A hybrid-Trefftz finite element platform for solid and porous elastodynamics

Abstract

Hybrid-Trefftz finite elements are well suited for modeling the response of materials under highly transient loading. Their approximation bases are built using functions that satisfy exactly the differential equations governing the problem. This option embeds relevant physical information into the approximation basis and removes the well-known sensitivity of the conventional finite elements to high solution gradients and short wavelength excitations. Despite such advantages, no public software using hybrid-Trefftz finite elements to model wave propagation through solid and porous media exists to date. This paper covers the formulation and implementation of hybrid-Trefftz finite elements for single-phase, biphasic and triphasic media, subjected to dynamic loads. The formulation is cast in a unified framework, valid for the three types of materials alike, and independent of the nature (harmonic, periodic or transient) of the applied load. Displacement, traction, elastic and absorbing boundary conditions are accommodated. The implementation is made in three novel, open-source and user-friendly computational modules which are freely distributed online.