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1. Introduction. The classical method of .solving boundary value problems in the linear quasi-static theory of viscoelasticity is to apply an integral transform (with respect to time) to the time-dependent field equations and boundary conditions. The transformed field equations then have the same form as the field equations of elasticity theory and if a solution to these, which is compatible with the transformed boundary conditions, can be found then the solution to the original problem is reduced to transform inversion. This method of solving viscoelastic stress analysis problems is referred to as the "correspondence principle".The correspondence principle is clearly applicable whenever the type of boundary condition prescribed is the same at all points of the boundary. For mixed boundary value problems (i.e., problems for which different field quantities are prescribed over separate parts of the boundary) the method is still applicable provided the regions over which different types of boundary conditions are given do not vary with time. (We are, of course, assuming that the region occupied by the body does not vary with time.) There remain those viscoelastic mixed boundary value problems where the regions, over which different types of boundary conditions are given, do vary with time. Particular examples are indentation and crack propagation problems. For problems of this type there will be points of the boundary at which only partial histories of some field quantities will be prescribed. When this is the case the transforms of these quantities are not directly obtainable and the classical correspondence principle is not applicable.Following a statement of the fundamental field equations of linear thermo-viscoelas-
Summary. A result, referred to as the generalized partial correspondence principle, is proved for noninertial viscoelastic boundary value problems. This states that if are the complementary regions of the boundary of a viscoelastic medium with a unique Poisson's ratio, on which displacements u,(r, t) and stresses <7jj(r, t)rij are specified, respectively, then if c B^\t) for all t' < t, the stresses satisfying this mixed boundary value problem at time t are the stresses for the elastic problem with the same boundary regions and the same specified stresses while known functions take the place of the specified displacements. It is noteworthy that B^(t'), t' < t, is not required to be monotonic increasing.Similarly, if has the property B\}\t') C Bu(t), t' < t, then the above statement holds but with stresses and displacements interchanged.In certain cases, it is not necessary to assume that the material has a unique Poisson's ratio, though in these cases the statement of the principle is altered and though somewhat restricted still has a useful range of application.The principle is applied to obtain certain nontrivial results of possible experimental interest for the normal contact problem, where the loading history is restricted only in the manner specified above.
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