This book covers a wide range of topics in localized damage with particular emphasis on recent advances in computational methods. It forms the proceedings of the Fourth International Conference on Localized Damage: Computer-Aided Assessment and Control, which took place on 3-5 June 1996, in Fukuoka, Japan. The Localized Damage conferences are now well-established as the preeminent forum for presentation of the research on advanced computational methods to problems in fracture, fatigue and damage mechanics.

This book resulted from a series of lecture notes presented in CISM, Udine in July 7 -11, 2008. The papers inform about recent advances in continuum damage mechanics for both metals and metal matrix composites as well as the micromechanics of localization in inelastic solids. Also many of the different constitutive damage models that have recently appeared in the literature and the different approaches to this topic are presented, making them easily accessible to researchers and graduate students in civil engineering, mechanical engineering, engineering mechanics, aerospace engineering, and material science.

The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.