A spectral/finite difference method for simulating large deformations of heterogeneous, viscoelastic materials

A numerical algorithm is presented that simulates large deformations of het erogeneous, viscoelastic materials in two dimensions. The algorithm is base d on a spectral/fnite difference method and uses the Eulerian formulation i ncluding objective derivatives of the stress tensor in the rheological equa tions. The viscoelastic rheology is described by the linear Maxwell model, which consists of an elastic and viscous element connected in series. The a lgorithm is especially suitable to simulate periodic instabilities. The der ivatives in the direction of periodicity are approximated by spectral expan sions, whereas the derivatives in the direction orthogonal to the periodici ty are approximated by finite differences. The 1-D Eulerian finite differen ce grid consists of centre and nodal points and has variable grid spacing. Time derivatives are approximated with finite differences using an implicit strategy with a variable time step. The performance of the numerical code is demonstrated by calculation, for the first time, of the pressure field e volution during folding of viscoelastic multilayers. The algorithm is stabl e for viscosity contrasts up to 5x10(5), which demonstrates that spectral m ethods can be used to simulate dynamical systems involving large material h eterogeneities. The successful simulations show that combined spectral/fini te difference methods using the Eulerian formulation are a promising tool t o simulate mechanical processes that involve large deformations, viscoelast ic rheologies and strong material heterogeneities.