We compare two approaches to modeling the response of (possibly anisotropic) viscoealstic solids to large deformations. The first approach is a general, nonlinear, hereditary (single) integral law. The second approach is based on the multiplicative decomposition of the deformation gradient into instantaneous elastic and viscoelastic parts, with the stress depending only on the instantaneous elastic part of the deformation gradient. To complete the theory an evolution equation must be provided for the viscoelastic part of the deformation gradient. We do not consider these evolution equations here, but merely postulate a qualitative property that should be satisfied by the viscoelastic part of the deformation gradient, namely, that it is a continuous function of time (even at those instants when the deformation gradient suffers a jump discontinuity). This type of model would seem to generalize more easily to the case where plastic (i.e., nonrecoverable) deformations are also permitted, although we will not consider plastic deformations here. The problem that is addressed is here is to determine the class of all constitutive relations that are common to both types of models discussed above.
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