Hybrid-Trefftz finite elements for biphasic elastostatics

This paper reports on the formulation and implementation of the displacement and stress models of the hybrid-Trefftz finite elements for elastostatic problems defined on saturated porous media. The supporting mathematical model is the (u–w) formulation of the Biot theory of porous media. The hybrid-Trefftz models are derived from the corresponding (pure) hybrid models by selecting the domain trial functions from the free-field solutions of the governing Navier equation. The resulting elements are highly robust and convergent, as they embody the physical characteristics of the modelled problem. Moreover, all coefficients present in the solving system are defined by boundary integral expressions.

► Hybrid-Trefftz finite elements are formulated for biphasic elastostatic problems. ► The implementation of alternative displacement and stress models is discussed. ► Convergence under p-refinement is substantially faster than under h-refinement. ► Both models are insensitive to mesh distortion and incompressibility of the medium. ► Compared to conventional elements, better accuracy is reached with less dofs.