Singular Solutions In Plasticity

This book deals with singular solutions that appear in the vicinity of maximum friction surfaces for several rigid plastic models. In particular, it discusses precise asymptotic expansions as a necessary ingredient for the development of efficient numerical methods to solve boundary value problems that involve the maximum friction law as a boundary condition. An applied aspect of the singular solutions considered is that these solutions are capable of predicting the development of narrow hard layers near frictional interfaces in manufacturing processes.

This volume gives an overview on recent developments for various applications of modern engineering design. Different engineering disciplines such as mechanical, materials, computer and process engineering provide the foundation for the design and development of improved structures, materials and processes. The modern design cycle is characterized by an interaction of different disciplines and a strong shift to computer-based approaches where only a few experiments are performed for verification purposes. A major driver for this development is the increased demand for cost reduction, which is also connected to environmental demands. In the transportation industry (e.g. automotive or aerospace), this is connected with the demand for higher fuel efficiency, which is related to the operational costs and the lower harm for the environment. One way to fulfil such requirements are lighter structures and/or improved processes for energy conversion. Another emerging area is the interaction of classical engineering with the health and medical sector. In this book, many examples of the mentioned design applications are presented.

Publisher Description

This book gathers papers presented at the international workshop PMSDAM’19. The respective contributions offer valuable insights for researchers working on numerical solutions to advanced materials problems. The problems concerning the remineralization of teeth are considered. Of particular interest are articles exploring topics at the interface of different disciplines.

Variational Methods in the Mechanics of Solids contains the proceedings of the International Union of Theoretical and Applied Mechanics Symposium on Variational Methods in the Mechanics of Solids, held at Northwestern University in Evanston, Illinois, on September 11-13, 1978. The papers focus on advances in the application of variational methods to a variety of mathematically and technically significant problems in solid mechanics. The discussions are organized around three themes: thermomechanical behavior of composites, elastic and inelastic boundary value problems, and elastic and inelastic dynamic problems. This book is comprised of 58 chapters and opens by addressing some questions of asymptotic expansions connected with composite and with perforated materials. The following chapters explore mathematical and computational methods in plasticity; variational irreversible thermodynamics of open physical-chemical continua; macroscopic behavior of elastic material with periodically spaced rigid inclusions; and application of the Lanczos method to structural vibration. Finite deformation of elastic beams and complementary theorems of solid mechanics are also considered, along with numerical contact elastostatics; periodic solutions in plasticity and viscoplasticity; and the convergence of the mixed finite element method in linear elasticity. This monograph will appeal to practitioners of mathematicians as well as theoretical and applied mechanics.

This book is concerned with the numerical solution of crack problems. The techniques to be developed are particularly appropriate when cracks are relatively short, and are growing in the neighbourhood of some stress raising feature, causing a relatively steep stress gradient. It is therefore practicable to represent the geometry in an idealised way, so that a precise solution may be obtained. This contrasts with, say, the finite element method in which the geometry is modelled exactly, but the subsequent solution is approximate, and computationally more taxing. The family of techniques presented in this book, based loosely on the pioneering work of Eshelby in the late 1950's, and developed by Erdogan, Keer, Mura and many others cited in the text, present an attractive alternative. The basic idea is to use the superposition of the stress field present in the unfiawed body, together with an unknown distribution of 'strain nuclei' (in this book, the strain nucleus employed is the dislocation), chosen so that the crack faces become traction-free. The solution used for the stress field for the nucleus is chosen so that other boundary conditions are satisfied. The technique is therefore efficient, and may be used to model the evolution of a developing crack in two or three dimensions. Solution techniques are described in some detail, and the book should be readily accessible to most engineers, whilst preserving the rigour demanded by the researcher who wishes to develop the method itself.

ICTAEM_1 treated all aspects of theoretical, applied and experimental mechanics including biomechanics, composite materials, computational mechanics, constitutive modeling of materials, dynamics, elasticity, experimental mechanics, fracture, mechanical properties of materials, micromechanics, nanomechanics, plasticity, stress analysis, structures, wave propagation. During the conference special symposia covering major areas of research activity organized by members of the Scientific Advisory Board took place. ICTAEM_1 brought together the most outstanding world leaders and gave attendees the opportunity to get acquainted with the latest developments in the area of mechanics. ICTAEM_1 is a forum of university, industry and government interaction and serves in the exchange of ideas in an area of utmost scientific and technological importance.