-Dimensional Griffith Crack / Luc Dormieux, Djimédo Kondo --
The Elliptic Crack Model in Plane Strains / Luc Dormieux, Djimédo Kondo --
Griffith Crack in 3D / Luc Dormieux, Djimédo Kondo --
Ellipsoidal Crack Model: The Eshelby Approach / Luc Dormieux, Djimédo Kondo --
Energy Release Rate and Conditions for Crack Propagation / Luc Dormieux, Djimédo Kondo --
Homogenization of Microcracked Materials. Fundamentals of Continuum Micromechanics / Luc Dormieux, Djimédo Kondo --
Homogenization of Materials Containing Griffith Cracks / Luc Dormieux, Djimédo Kondo --
Eshelby-Based Estimates of Strain Concentration and Stiffness / Luc Dormieux, Djimédo Kondo --
Stress-Based Estimates of Stress Concentration and Compliance / Luc Dormieux, Djimédo Kondo --
Bounds / Luc Dormieux, Djimédo Kondo --
Micromechanics-Based Damage Constitutive Law and Application / Luc Dormieux, Djimédo Kondo.
