The book considers the theoretical basis of nonlinear computational mechanics of solids. There are a number of excellent and widely used commercially available software packages for simulating the response of structural and mechanical systems in the nonlinear realm. Nevertheless, the justification and verification of results from large-scale simulations have become more critical than the modeling and analysis itself. Engineering practitioners need a thorough understanding of the underlying fundamentals on which these computational tools are based in order to utilize them most effectively in their work. This book is intended to provide much of that necessary background in an accessible form. The book can serve as a reference for engineers, analysts and software developers in practice, as well as a graduate course text. It is assumed that the reader is familiar with the basics of linear finite element analysis.
The book contains 12 chapters. An overview of linear and nonlinear mechanics and some simple examples of nonlinear behavior are presented in Chapter 1. This is followed by three chapters (2–4) discussing the fundamentals of nonlinear continuum mechanics, including the treatment of large displacements and strains. Chapters 5 to 7 describe constitutive laws governing stress-strain relations. The nonlinear finite elements are discussed in Chapter 8. The treatment of large rotations is given in Chapter 9. Formulations for structural elements, including beams, plates and shells are covered in Chapter 10, before the discussion of incremental-iterative numerical methods for computational simulation in Chapter 11. Some computing methods inspired by problems in biology are discussed in the last chapter.