Complementarity, Duality and Symmetry in Nonlinear Mechanics: Proceedings of the IUTAM Symposium (Advances in Mechanics and Mathematics Book 6)

Complementarity, duality, and symmetry are closely related concepts, and have always been a rich source of inspiration in human understanding through the centuries, particularly in mathematics and science. The Proceedings of IUTAM Symposium on Complementarity, Duality, and Symmetry in Nonlinear Mechanics brings together some of world's leading researchers in both mathematics and mechanics to provide an interdisciplinary but engineering flavoured exploration of the field's foundation and state of the art developments. Topics addressed in this book deal with fundamental theory, methods, and applications of complementarity, duality and symmetry in multidisciplinary fields of nonlinear mechanics, including nonconvex and nonsmooth elasticity, dynamics, phase transitions, plastic limit and shakedown analysis of hardening materials and structures, bifurcation analysis, entropy optimization, free boundary value problems, minimax theory, fluid mechanics, periodic soliton resonance, constrained mechanical systems, finite element methods and computational mechanics. A special invited paper presented important research opportunities and challenges of the theoretical and applied mechanics as well as engineering materials in the exciting information age. __Audience:__ This book is addressed to all scientists, physicists, engineers and mathematicians, as well as advanced students (doctoral and post-doctoral level) at universities and in industry. Front Matter....Pages i-lvii Mechanics and Materials: Research and Challenges in the Twenty-First Century....Pages 1-11 Non-Convex Duality....Pages 13-19 Duality, Complementarity, and Polarity in Nonsmooth/Nonconvex Dynamics....Pages 21-65 Tri-Duality Theory in Phase Transformations of Ferroelectric Crystals with Random Defects....Pages 67-84 Mathematical Modeling of Three-Dimensional Delamination Processes of Laminated Composites....Pages 85-99 Newton’s and Poisson’s Impact Law for the Non-Convex Case of Reentrant Corners....Pages 101-125 Duality in Kinematic Approaches of Limit and Shakedown Analysis of Structures....Pages 127-148 Bifurcation Analysis of Shallow Spherical Shells with Meridionally Nonuniform Loading....Pages 149-165 Duality for Entropy Optimization and its Applications....Pages 167-178 Dual Variational Principles for the Free-Boundary Problem of Cavitated Bearing Lubrication....Pages 179-189 Finite Dimensional Frictional Contact Quasi-Static Rate and Evolution Problems Revisited....Pages 191-208 Minimax Theory, Duality and Applications....Pages 209-223 Min-Max Duality and Shakedown Theorems in Hardening Plasticity....Pages 225-240 A Fluid Problem with Navier-Slip Boundary Conditions....Pages 241-254 An Extension of Limit Analysis Theorems to Incompressible Material with a Non-Associated Flow Rule....Pages 255-275 Periodic Soliton Resonances....Pages 277-287 Generalized Legendre-Fenchel Transformation....Pages 289-311 A Robust Variational Formulation for a Rod Subject to Inequality Constraints....Pages 313-325 Computing FEM Solutions of Plasticity Problems via Nonlinear Mixed Variational Inequalities....Pages 327-338 Finite Element Dual Analysis in Piezoelectric Crack Estimation....Pages 339-353 Duality and Complementarity in Constrained Mechanical Systems....Pages 355-373 Mixed Energy Method for Solution of Quadratic Programming Problems....Pages 375-389