Hemivariational Inequalities

The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.

Inhalt
I Introductory Topics.- 1 Elements of Nonsmooth Analysis.- II Mechanical Theory.- 2 Nonsmooth Mechanics I.- 3 Nonsmooth Mechanics II.- 4 Hemivariational Inequalities.- 5 Multivalued Boundary Integral Equations.- III Mathematical Theory.- 6 Static Hemivariational Inequalities.- 7 Eigenvalue and Dynamic Problems.- 8 Optimal Control and Identification Problems.- IV Numerical Applications.- 9 On the Numerical Treatment of Hemivariational Inequalities.- 10 On the Approximation of Hemivariational Inequalities by Variational Inequalities.- 11 The Method of Substationary Point Search.- 12 On a Decomposition Method into Two Convex Problems.- 13 Dynamic Hemivariational Inequalities and Crack Problems.- 14 Applications of the Theory of Hemivariational Inequalities in Robotics.- 15 Addenda: Hemivariational Inequalities, Fractals and Neural Networks.- References.