Tessellated continuum mechanics: A Galerkin finite element method

This paper tests the hypothesis that the tessellation used in tessellated continuum mechanics can form a mesh in a continuous Galerkin finite element method. Although the tessellation is not unique, neither is it arbitrary, and its construction imposes constraints on any numerical analysis. A distinctive feature of the tessellation is that it can possess highly distorted elements yet—as a consequence of associated anisotropy in material properties—can still return accurate results. The numerical procedure is tested on classical fractal porous geometries to demonstrate the potential of the method, and also illustrate the capability for analysis of disparate porous materials on continua.