Trends and applications of mathematics to mechanics : STAMM 2002

The book collects a selection of papers most of which are revised and enriched versions of the contributions presented at the 12th Symposium on Trends of Applications of Mathematics to Mechanics (STAMM) which was sponsored by the International Society for the Interaction between Mathematics and Mechanics (ISIMM) and held in Maiori (Salerno), Italy from September 29th to October 4th, 2002. The Symposium attracted many leading researchers from around the world who are working at the interface between Mathematics and Mechanics. The importance of a close link between these two disciplines have long been recognized and each of them get benefits and stimuli by open problems, methods and results emerging from the other one. The book collects 22 papers which contribute special investigations and more wide presentations of linear and nonlinear problems. It is with the deepest gratitude to the authors that have contributed to the volume and to the publisher, for his highly professional assistance, that the editors submit this book to the international mathematics and mechanics communities. On the instability of double diffusive convection in porous media under boundary data periodic in space....Pages 1-8 Modelling of a free piston problem....Pages 9-17 Reflections on frequently used viscoplastic constitutive models....Pages 19-31 On hereditary models of polymers....Pages 33-38 Edge contact forces in continuous media....Pages 39-48 Tangent stiffness of a Timoshenko beam undergoing large displacements....Pages 49-66 Qualitative estimates for cross-sectional measures in elasticity....Pages 67-76 On nonlinear global stability of Jeffery-Hamel flows....Pages 77-83 Energy penalty, energy barrier and hysteresis in martensitic transformations....Pages 85-99 On the applicability of generalized strain measures in large strain plasticity....Pages 101-113 A nonlocal formulation of plasticity....Pages 115-125 Consistent order extended thermodynamics and its application to light scattering....Pages 127-139 On instability sources in dynamical systems....Pages 141-153 Tangent stiffness of elastic continua on manifolds....Pages 155-184 Basic issues in convex homogenization....Pages 185-202 Tangent stiffness of polar shells undergoing large displacements....Pages 203-214 Global existence of smooth solutions and stability of the constant state for dissipative hyperbolic systems with applications to extended thermodynamics....Pages 215-224 Central schemes for conservation laws with application to shallow water equations....Pages 225-246 Regularized 13 moment equations for rarefied gas flows....Pages 247-267 Hydrodynamic calculation for extended differential mobility in semiconductors....Pages 269-285 Small planar oscillations of an incompressible, heavy, almost homogeneous liquid filling a container....Pages 287-292 Thermodynamics of simple two-component thermo-poroelastic media....Pages 293-306 "The book offers a selection of papers most of which are revised and enriched versions of the contributions presented at the 12th Symposium on Trends of Applications of Mathematics of Mechanics (STAMM) which was sponsored by the International Society for the Interaction between Mathematics and Mechanics (ISIMM) and held in Maiori (Salerno), Italy from September 29th to October 4th, 2002." "The Symposium attracted leading researchers from around the world who are working at the interface between mathematics and mechanics. The importance of a close link between these two disciplines has long been recognized; each benefits from and is stimulated by open problems, methods and results emerging from the other." "The book comprises 22 pagers which report specialized investigations and which contribute broader presentations of linear and nonlinear problems."--Jacket In non-smooth plasticity and viscoplasticity the appropriate mathematical framework is determined by the tools and concepts of convex analysis and subdifferential calculus (Rockafellar [1], Hiriart-Urruty and Lemaréchal [2]), which are capable of dealing with convex non-differentiable functions and multivalued operators (see, e.g., Halphen and Nguyen [3], Moreau [4], Eve et al. [5], Romano et al. [6]).