Time integration in linear viscoelasticity:a comparative study

One of the key tasks in computational viscoelasticity is the time integration of the constitutive equation. It is important that the behaviour of the integrators is well understood since they are used in a variety of applications. In the present paper, the performance of conventional semi-analytical methods and implicit Runge-Kutta methods for the integral model of linear viscoelasticity with Prony series is evaluated analytically and numerically. Although a linear viscoelastic constitutive equation is considered, the analyzed integrators can be extended to handle also Schapery-type nonlinear constitutive equations. Numerical examples involving a simple uniaxial problem and multiaxial simulations are presented in order to analyze and compare the time integrators