On uniqueness in general linear viscoelasticity

Abstract

On the basis of two theorems pertaining to the asymptotic behavior of certain Laplace transforms, the uniqueness of the displacement field in a general linear viscoelastic body (i.e., one with time-variable properties) throughout a time interval is demonstrated, provided the instantaneous elasticity tensor (or, in the case of a generalized Kelvin—Voigt material, the instantaneous viscosity tensor) is positive definite and a continuous function of time, and provided the following information is specified: the displacement field, to within a rigid-body motion, throughout the body and at all times before the given interval; the displacement and velocity fields throughout the body at the beginning of the interval (initial conditions); the body force throughout the body and throughout the interval; and, at each point of the boundary, in each of three orthogonal directions, a component of the traction or of the displacement throughout the time interval. If inertia is neglected, the initial conditions may be dispensed with, but the displacement field is unique only to within a rigid-body motion.