This monograph provides a systematic study of asymptotic models of continuum mechanics for composite structures, which are either dilute (for example, two-phase composite structures with small inclusions) or densely packed (in this case inclusions may be close to touching). It is based on the results of recent research and includes a comprehensive analysis of dipole and multipole fields associated with defects in solids. The text covers static problems of elasticity in dilute composites as well as spectral problems. Applications of the mathematical models included in the book are in damage...

This volume illustrates approaches to analyzing problems in fracture mechanics. It examines the application of asymptotic analysis to strength evaluation in models of elastic structures and geophysics. In addition, it provides analytical techniques for studying singularly perturbed problems.

This volume contains the Proceedings of the IUTAM Symposium held in Liverpool in 2002. It includes the articles presenting the results of recent work in mathematical modelling that covers the following areas of continuum mechanics and theoretical physics: Perturbation problems for partial differential equations and their applications in mechanics;Analysis of singular fields;Homogenisation theory in models of composite structures;Mathematical models of cracks in solids;Wave propagation, scattering;Models of photonic and phononic band gap composite structures;Advanced numerical techniques.