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Scalable Molecular Dynamics with NAMD

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.

Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures

Publisher Summary The fundamental assumption of all theories of plasticity—that of time independence of the equations of state—makes simultaneous description of the plastic and rheologic properties of a material impossible. I t is well-known that in many practical problems, the actual behaviour of a material is governed by plastic as well as by rheologic effects. It can even be said that for many important structural materials, rheologic effects are more pronounced after the plastic state has been reached. Every material shows more or less pronounced viscous properties. In some problems, the influence of viscous properties of the material may be negligible, while in others, it may be essential. Both sciences—plasticity and rheology—are concerned with the description of important mechanical properties of structural materials. Each of them has created its own methods of investigation and has developed within the framework of certain assumptions which, unfortunately, cannot always be satisfied in reality. The results of rheology are confined to cases where plastic strain is of no decisive importance.

Fundamental Problems in Viscoplasticity

Soils can rarely be described as ideally elastic or perfectly plastic and yet simple elastic and plastic models form the basis for the most traditional geotechnical engineering calculations. With the advent of cheap powerful computers the possibility of performing analyses based on more realistic models has become widely available. One of the aims of this book is to describe the basic ingredients of a family of simple elastic-plastic models of soil behaviour and to demonstrate how such models can be used in numerical analyses. Such numerical analyses are often regarded as mysterious black boxes but a proper appreciation of their worth requires an understanding of the numerical models on which they are based. Though the models on which this book concentrates are simple, understanding of these will indicate the ways in which more sophisticated models will perform.

Soil Behaviour and Critical State Soil Mechanics

: The principal im is to generalize h one- im ion l con itutive equ tions for r te-sensi ive plastic materials to general sta s of s ress. T HE DYNAMIC L YIELD CONDITIONS FOR LASTIC, VISCO-PLASTIC MATERIALS ARE DISCUS ED A D NEW R L XATION FUNCTIONS ARE INTRODUCED. S OLUTION OF THE RELAXATION EQUATIONS FOR SUCH MATERIALS ARE GIVEN. (Author)

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The Constitutive Equations for Rate Sensitive Plastic Materials

Publisher Summary This chapter reviews the thermodynamic foundations of the theory of viscoplasticity. The essential feature of viscoplasticity is the simultaneous description of rheologic and plastic effects of a material. The necessity for simultaneous consideration of viscoelastic and plastic properties of a material is indicated by the experimental investigations of dynamic loads. The thermodynamic theory of elastic-viscoplastic materials presents for finite strains two basic difficulties. The first of these is connected with the kinematic description of plastic deformation. The second difficulty concerns the problem of choice of thermodynamic variables of state. The chapter discusses development of the thermodynamic theory of plasticity for finite strains using the rate-type theory, and generalized the inviscid theory of plasticity to nonisothermal finite deformations. The principle of material frame indifference called “invariance requirements under superposed rigid body motions,” was used and explored the thermodynamical restrictions. The chapter presents the formulation of the thermodynamic theory of a rate-sensitive plastic material within the framework of thermodynamics of a material with internal state variables. In this thermodynamic theory of an inelastic material, the deformation tensor and temperature are considered as thermodynamic state variables, while the components of the inelastic deformation tensor appear as internal state parameters.

Piotr Perzyna

Papers

Fundamental Problems in Viscoplasticity

The Constitutive Equations for Rate Sensitive Plastic Materials

Thermodynamic Theory of Viscoplasticity

Internal state variable description of dynamic fracture of ductile solids

Constitutive Modeling of Dissipative Solids for Postcritical Behavior and Fracture