(Mechanical Engineering and Solid Mechanics: Micromechanics Set) 1st Edition
by Luc Dormieux (Author), Djimedo Kondo (Author)
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.
