Finite-Element Implementation of Schapery-Type Constitutive Theories Based on an Internal Variable Approach

摘要

This paper presents two new strategies for implementing Schapery-typernnonlinearly viscoelastic constitutive theories into Finite Element (FE) codes. The firstrnstrategy uses the original differential equations that lead to the integral formulation ofrnSchapery-type constitutive theories and Finite Difference (FD) scheme. This strategyrnis quite different from all the other strategies found in the literature. The secondrnstrategy is an improvement of recursive strategies, used by many authors, based on thernintegral formulation of the constitutive theory. The performances of the newrnalgorithms are compared to that of existing strategies for various loading histories andrnnonlinearities. It is shown that the newly developed strategy relying on FD schemesrncan exhibit quadratic convergence rate when one time step is stored and 4th orderrnconvergence rate when two time steps are stored, which is a major improvement overrnthe recursive strategies.