Variational-Hemivariational Inequalities with Applications

I. Variational Problems in Solid Mechanics. 1. Elliptic Variational Inequalities. 1.1. Background on functional analysis. 1.2. Existence and uniqueness results. 1.3. Convergence results. 1.4. Optimal control. 1.5. Well-posedness results. 2. History-Dependent Operators. 2.1. Spaces of continuous functions. 2.2. Definitions and basic properties. 2.3. Fixed point properties. 2.4. History-dependent equations in Hilbert spaces. 2.5. Nonlinear implicit equations in Banach spaces. 2.6. History-dependent variational inequalities. 2.7. Relevant particular cases. 3. Displacement-Traction Problems in Solid Mechanics. 3.1. Modeling of displacement-traction problems. 3.2. A displacement-traction problem with locking materials. 3.3. One-dimensional elastic examples. 3.4. Two viscoelastic problems. 3.5. One-dimensional examples. 3.6. A viscoplastic problem. II. Variational-Hemivariational Inequalities. 4. Elements of Nonsmooth Analysis. 4.1. Monotone and pseudomonotone operators. 4.2. Bochner-Lebesgue spaces. 4.3. Subgradient of convex functions. 4.4. Subgradient in the sense of Clarke. 4.5. Mixed equilibrium problem. 4.6. Miscellaneous results. 5. Elliptic Variational-Hemivariational Inequalities. 5.1. An existence and uniqueness result. 5.2. Convergence results. 5.3. Optimal control. 5.4. Penalty methods. 5.5. Well-posedness results. 5.6. Relevant particular cases. 6. History-Dependent Variational-Hemivariational Inequalities. 6.1. An existence and uniqueness result. 6.2. Convergence results. 6.3. Optimal control. 6.4. A penalty method. 6.5. A well-posedness result. 6.6. Relevant particular cases. 7. Evolutionary Variational-Hemivariational Inequalities. 7.1. A class of inclusions with history-dependent operators. 7.2. History-dependent inequalities with unilateral constraints. 7.3. Constrainted differential variational-hemivariational inequalities. 7.4. Relevant particular cases. III. Applications to Contact Mechanics. 8. Static Contact Problems. 8.1. Modeling of static contact problems. 8.2. A contact problem with normal compliance. 8.3. A contact problem with unilateral constraints. 8.4. Convergence and optimal control results. 8.5. A contact problem for locking materials. 8.6. Convergence and optimal control results. 8.7. Penalty methods. 9. Time-Dependent and Quasistatic Contact Problems. 9.1. Physical setting and mathematical models. 9.2. Two time-dependent elastic contact problems. 9.3. A quasistatic viscoplastic contact problem. 9.4. A time-dependent viscoelastic contact problem. 9.5. Convergence and optimal control results. 9.6. A frictional viscoelastic contact problem. 9.7. A quasistatic contact problem with locking materials. 10. Dynamic Contact Problems. 10.1. Mathematical models of dynamic contact. 10.2. A viscoelastic contact problem with normal damped response. 10.3. A unilateral viscoelastic frictional contact problem. 10.4. A unilateral viscoplastic frictionless contact problem.