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This volume contains a selection of the invited papers presented at a LMS Durham Symposium on modern developments in non-classical continuum mechanics. A major aim was to bring together workers in both the abstract and practical aspects of the subject in order to achieve enhanced appreciation of each others' approach and hence of the mathematical techniques and physical intuition essential for successful research in this field. As a result, the present collection consists of a series of concise articles which are introductions to, and succinct accounts of, current activity in many branches of non-classical continuum mechanics. Research workers in applied mathematics, physics, theoretical mechanics, and structural and aeronautical engineering will find much of interest in this collection.
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This best-selling textbook presents the concepts of continuum mechanics in a simple yet rigorous manner. It introduces the invariant form as well as the component form of the basic equations and their applications to problems in elasticity, fluid mechanics and heat transfer, and offers a brief introduction to linear viscoelasticity. The book is ideal for advanced undergraduates and graduate students looking to gain a strong background in the basic principles common to all major engineering fields, and for those who will pursue further work in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary areas such as geomechanics, biomechanics, mechanobiology and nanoscience. The book features derivations of the basic equations of mechanics in invariant (vector and tensor) form and specification of the governing equations to various co-ordinate systems, and numerous illustrative examples, chapter summaries and exercise problems. This second edition includes additional explanations, examples and problems.
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This is a modern textbook for courses in continuum mechanics. It provides both the theoretical framework and the numerical methods required to model the behaviour of continuous materials. This self-contained textbook is tailored for advanced undergraduate or first-year graduate students with numerous step-by-step derivations and worked-out examples. The author presents both the general continuum theory and the mathematics needed to apply it in practice. The derivation of constitutive models for ideal gases, fluids, solids and biological materials, and the numerical methods required to solve the resulting differential equations, are also detailed. Specifically, the text presents the theory and numerical implementation for the finite difference and the finite element methods in the Matlab® programming language. It includes thirteen detailed Matlab® programs illustrating how constitutive models are used in practice.
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