On the accretion of inhomogeneous viscoelastic bodies under finite deformations

Abstract

A formulation is given of the problem of the state of stress and strain of a continuously accreting body under finite deformations. The concept of a deformation gradient in an accreting body taking the deformation prehistory of the attached elements into account, is introduced. Boundary conditions are considered on the growth surface, which differ from the usual conditions in stresses or displacements. A solution is obtained for problems on the accretion of an inhomogeneous viscoelastic cylinder subjected to the preliminary deformation of the attached elements, to twisting, stretching, and imprinting loads, as well as on the simultaneous accretion and removal of a hollow sphere. Results of computations for the problem of winding a viscoelastic inhomogeneous cylinder with tension are presented.