From Stokes to Viscoelastic Rheology: A Unified Theoretical and Numerical Framework
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We present a unified theoretical and numerical framework aimed at reproducing in a computational workbench the rheological behavior of hyperelastic materials. Starting from the formalism of generalized Stokes-type problems, we investigate theoretically and numerically the solution to the considered initial and boundary value problems, and their discrete counterparts with low-order finite elements. By systematically questioning and comparing the different formulations, we propose a coherent methodology for the simulation of visco-hyperelastic materials, under the form of classical virtual rheological tests; in particular mechanical spectroscopy. The study shows how these schemes approach the linear elastic stress and analyzes under which conditions numerical dissipation exceeds spurious discrete dispersion, thus offering guidelines for the simulation of non-linear quasi-elastic materials with long relaxation times like PVB .
