The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.

L.A. Galin’s book on contact problems is a remarkable work. Actually there are two books: the first, published in 1953 deals with contact problems in the classical theory of elasticity; this is the one that was translated into English in 1961. The second book, published in 1980, included the first, and then had new sections on contact problems for viscoelastic materials, and rough contact problems; this section has not previously been translated into English. In this new translation, the original text and the mathematical analysis have been completely revised, new material has been added, and the material appearing in the 1980 Russian translation has been completely rewritten. In addition there are three essays by students of Galin, bringing the analysis up to date.

Overcoming Parent-Child Contact Problems describes interventions for families experiencing a high conflict divorce impasse where a child is resisting contact with a parent.

This book presents a comprehensive and self-contained treatment of the authors’ newly developed scalable algorithms for the solutions of multibody contact problems of linear elasticity. The brand new feature of these algorithms is theoretically supported numerical scalability and parallel scalability demonstrated on problems discretized by billions of degrees of freedom. The theory supports solving multibody frictionless contact problems, contact problems with possibly orthotropic Tresca’s friction, and transient contact problems. It covers BEM discretization, jumping coefficients, floating bodies, mortar non-penetration conditions, etc. The exposition is divided into four parts, the first of which reviews appropriate facets of linear algebra, optimization, and analysis. The most important algorithms and optimality results are presented in the third part of the volume. The presentation is complete, including continuous formulation, discretization, decomposition, optimality results, and numerical experiments. The final part includes extensions to contact shape optimization, plasticity, and HPC implementation. Graduate students and researchers in mechanical engineering, computational engineering, and applied mathematics, will find this book of great value and interest.

Research into contact problems continues to produce a rapidly growing body of knowledge. Recognizing the need for a single, concise source of information on models and analysis of contact problems, accomplished experts Sofonea, Han, and Shillor carefully selected several models and thoroughly study them in Analysis and Approximation of Contact P

In recent years there has been heightened interest in the clinical and legal management of families in which children resist contact with one parent and become aligned with the other following divorce. Families affected by these dynamics require disproportionate resources and time from mental health and legal professionals, and cases require a specialized clinical approach. Traditional models of individual and family therapy are not designed to address these issues, and strategies and resources for mental health and legal professionals have been extremely limited. Overcoming Parent-Child Contact Problems describes interventions for families experiencing a high conflict divorce impasse where a child is resisting contact with a parent. It examines in detail one such intervention, the Overcoming Barriers approach, involving the entire family and combining psycho-education and clinical intervention. The book is divided into two parts: Part I presents an overview of parental alienation, including clinical approaches and a critical analysis of the many challenges associated with traditional outpatient family-based interventions. Part II presents the Overcoming Barriers approach, describing core aspects of the intervention and ways to adapt its clinical techniques to outpatient practice. Overcoming Parent-Child Contact Problems is geared toward mental health clinicians and legal professionals who work with families in high conflict and where a child resists visitation with a parent.

The aim of this book is to describe an efficient procedure to model dynamical contact problems with friction. This procedure is applied to different practical problems and validated by experiments. Friction contacts are used to transmit forces or to dissipate energy. Examples for dynamical engineering systems with friction are brakes, machine tools, motors, turbines, bearings or wheel-rail systems. A better understanding of friction phenomena can result in improvements like the reduction of noise and maintenance costs, increased life time of machines and improved energy efficiency. Dependent on the features of the friction contact, different contact models and solution methods are applied.