An efficient finite element scheme for viscoelasticity with moving boundaries

An efficient finite element scheme is devised for problems in linear viscoe lasticity of solids with a moving boundary. Such problems arise, for exampl e, in the burning process of solid fuel (propellant). Since viscoelastic co nstitutive behavior is inherently associated with a "memory," the potential need to store and operate on the entire history of the numerical solution has been a source of concern in computational viscoelasticity. A well-known "memory trick" overcomes this difficulty in the fixed-boundary case. Here the "memory trick" is extended to problems involving moving boundaries. The computational aspects of this extended scheme are discussed, and its perfo rmance is demonstrated via a numerical example. In addition, a special nume rical integration rule is proposed for the viscoelastic integral, which is more accurate than the commonly-used trapezoidal rule and does not require additional computational effort.