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The object of this book is to study, from a mathematical standpoint, the problem of the equilibrium of a perfectly plastic body under certain conditions. This involves the solution of two problems in the calculus of variations: the strain problem and the stress problem. These problems have only recently been solved, and this volume aims to give an up-to-date account of this work. The tools and methods used should be useful in a number of fields, in particular in solving problems relating to the 'evolution' of certain plastic phenomena, the mechanics of fracture, and certain optimal control problems.
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A mathematical study of the problem of the equilibrium of a perfectly plastic body subject to forces, presenting recent solutions of two well-known variational problems: the strain problem and the stress problem. The relationship between the stress problem and the strain problem is described--they are dual to each other, as can be expressed through general convex analytical methods. The stress problem has a unique solution, except in the case where the set of admissible stresses is empty. The strain problem is much more difficult, and was solved only recently; the author presents a thorough discussion of all phases of the solution of this long-intractable problem.Language Notes:
Text: English, French (translation)
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