Numerical solution methods for viscoelastic orthotropic materials

Abstract

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time