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Finite Elasticity and Viscoelasticity: A Course in the Nonlinear Mechanics of Solids
TLDR
In this article, the authors provide a systematic and self-consistent introduction to nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory, and 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.Abstract:
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.read more
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Mathematical Models in Contact Mechanics
Mircea Sofonea,Andaluzia Matei +1 more
TL;DR: In this paper, a complete introduction to the theory of variational inequalities with emphasis on contact mechanics is provided, including the modelling and variational analysis of specific frictional contact problems with elastic, viscoelastic and viscoplastic materials.
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A micro–macro approach to rubber-like materials. Part II: The micro-sphere model of finite rubber viscoelasticity
Christian Miehe,Serdar Göktepe +1 more
TL;DR: In this paper, the authors extended the non-affine micro-sphere model towards the description of time-dependent viscoelastic effects, and proposed a micro-kinematic model for the viscous overstress.
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How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity.
L. Angela Mihai,Alain Goriely +1 more
TL;DR: Several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests are reviewed.
Journal ArticleDOI
Deflections of a rubber membrane
TL;DR: In this paper, the authors deal with the problem of the transverse deflection of a natural rubber membrane that is fixed along a circular boundary and provide a comparison of the experimental results for the membrane deflections with results derived from computational simulations.
Journal ArticleDOI
Implications and Constraints of Time-Independent Poisson Ratios in Linear Isotropic and Anisotropic Viscoelasticity
TL;DR: In this article, it is proven that time-independent viscoelastic Poisson ratios can only exist under separation of variable solutions, which severely limits the class of applicable problems to quasi-static ones with incompressible homogeneous materials and non-moving boundaries under separable stress or displacement boundary conditions without any thermal expansions.
Related Papers (5)
Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity
Weimin Han,Mircea Sofonea +1 more
Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods
Noboru Kikuchi,J. T. Oden +1 more