Unstable Elastic Materials and the Viscoelastic Response of Bars in Tension

Abstract

Some homogeneous elastic materials are capable of sustaining finite equilibrium deformations with discontinuous strains. For materials of this kind, the energetics of isothermal, quasi-static motions may differ from those conventionally associated with elastic behavior. When equilibrium states involving strain jumps occur during such motions, the rate of increase of stored energy in a portion of the body may no longer coincide with the rate of work of the external forces present. In general, energy balance now includes an additional effect due to the presence of moving strain discontinuities. As a consequence, the macroscopic response of the body may be dissipative. This fact makes it possible to model certain types of inelastic behavior in solids with the help of such "unstable" elastic materials; see, for example, Abeyaratne and Knowles (1987a,b,c).

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