A spline-based enrichment function for arbitrary inclusions in extended finite element method with applications to finite deformations

摘要

A novel enrichment function, which can model arbitrarily shaped inclusions within the framework of the extended finite element method, is proposed. The internal boundary of an arbitrary-shaped inclusion is first discretized, and a numerical enrichment function is constructed 'on the fly' using spline interpolation. We consider a piecewise cubic spline which is constructed from seven localized discrete boundary points. The enrichment function is then determined by solving numerically a nonlinear equation which determines the distance from any point to the spline curve. Parametric convergence studies are carried out to show the accuracy of this approach compared with pointwise and linear segmentation of points for the construction of the enrichment function in the case of simple inclusions and arbitrarily shaped inclusions in linear elasticity. Moreover, the viability of this approach is illustrated on a neo-Hookean hyperelastic material with a hole undergoing large deformation. In this case, the enrichment is able to adapt to the deformation and effectively capture the correct response without remeshing.