A boundary element model for nonlinear viscoelasticity

Abstract

The boundary element methodology is applied to the analysis of non-linear viscoelastic solids. Theadopted non-linear model uses the same relaxation moduli as the respective linear relations but with a time shiftdepending on the volumetric strain. Nonlinearity introduces an irreducible domain integral into the originalintegral equation derived for linear viscoelastic solids. This necessitates the evaluation of domain strains, whichrelies on proper differentiation of an integral with a strong kernel singularity. A time domain formulation isimplemented through a numerical integration algorithm. The effectiveness of the developed numerical tool isdemonstrated through the analysis of a plate with a central crack. The results are compared with respectivepredictions by the finite element metho