Description
This book is about elasticity and how it can be applied to various fields of physics. It covers all the necessary concepts of continuum mechanics, deformation theory, and differential geometry, and then goes on to discuss material inhomogeneities in detail. This book will be a great help to those who are new to elasticity, and will also be useful to those who are already familiar with the subject, as it provides a more in-depth look at the theory. The book also provides methods for evaluating characteristic parameters, which are useful in various branches of physics.
Self contained, this book presents a thorough introduction to the complementary notions of physical forces and material (or configurational) forces. All the required elements of continuum mechanics, deformation theory and differential geometry are also covered. This book will be a great help to many, whilst revealing to others a rather new facet of continuum mechanics in general, and elasticity in particular. An organized exposition of continuum mechanics on the material manifold is given which allows for the consideration of material inhomogeneities in their most appropriate framework. In such a frame the nonlinear elasticity of anisotropic inhomogenous materials appears to be a true field theory. Extensions to the cases of electroelasticity and magnetelasticity are then straightforward. In addition, this original approach provides systematic computational means for the evaluation of characteristic parameters which are useful in various branches of applied mechanics and mathematical physics. This is the case for path-independent integrals and energy-release rates in brittle fracture, the influence of electromagnetic fields on fracture criteria (such as in ceramics), the notion of momentum of electromagnetic fields in matter in optics, and the perturbation of solitons propagating in elastic dispersive systems.
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