Finite Elasticity and Viscoelasticity: A Course in the Nonlinear Mechanics of Solids
This book provides a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory. The objective is to expose the most intriguing aspects of elasticity and viscoelasticity with finite strains in such a way as to ensure mathematical correctness, on the one hand, and to demonstrate a wide spectrum of physical phenomena typical only of nonlinear mechanics, on the other.A novel aspect of the book is that it contains a number of examples illustrating surprising behaviour in materials with finite strains, as well as comparisons between theoretical predictions and experimental data for rubber-like polymers and elastomers.The book aims to fill a gap between mathematicians specializing in nonlinear continuum mechanics, and physicists and engineers who apply the methods of solid mechanics to a wide range of problems in civil and mechanical engineering, materials science, and polymer physics. The book has been developed from a graduate course in applied mathematics which the author has given for a number of years.
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Mechanics of continua
Constitutive equations in finite elasticity
Boundary problems in finite elasticity
Variational principles in elasticity
Constitutive models in finite viscoelasticity
Boundary problems in finite viscoelasticity
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According actual configuration aging applied arbitrary assume behavior body boundary calculate called Cauchy characteristic Check circles correspond coincides condition consider constant constitutive equation continuous coordinates creep curve cylinder Definition deformation demonstrate depends derive described determined differential discuss displacement domain elastic element employed equality example Exercise existence experimental data field Finger follows from Eqs forces formula function growing implies inequality initial instant integral introduce linear loads material means mechanics medium motion natural nonlinear objective obtain operator positive presented principal invariants principle problem Proof Proposition Prove reference relaxation replace respect result satisfies shear side similar smooth solid solutions strain energy density strain tensor stress tensor Substitution of expression surface tangent vectors tensor ô theory transform transition unit vector versus viscoelastic viscoelastic medium waves yields