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The book offers a careful introduction to modern non-linear mechanics. The used mathematical tools, such as tensor algebra and analysis are given in detail. The general theory of mechanical behaviour is particularized for the broad and important classes of elasticity and plasticity. It is intended to bring the reader close to the fields of today's research activities. A list of notations and an index help the reader to find specific topics. The book is based on three decades of teaching experience in this field.
Elasticity --- Plasticity --- Deformations (Mechanics) --- Elastic solids --- Mechanics --- Rheology --- Strains and stresses --- Structural failures --- Cohesion --- Plastics --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Strength of materials --- Properties --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- ELASTICITE --- PLASTICITE --- Grandes déformations --- MECANIQUE
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This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is devoted to the detailed study of illuminating specific problems of nonlinear elasticity, directed toward the scientist, engineer, and mathematician who wish to see careful treatments of precisely formulated problems. Special emphasis is placed on the role of nonlinear material response. The mathematical tools from nonlinear analysis are given self-contained presentations where they are needed. This book begins with chapters on (geometrically exact theories of) strings, rods, and shells, and on the applications of bifurcation theory and the calculus of variations to problems for these bodies. The book continues with chapters on tensors, three-dimensional continuum mechanics, three-dimensional elasticity, large-strain plasticity, general theories of rods and shells, and dynamical problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises. Reviews of the first edition: ``A scholarly work, it is uncompromising in its approach to model formulation, while achieving striking generality in the analysis of particular problems. It will undoubtedly become a standard research reference in elasticity but will be appreciated also by teachers of both solid mechanics and applied analysis for its clear derivation of equations and wealth of examples.'' --- J. M. Ball, (Bulletin of the American Mathematical Society), 1996. ``It is destined to become a standard reference in the field which belongs on the bookshelf of anyone working on the application of mathematics to continuum mechanics. For graduate students, it provides a fascinating introduction to an active field of mathematical research.'' --- M. Renardy, (SIAM Review), 1995. ``The monograph is a masterpiece for writing a modern theoretical treatise on a field of natural sciences. It is highly recommended to all scientists, engineers and mathematicians interested in a careful treatment of uncompromised nonlinear problems of elasticity, and it is a `must' for applied mathematicians working on such problems.'' --- L. v Wolfersdorf, (Zeitschrift fur Angewandte Mathematik und Mechanik), 1995.
Elasticity. --- Nonlinear theories. --- Elasticité --- Théories non linéaires --- Elasticity --- Nonlinear theories --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Applied Mathematics --- Elasticité --- Théories non linéaires --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Nonlinear problems --- Nonlinearity (Mathematics) --- Elastic properties --- Young's modulus --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Physics. --- Computational intelligence. --- Analysis. --- Theoretical, Mathematical and Computational Physics. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Soft computing --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Calculus --- Properties --- Global analysis (Mathematics). --- Engineering. --- Construction --- Industrial arts --- Technology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical physics. --- Physical mathematics --- Physics
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