Fracture Mechanics [electronic resource] : Inverse Problems and Solutions / by H. D. Bui.

Deformation and Fracture -- Energetic Aspects of Fracture -- Solutions of Cracks Problems -- Thermodynamics of Crack Propagation -- Dynamic Fracture Mechanics -- Three-Dimensional Crack Problems -- Non Linear Fracture Mechanics -- The Fluid-Filled Crack -- Crack Detection by Scattering of Waves -- Tomographic Evaluation of Materials -- The Reciprocity Gap Functional for Crack Detection -- Methods of Solution to Inverse Problems.

This book is an attempt to present, in a unified manner, different topics of Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems. Moreover, a series of new subjects is presented in a straightforward manner, accessible to under-graduate students. These new topics take into consideration the thermodynamics of continuous media, including thermal and dynamical aspects. In addition, the book introduces the notion of duality or symmetry in Solids Mechanics. The loss of symmetry is exploited to provide a unique and powerful tool, called the reciprocity gap functional introduced by the author's groups, to solve explicitly some important inverse problems arising in crack determination as well as in the earthquake inverse problem. With its emphasis, initially on physical or experimental backgrounds, and then on analysis and theoretical results, rather than on numerical computations, this monograph is intended to be used by students and researchers in solids mechanics, mechanical engineering and applied mathematics.