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.
General
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