Mechanics of incremental deformations: Theory of elasticity and viscoelasticity of initially stressed solids and fluids, including thermodynamic foundations and applications to finite strainReport as inadecuate




Mechanics of incremental deformations: Theory of elasticity and viscoelasticity of initially stressed solids and fluids, including thermodynamic foundations and applications to finite strain - Download this document for free, or read online. Document in PDF available to download.

1 Columbia University New York

Abstract : This book embodies an approach to non-linear elasticity which marks a fundamental departure from classical and current trends. The basic theory was first published between the years 1934 and 1940 in seven papers listed at the end of this Preface. In addition to a systematic treatment of the general theory and extensions to viscoelasticity, the book includes comprehensive new developments and applications, many of which are presented here for the first time.The work is characterized by the use of cartesian concepts and of elementary mathematical methods that do not require a knowledge of the tensor calculus or other more specialized techniques. The explicit introduction of a local rotation field in the three-dimensional equations leads to a theory which separates the physics from the geometry and is equally valid for elastic and non-elastic materials, using either rectangular or curvilinear coordinates.As this book demonstrates, the scope of problems solved by these new methods goes far beyond the results which it has been possible to obtain by the more elaborate and less general traditional approach. New insights, leading to many discoveries and a unified outlook have been brought into such widely diversified areas as rubber elasticity, internal gravity waves in a fluid and tectonic folding in geodynamics.The theory provides rigorous and completely general equations governing the dynamics and stability of solids and fluids under initial stress in the context of small perturbations. It does not require that the medium be elastic or isotropic but is applicable to anisotropic, viscoelastic, or plastic media. No assumptions are introduced regarding the physical process by which the initial stress has been generated. The treatment of viscoelasticity, which constitutes a substantial portion of the book, incorporates some of the results established in my previous work on non-equilibrium thermodynamics.Non-linear theories of deformation and applications to problems of finite strain are obtained by extension ofthe concept of incremental deformation in a medium under initial stress. In contrast to the presentation in the papers listed at the end of this Preface, the concepts and methods are developed primarily in the context of the linearized mechanics of continuous media under initial stress as an independent theory.





Author: Maurice A. Biot -

Source: https://hal.archives-ouvertes.fr/



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