# Multiple Crack Problems in Elasticity

## Multiple Crack Problems in Elasticity

The authors investigate various integral equations for multiple crack problems in plane elasticity. Formulation of the problems is based on relevant elementary solutions in which the complex variable function method is used.

# Stress Analysis in Elastic Solids with Many Cracks

## Stress Analysis in Elastic Solids with Many Cracks

To develop a new method of analysis of many cracks problems in elastic solids that is sufficiently simple and applicable to both two- and three dimensional configurations, and to apply it to a number of practically important problems involving multiple cracking. Such methods has been developed and its accuracy was verified by checking the results against the solutions available in the literature. The new method has been applied to solving a number of problems. Keywords: Stress analysis, Elastic solids, Crack problems, Multiple cracking.

# Boundary Integral Equations in Elasticity Theory

## Boundary Integral Equations in Elasticity Theory

by the author to the English edition The book aims to present a powerful new tool of computational mechanics, complex variable boundary integral equations (CV-BIE). The book is conceived as a continuation of the classical monograph by N. I. Muskhelishvili into the computer era. Two years have passed since the Russian edition of the present book. We have seen growing interest in numerical simulation of media with internal structure, and have evidence of the potential of the new methods. The evidence was especially clear in problems relating to multiple grains, blocks, cracks, inclusions and voids. This prompted me, when preparing the English edition, to place more emphasis on such topics. The other change was inspired by Professor Graham Gladwell. It was he who urged me to abridge the chain of formulae and to increase the number of examples. Now the reader will find more examples showing the potential and advantages of the analysis. The first chapter of the book contains a simple exposition of the theory of real variable potentials, including the hypersingular potential and the hypersingular equations. This makes up for the absence of such exposition in current textbooks, and reveals important links between the real variable BIE and the complex variable counterparts. The chapter may also help readers who are learning or lecturing on the boundary element method.

# Advances in Conservation Laws and Energy Release Rates

## Advances in Conservation Laws and Energy Release Rates

This book summarizes two significant tendencies for application of conservation laws and energy release rates. The first is to establish a bridge between some famous invariant integrals and microcrack damage descriptions. The second is the direct extension from the understandings established in Fracture Mechanics for conventional materials to those for functional materials. In the first point it discusses the vanishing nature for both components of the Jk-integral vector when the closed contour encloses all discontinuities completely. Both mathematical manipulations and numerical examinations are given. Thus the M-integral and the L-integral are independent of coordinate shifts and, more significantly, the M-integral presents a new description for the damage level of a microcracking brittle solid. In the second point it discusses the direct extension from the basic understandings established in Linear Elastic Fracture Mechanics to those for functional materials, e.g., piezoelectric ceramics. Owing to the mechanical and electric coupling, some new insights of energy release rates are discussed in detail.