Anisotropic Invariants and Additional Results for Invariant and Tensor Representations
The transformation groups which characterize transverse isotropy were listed in (c) of Section 3 of Chapter 8. For simplicity, we consider Case (ii), which is invariance under the group generated by the rotations and the reflection . If only second-order
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APPLICATION S OF TENSOR FUNCTIONS IN SOLID MECHANICS
EDITED BY
J.P. BOEHLER UNIVERSITY OF GRENOBLE
SPRINGER-VERLAG WIEN GMBH
Le spese di stampa di questo volume sono in parte coperte da contributi del Consiglio Nazionale delle Ricerche.
This volume contains 36 illustrations.
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
© 1987 by Springer-Verlag Wien Originally published by Springer Verlag Wien-New York in 1987
ISBN 978-3-211-81975-3 DOI 10.1007/978-3-7091-2810-7
ISBN 978-3-7091-2810-7 (eBook)
PREFACE
The mechanical behavior of materials with oriented internal structures, produced by formation processes and manufacturing procedures (crystal arrangements, stratification, fibrosity, porosity, etc.) or induced by permanent deformation (anisotropic hardening, softening,
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internal darnage growth, etc.) requires a suitable mathematical modelllng. The properties of tensor valued functions of tensor variables constltute a rational basis for a consistent mathematical modelling of complex material behavior. This book, which contains lectures presented at a CISM Advanced School, presents the principles, methods and results of applications in solid mechanics of the general laws governing tensor functions. The principles of mathematical techniques employed to derive representations of tensor functions are explained. The rules of specifying irreducible sets of tensor invariants and tensor generators for various classes of material symmetries are discussed. Representations of isotropic and anisotropic tensor functions arederived, in order to develop the general invariant forms of non-linear constitutive laws in mechanics of solids. Within this approach, the mathematical modellization of the materials' mechanical response is explained and specific models are presented in elasticity, plasticity, hardening, internal darnage and failure, for materials such as metals, composites, stratified rocks, consolidated soils and granular materials. The approach specifies a rational way to develop approximate theories and gives the necessary precision as to the number and the type of independent variables entering the mechanical laws to be used in engineering applications.
Experimental justifications as to the pertinence of the approach are given on examples of composite materials, rolled sheet-steel and stratified rocks. Information concerning proper experimental setting of tests for materials with oriented internal structures is developed. This book is addressed to specialists in solid mechanics, both theoretical and applied, material scientists concerned with metals and composites, specialists in soil and rock mechanics and to structural engineers facing problems involving anisotropic and inelastic solids at various environments, nonlinearity and couplings. I wish here to pay homage to t
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