Pathologies associated with the numerical analysis of hyper‐anisotropic materials

The rise in popularity of composite materials has brought to light the necessity of analysing materials exhibiting the kinematic constraint of directional inextensibility. Numerical phenomena associated with the analysis of such hyperanisotropic materials are described herein. The phenomena include: element locking dependent on fibre orientation, spurious tension modes and difficulties associated with elements possessing large material parameter ratios. To facilitate the present description, these phenomena are compared to, and contrasted with the well-documented problems associated with the analysis of incompressible or nearly incompressible media. Based on the results of eigenvalue analyses, elements satisfying the Babuska-Brezzi condition for incompressible media are found to perform rather poorly when analysing hyperanisotropic materials. These findings are supported by the results of a simple example.