David F. Parker - Böcker

This volume records the Symposium on 'Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics', held at the University of Nottingham from 30th August to 3rd September 1994, sponsored by the International Union of Theoretical and Applied Mechanics and held in conjunction with the In- ternational Society for the Interaction of Mechanics and Mathematics. The advent of composite materials, together with their widespread use in recent years, has provided a powerful stimulus for advances in several somewhat ne- glected areas of solid mechanics. Exploitation of fibre-reinforced solids and laminates has rekindled interest in the theory and application of anisotropic elasticity and motivated study of many aspects of material inhomogeneity. The need to understand fibre-matrix interactions, especially in modelling metal- matrix composites and the forming of thermoplastic components has fostered advances in plasticity and viscoelasticity theory, to describe phenomena such as deformation-induced inhomogeneity and anisotropy.Plasticity and flow of granular media are also intrinsically nonlinear, giving rise, for example, to highly anisotropic and strongly localized effects, such as shear bands. Most materials contain impurities. These inclusions, even if microscopically isotropic, cause macroscopic anisotropy in an 'effective-medium' theory. Dy- namic behaviour is even more complex, since wave propagation reveals both attenuation and dispersion effects. Increased interest in finer-scaled compos- ites (nanotechnology and superlattices) and ultra-high frequency techniques continue to reveal new effects, due to inhomogeneity and microstructure. An example included here is lattice-induced dispersion for certain surface waves of relatively long wavelength.

This book, derived from an innovative course of lectures, is a first introduction to the mathematical description of fields, flows and waves. It shows students, early in their studies, how many of the topics they have encountered are useful in constructing, analysing and interpreting phenomena in the real world. Designed for second-year undergraduate students in mathematics, mathematical physics, and engineering, it presumes only a limited familiarity with several variable calculus and vector fields. It develops the concepts of flux, conservation law and boundary value problem through simple examples of heat flow, electric potentials and gravitational fields. The ideas are developed through worked examples, and a range of exercises (with solutions) is provided to test understanding. Chapters 1-7 contain ample material for an introductory lecture course, while later chapters on waves in fluids, solids and electromagnetism, and on bio-mathematics, show how the extension of earlier ideas leads to the description and explanation of important topics in modern technology and science.

The topic of surface waves lies at the interface between a number of disci­ plines - physics, theoretical and applied mechanics, electroacoustics, ap­ plied mathematics, surface science and seismology. This volume, based on papers delivered at European Mechanics Colloquium 226, reflects this diversity in approach and background, while showing strong links between phenomena arising from different fields. The emphasis is on recent de­ velopments such as nonlinear and other nonclassical effects,which have great importance for both pure science and for applications such as signal processing, nondestructive evaluation and seismic studies. In recent years there has been considerable progress in the mathe­ matical treatment of nonlinear effects, of viscoelastic and of more novel constitutive effects which modify the predictions of linear elastic and piezo­ electric theory for surface acoustic wave (SAW) propagation. A number of these themes serve to group the contents of this volume. Part I contains recent advances in the rigorous mathematical treatment of nonlinearity, together with a paper giving experimental results showing the need for further theoretical development. Part II deals with anisotropic elasticity, showing that even the linear theory presents many possible behaviours, which are still not fully categorized.