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RESEARCH PAPERS

On the Uniqueness of Solution of the Initial Value Problem in Softening Materials

[+] Author and Article Information
K. C. Valanis

College of Engineering, University of Cincinnati, Cincinnati, Ohio 45221

J. Appl. Mech 52(3), 649-653 (Sep 01, 1985) (5 pages) doi:10.1115/1.3169115 History: Received April 01, 1984; Revised September 01, 1984; Online July 21, 2009

Abstract

The initial value problem in finite “softening” material domains is discussed. An inequality that is true of all materials irrespective of their constitution is first established. It is then shown that the solution to this problem is unique when the attending constitutive equation satisfies another inequality, which is characteristic of material models that we call “positive.” A number of constitutive equations that give rise to realistic softening behavior are shown to lead to a unique solution of the initial value problem.

Copyright © 1985 by ASME
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