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On controllable deformations in a mixture of two non-linear elastic solids

Published online by Cambridge University Press:  26 February 2010

T. R. Steel
T. R. Steel
Affiliation:
Center for the Application of Mathematics, Lehigh University, Bethlehem, Pennsylvania, U.S.A.
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Abstract

Recently there has been much interest in theories describing the behaviour of a mixture of two or more continua, which are allowed to diffuse through each other and which interact mechanically and thermally. In the present note we consider such a mixture consisting of two isotropic incompressible non-linear elastic solids; physically this may describe a composite of two rubber-like materials. Such a mixture possesses internal friction between the constituents when deformed (called diffusive resistance or diffusive force), which acts as a damping mechanism. This damping mechanism has a static part and a dynamic part, and we here show that the exact static solutions which exist for an isotropic incompressible non-linear elastic solid are such that the damping mechanism is expressible as a gradient, and hence are also controllable for such a mixture. We also discuss the corresponding dynamic solutions.

From a practical viewpoint, some experiments carried out on vulcanized synthetic rubber-like materials may involve a mixture rather than a pure solid.

Type
Research Article
Information
Mathematika , Volume 16 , Issue 1 , June 1969 , pp. 50 - 56
Copyright
Copyright © University College London 1969

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