Accounting for differences in element size and homogeneity when comparing Finite Element models: Armadillos as a case study

Abstract

Computing the average Von Mises stress of Finite Element Models to obtain a single measurement that represents the relative strength of vertebrate structures has been used recently in different works in palaeobiology. However, due to the nature of the Finite Element Analysis (FEA) data, which depends on the size of the elements of the mesh, this approach needs to be fully developed taking into account this influence of the size elements in the results. In this work, we proposed a Mesh-Weighted Arithmetic Mean as the adequate central tendency statistic for non-uniform meshes. On the other hand, when other statistical tools are used, we propose a Quasi-Ideal Mesh that takes into account the differences in size of the elements. Firstly, in order to analyse our proposed approach, one Cingulata mandible has been used generating different meshes. Afterwards, FEA has been applied in a case study in 20 different mandibles belonging to 14 species of Cingulata. Our results suggest that the proposed methodologies are suitable to compare different patterns of stress distribution. In particular, the methods proposed have been shown to be extremely useful when analysing the biomechanics of vertebrate bone structures that can be modelled as planar models in an interspecific comparative framework.