A variational multiscale method with linear tetrahedral elements for multiplicative viscoelasticity

摘要

We present a computational approach to solve problems in multiplicative nonlinear viscoelasticity using piecewise linear finite elements on triangular and tetrahedral grids, which are very versatile for simulations in complex geometry. Our strategy is based on (1) formulating the equations of mechanics as a mixed first-order system, in which a rate form of the pressure equation is utilized in place of the standard constitutive relationship, and (2) utilizing the variational multiscale approach, in which the stabilization parameter is scaled with the viscous energy dissipation.