This volume is dedicated to Jacob Aboudi, a ?ne scientist who has made seminal c- tributions in applied mechanics. The papers presented here re?ect the appreciation of many of Jacob s colleagues. A publication list f- lowing this introduction provides an indi- tion of his distinguished academic career, c- rently in its ?fth decade, and the breadth of hisknowledge. His papersconsistentlydem- strate originality, innovation and diligence. This list uncovers the methodical work of a dedicated researcher whose achievements established him as a leading authority in the area of mathematical modeling of the beh- ior of heterogeneous materials, the area which became known as homogenization theory. Starting in 1981, Jacob established a micromechanical model known as the Method of Cells (MOC) which evolved into the Generalized Method of Cells (GMC) that predicts the macroscopic response of composite materials as a function of the pr- erties, volume fractions, shapes, and constitutive behavior of its constituents. The versatility of the model has been demonstrated to effectively incorporate various types of constituent material behavior (i. e., both coupled and uncoupled mecha- cal, thermal, electrical and magnetic effects). As a result of its potential in providing an ef?cient tool for the emerging ?eld of multiscale analysis, the method gained increasing attention and became a subject for further research."

This volume is dedicated to Jacob Aboudi, a ?ne scientist who has made seminal c- tributions in applied mechanics. The papers presented here re?ect the appreciation of many of Jacob's colleagues. A publication list f- lowing this introduction provides an indi- tion of his distinguished academic career, c- rently in its ?fth decade, and the breadth of hisknowledge. His papersconsistentlydem- strate originality, innovation and diligence. This list uncovers the methodical work of a dedicated researcher whose achievements established him as a leading authority in the area of mathematical modeling of the beh- ior of heterogeneous materials, the area which became known as homogenization theory. Starting in 1981, Jacob established a micromechanical model known as the Method of Cells (MOC) which evolved into the Generalized Method of Cells (GMC) that predicts the macroscopic response of composite materials as a function of the pr- erties, volume fractions, shapes, and constitutive behavior of its constituents. The versatility of the model has been demonstrated to effectively incorporate various types of constituent material behavior (i. e. , both coupled and uncoupled mecha- cal, thermal, electrical and magnetic effects). As a result of its potential in providing an ef?cient tool for the emerging ?eld of multiscale analysis, the method gained increasing attention and became a subject for further research.

Part I of this SpringerBrief presents the problem of a crack between two dissimilar isotropic materials and describes the mathematical background. A fracture criterion is discussed and Methods for calculating fracture parameters such as stress intensity factors using the finite element method and three post-processors are considered. Actual test data and both deterministic and statistical failure curves are presented.In Part II of the book, similar descriptions are given for delaminations in composite laminates. The mathematical treatment of this type of damage including the first term of the asymptotic expansion of the stress and displacement fields is considered. Numerical post-processors for determining stress intensity factors for these cases are reviewed. Two examples of specific laminates are presented: one with a failure curve and the other with a failure surface. Finally, beam specimens used for testing such failures are discussed.