An efficient finite element scheme for viscoelasticity with moving boundaries

Abstract

An ef®cient ®nite element scheme is devised for problems in linear viscoelasticity of solids with a moving boundary. Such problems arise, for example, in the burning process of solid fuel (propellant). Since viscoelastic constitutive behavior is inherently associated with à`m emory,'' 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-knowǹ`m emory trick'' overcomes this dif®culty in the ®xed-boundary case. Here the``memory trick'' is extended to problems involving moving boundaries. The computational aspects of this extended scheme are discussed, and its performance is demonstrated via a numerical example. In addition, a special numerical 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.