Nonlinear Solid Mechanics

This book offers a recipe for constructing the numerical models for representing the complex nonlinear behavior of structures and their components, represented as deformable solid bodies. Its appeal extends to those interested in linear problems of mechanics.

This volume provides insight into modelling and ultimate limit computation of complex structures, with their components represented by solid deformable bodies. The book examines practically all the important questions of current interests for nonlinear solid mechanics: plasticity, damage, large deformations, contact, dynamics, instability, localisation and failure, discrete models, multi-scale, multi-physics and parallel computing, with special attention given to finite element solution methods. The presentation of topics is structured around different aspects of typical boundary value problems in nonlinear solid mechanics, which provides the best pedagogical approach while keeping the book size reasonable despite its very broad contents. Other strong points are the exhaustive treatment of subjects, with each question studied from different angles of mechanics, mathematics and computation, as well as a successful merger of scientific cultures and heritage from Europe and the USA. The book content and style is also the product of rich international experience in teaching Master and Doctoral level courses, as well as the courses organized for participants from industry (IPSI courses) in France, and similar courses in Germany and Italy. Every effort was made to make the contents accessible to non-specialists and users of computer programs.

The original French edition published by Hermes Science - Lavoisier Paris in 2006 was nominated for the Roberval Award for University Textbooks in French.

Provides the readers with well-balanced developments regarding both the theoretical formulations and finite element based numerical solution of nonlinear problems This extensive-coverage role is also the main originality of this book with respect to the books that consider the theoretical formulation of nonlinear problems in solid mechanics with no discussion of the numerical implementation issues, and those that consider only the finite element method With such a well-balanced presentation of both theoretical formulation and numerical implementation, this book will also have a place in English speaking research community in computational solid mechanics, despite a number of available books exploring different aspects of this field Completeness in covering all the main topics of interest for nonlinear solid mechanics

Inhalt
Boundary value problem in linear and nonlinear elasticity.- Inelastic behavior at small strains.- Large displacements and deformations.- Changing boundary conditions: contact problems.- Dynamics and time-integration schemes.- Thermodynamics and solution methods for coupled problems.- Geometric and material instabilities.- Multi-scale modelling of inelastic behavior.