Designing engineering components that make optimal use of materials requires consideration of the nonlinear static and dynamic characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, which requires an understanding of both the theoretical background and associated computer solution techniques. By presenting nonlinear solid mechanics, dynamic conservation laws and principles, and the associated finite element techniques together, the authors provide in this second book a unified treatment of the dynamic simulation of nonlinear solids. Alongside a number of worked examples and exercises are user instructions, program descriptions, and examples for two MATLAB computer implementations for which source codes are available online. While this book is designed to complement postgraduate courses, it is also relevant to those in industry requiring an appreciation of the way their computer simulation programs work.

A clear and complete postgraduate introduction to the theory and computer programming for the complex simulation of material behavior.

A unified treatment of nonlinear continuum analysis and finite element techniques.

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.

Many processes in materials science and engineering, such as the load deformation behaviour of certain structures, exhibit nonlinear characteristics. The computer simulation of such processes therefore requires a deep understanding of both the theoretical aspects of nonlinearity and the associated computational techniques. This book provides a complete set of exercises and solutions in the field of theoretical and computational nonlinear continuum mechanics and is the perfect companion to Nonlinear Continuum Mechanics for Finite Element Analysis, where the authors set out the theoretical foundations of the subject. It employs notation consistent with the theory book and serves as a great resource to students, researchers and those in industry interested in gaining confidence by practising through examples. Instructors of the subject will also find the book indispensable in aiding student learning.

A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in mastering the explicit finite element method and programming code without requiring extensive background knowledge of the general finite element. The authors present topics relating to the variational principle, numerical procedure, mechanical formulation, and fundamental achievements of the convergence theory. In addition, key topics and techniques are provided in four clearly organized sections: • Fundamentals explores a framework of the explicit finite element method for nonlinear transient dynamics and highlights achievements related to the convergence theory • Element Technology discusses four-node, three-node, eight-node, and two-node element theories • Material Models outlines models of plasticity and other nonlinear materials as well as the mechanics model of ductile damage • Contact and Constraint Conditions covers subjects related to three-dimensional surface contact, with examples solved analytically, as well as discussions on kinematic constraint conditions Throughout the book, vivid figures illustrate the ideas and key features of the explicit finite element method. Examples clearly present results, featuring both theoretical assessments and industrial applications. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is an ideal book for both engineers who require more theoretical discussions and for theoreticians searching for interesting and challenging research topics. The book also serves as an excellent resource for courses on applied mathematics, applied mechanics, and numerical methods at the graduate level.

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.