S. Rionero G. Romano Trends and Applications of Mathematics to Mechanics
S. Rionero (Editor) G. Romano (Editor) Trends and Applications of Mathematics to Mechanics STAMM 2002 With 35 Figures
Salvatore Rionero Dept. of Mathematics Renato Caccioppoli University of Naples Federico II Naples, Italy Giovanni Romano Dept. of Scienza delle Costruzioni University of Naples Federico II Naples, Italy Library of Congress Control Number: 2004116220 ISBN 88-470-0269-9 Springer Milan Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the Italian Copyright Law in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the Italian Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com c Springer-Verlag Italia 2005 Printed in Italy Cover-Design: Simona Colombo, Milan Typesetting: PTP-Berlin Protago-TEX-Production Gmbh, Germany Printing and Binding: Signum, Bollate (Mi)
Preface 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 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 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 papers which report specialized investigations and which contribute broader presentations of linear and nonlinear problems. It is with the deepest gratitude to the authors who have contributed to the volume and to the publisher, for its highly professional assistance, that the editors submit this book to the international mathematics and mechanics communities. The editors gratefully acknowledge the financial support of the following institutions: Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale dialta Matematica (INDAM), Università degli Studi di Napoli Federico II and Regione Campania. Naples, Italy, October 2004 Salvatore Rionero Giovanni Romano
Contents On the instability of double diffusive convection in porous media under boundary data periodic in space F. Capone, S. Rionero ::::::::::::::::::::::::::::::::::::::::::::: 1 Modelling of a free piston problem B. D Acunto, A. Monte::::::::::::::::::::::::::::::::::::::::::::: 9 Reflections on frequently used viscoplastic constitutive models F. De Angelis :::::::::::::::::::::::::::::::::::::::::::::::::::: 19 On hereditary models of polymers M. De Angelis ::::::::::::::::::::::::::::::::::::::::::::::::::: 33 Edge contact forces in continuous media M. Degiovanni, A. Marzocchi, A. Musesti ::::::::::::::::::::::::::::: 39 Tangent stiffness of a Timoshenko beam undergoing large displacements M. Diaco, A. Romano, C. Sellitto :::::::::::::::::::::::::::::::::::: 49 Qualitative estimates for cross-sectional measures in elasticity J.N. Flavin, B. Gleeson :::::::::::::::::::::::::::::::::::::::::::: 67 On nonlinear global stability of Jeffery-Hamel flows M. Gentile, S. Rionero::::::::::::::::::::::::::::::::::::::::::::: 77 Energy penalty, energy barrier and hysteresis in martensitic transformations Y. Huo, I. Müller ::::::::::::::::::::::::::::::::::::::::::::::::: 85 On the applicability of generalized strain measures in large strain plasticity M. Itskov ::::::::::::::::::::::::::::::::::::::::::::::::::::::: 101 A nonlocal formulation of plasticity F. Marotti de Sciarra, C. Sellitto::::::::::::::::::::::::::::::::::::: 115
VIII Contents Consistent order extended thermodynamics and its application to light scattering I. Müller, D. Reitebuch :::::::::::::::::::::::::::::::::::::::::::: 127 On instability sources in dynamical systems S. Rionero :::::::::::::::::::::::::::::::::::::::::::::::::::::: 141 Tangent stiffness of elastic continua on manifolds G. Romano, M. Diaco, C, Sellitto :::::::::::::::::::::::::::::::::::: 155 Basic issues in convex homogenization G. Romano, A. Romano ::::::::::::::::::::::::::::::::::::::::::: 185 Tangent stiffness of polar shells undergoing large displacements G. Romano, C. Sellitto :::::::::::::::::::::::::::::::::::::::::::: 203 Global existence of smooth solutions and stability of the constant state for dissipative hyperbolic systems with applications to extended thermodynamics T. Ruggeri :::::::::::::::::::::::::::::::::::::::::::::::::::::: 215 Central schemes for conservation laws with application to shallow water equations G. Russo ::::::::::::::::::::::::::::::::::::::::::::::::::::::: 225 Regularized 13 moment equations for rarefied gas flows H. Struchtrup, M. Torrilhon :::::::::::::::::::::::::::::::::::::::: 247 Hydrodynamic calculation for extended differential mobility in semiconductors M. Trovato :::::::::::::::::::::::::::::::::::::::::::::::::::::: 269 Small planar oscillations of an incompressible, heavy, almost homogeneous liquid filling a container D. Vivona ::::::::::::::::::::::::::::::::::::::::::::::::::::::: 287 Thermodynamics of simple two-component thermo-poroelastic media K. Wilmanski :::::::::::::::::::::::::::::::::::::::::::::::::::: 293
List of Contributors Florinda Capone, Dept. of Mathematics Renato Caccioppoli, University of Naples Bernardino D Acunto, Dept. of Mathematics Renato Caccioppoli, University of Naples Fabio De Angelis, Dept. of Scienza delle Costruzioni, University of Naples Monica De Angelis, Dept. of Mathematics Renato Caccioppoli, University of Naples Marco Degiovanni, Dept. of Mathematics and Physics, Università Cattolica del Sacro Cuore, Brescia, Italy Marina Diaco, Dept. of Scienza delle Costruzioni, University of Naples Federico II, Naples, Italy James N. Flavin, Dept. of Mathematical Physics, National University of Ireland, Galway, Ireland Maurizio Gentile, Dept. of Mathematics Renato Caccioppoli, University of Naples Barry Gleeson, Dept. of Geomatic Engineering, University College London, London U.K. Yongzhong Huo, Shanghai Institute of Ceramics, Shanghai Mikhail Itskov, Dept. of Applied Mechanics and Fluid Dynamics, Lehrstuhl für Technische Mechanik und Strömungsmechanik, University of Bayreuth, Bayreuth, Germany Francesco Marotti de Sciarra, Dept. of Scienza delle Costruzioni, University of Naples Alfredo Marzocchi, Dept. of Mathematics, University of Brescia, Brescia, Italy Ingo Müller, Technical University Berlin, Institute of Process Engineering, Thermodynamics, Berlin, Germany Alessandro Musesti, Dept. of Mathematics and Physics, Università Cattolica del Sacro Cuore, Brescia, Italy AnnaMaria Monte, Dept. of Mathematics Renato Caccioppoli, University of Naples Daniel Reitebuch, Technical University Berlin, Institute of Process Engineering, Thermodynamics, Berlin, Germany Salvatore Rionero, Dept. of Mathematics Renato Caccioppoli, University of Naples
X List of Contributors Alessandra Romano, Dept. of Scienza delle Costruzioni, University of Naples Giovanni Romano, Dept. of Scienza delle Costruzioni, University of Naples Tommaso Ruggeri, Research Center of Applied Mathematics, C.I.R.A.M., University of Bologna, Bologna, Italy Giovanni Russo, Dept. of Mathematics and Informatics, University of Catania, Catania, Italy Carmen Sellitto, Dept. of Scienza delle Costruzioni, University of Naples Federico II, Naples, Italy Henning Struchtrup, Dept. of Mechanical Engineering, University of Victoria, Victoria, Canada Manuel Torrilhon, Seminar for Applied Mathematics, ETH Zurich, Switzerland Massimo Trovato, Dept. of Mathematics and Informatics, University of Catania, Catania, Italy Doretta Vivona, Dept. of Mathematical Models for Applied Science, University of Rome La Sapienza, Rome, Italy Krzysztof Wilmanski, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany