Functional and numerical methods in viscoplasticity

I. R. Ionescu and M. Sofonea

Oxford Mathematical Monographs, Oxford University Press, 265 p., 1993


The book covers topics ranging from the mechanical models used in viscoplasticity and viscoelasticity, and ending with numerical solutions of the associated mathematical formulation of specific applications. It gives a complete treatment of the studied problems. Thus, theoretical results (existence and uniqueness of the local and global solutions, continuous or singular dependence upon the data and parameters, stability, long-term behavior), as well as numerical approaches (convergence of numerical solutions, error estimates) and engineering problems (wire drawing, penetration, mining engineering) are presented. Chapters 3, 4, and 5, which constitute the main part of the book, deal with quasistatic and dynamic processes in rate-type viscoplasticity and viscoelasticity, and the stationary flow of the Bingham fluid with friction. Each chapter begins with a discussion on the mechanical constitutive model, and ends with a numerical approach and an application to an engineering problem. Bibliographical notes are given at the end of each chapter. The book ends with an appendix, containing some mathematical concepts necessary for the reading of the book, references and index. The book may be of interest to a wide spectrum of readers, starting from students interested in applied mathematics and engineering, and researchers in various applied mathematics fields.

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