Finite Elasticity and Viscoelasticity: A Course in the Nonlinear Mechanics of SolidsThis 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. |
Contents
Tensor calculus | 1 |
Mechanics of continua | 54 |
Constitutive equations in finite elasticity | 88 |
Boundary problems in finite elasticity | 126 |
Variational principles in elasticity | 207 |
Constitutive models in finite viscoelasticity | 228 |
Boundary problems in finite viscoelasticity | 326 |
413 | |
429 | |
Other editions - View all
Common terms and phrases
According to Eq accretion actual configuration arbitrary calculate Cauchy stress tensor constitutive equation constitutive models correspond to experimental covariant derivative curve cylinder Definition deformation gradient deformation tensor Derive the following differential dimensionless displacement field displacement vector equality Exercise expression into Eq extension ratio Finger tensor finite elasticity finite strains follows from Eqs formula implies incompressible inequality infinitesimal strains initial configuration instant integral introduce Lagrangian coordinates Laplace transform Large circles correspond linear loads material parameters modulus natural configuration nonlinear principal invariants principle problem Proposition Qo(t radius-vector relaxation kernel relaxation measure right-hand side side of Eq simple shear smooth smooth function solutions Stokes formula strain energy density strain tensor subsection substitute expression Substitution of expression tensor Q transform unit tensor versus viscoelastic medium yields Young's modulus θεί ди მა მე მი