Publisher Description

Historically, a major problem for the study of the large deformation of crystalline solids has been the apparent lack of unity in experimentally determined stress-strain functions. The writer's discovery in 1949 of the unexpectedly high velocity of incremental loading waves in pre-stressed large deformation fields emphasized to him the pressing need for the independent, systematic experimental study of the subject, to provide a firm foundation upon which physically plausible theories for the finite deformation of crystalline solids could be constructed. Such a study undertaken by the writer at that time and continued uninterruptedly to the present, led in 1956 to the development of the diffraction grating experiment which permitted, for the first time, the optically accurate determination of the strain-time detail of non-linear finite amplitude wave fronts propagating into crystalline solids whose prior history was precisely known. These experimental diffraction grating studies during the past decade have led to the discovery that the uniaxial stress-strain functions of 27 crystalline solids are unified in a single, generalized stress-strain function which is described, much of it hitherto unpublished, in the present monograph. The detailed study of over 2,000 polycrystal and single crystal uni axial stress experiments in 27 crystalline solids, in terms of the variation of a large number of pertinent parameters, has provided new unified pat terns of understanding which, it is hoped, will be of interest and value to theorists and experimentalists alike.

This book provides a comprehensive background for analysis of the finite deformation of materials. It is intended for engineering scientists, applied mathematicians, and advanced students beginning their studies in the field. The book begins with the geometry of deformation and motion in finite straining. This is followed by the general theory of stress and stress measures (corresponding to each strain measure) and balance laws of continuum physics. Rotating reference frames and related issues of invariance, objective stress-rates, and material spin are then covered. Simple shearing examples illustrate and clarify stress and deformation measures in these chapters. Applications of the general equations to specific material behaviors are presented in chapters 4 to 6. Nonlinear elasticity of rubber, plastic deformation of polycrystalline metals, and multiple-slip (with additional kinematics) in metal crystals are covered. Selected original experiments and nonlinear analyses are included, with precise attributions and numerous illustrations.

Certain fundamentals of finite-deformation elastoplastic flow of crystalline solids and geomaterials are discussed in this reprint from microscopic and macroscopic phenomenological points of view. In the first case, physically based constitutive relations for microelements are formulated on the basis of slip-induced plastic deformation with due account of possible frictional or pressure dependencies and inelastic volumetric changes. The close relation between the double-slip theory of single crystals and that og granular materials is discussed. The calculation of overall instantaneous moduli in terms of the local quantities for arbitrary strains and rotations are reviewed. Then, attention is focused on phenomenological constitutive relations which apply to both metals and geomaterials. Specific results are given for an isotropic-kinematic hardening model, including frictional and plastic dilatancy effects. Finally, certain fundamental thermodynamic aspects of finite-deformation inelasticity are reviewed, emphasizing conditions under which flow potentials exist.

Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.