The intervals method : a new approach to analyse finite element outputs using multivariate statistics

Background. In this paper, we propose a new method, named the intervals' method, to analyse data from finite element models in a comparative multivariate framework. As a case study, several armadillo mandibles are analysed, showing that the proposed method is useful to distinguish and characterise biomechanical differences related to diet/ecomorphology. - Methods. The intervals' method consists of generating a set of variables, each one defined by an interval of stress values. Each variable is expressed as a percentage of the area of the mandible occupied by those stress values. Afterwards these newly generated variables can be analysed using multivariate methods. - Results. Applying this novel method to the biological case study of whether armadillo mandibles differ according to dietary groups, we show that the intervals' method is a powerful tool to characterize biomechanical performance and how this relates to different diets. This allows us to positively discriminate between specialist and generalist species. - Discussion. We show that the proposed approach is a useful methodology not affected by the characteristics of the finite element mesh. Additionally, the positive discriminating results obtained when analysing a difficult case study suggest that the proposed method could be a very useful tool for comparative studies in finite element analysis using multivariate statistical approaches

Quasi-homothetic transformation for comparing the mechanical performance of planar models in biological research

The potential of Finite Element Analysis (FEA) as an analytical technique in biological research has been widely highlighted in recent years. In spite of its great power, only in the best of circumstances one can compare the behaviour of models that differ in size and shape. Here, a new and easy procedure to scale FE models of plane elasticity is presented for several species of extant bovids that significantly differ in size and morphology. The method is based on the modification of the values of the forces applied by taking into account the particularities of the elasticity plane models (plane strain and plane stress equations) using quasi-homothetic transformations. This approach is shown to be extremely useful when exploring the effect of the shape in front of the strength and the stiffness of vertebrate bone structures. Thus, the quasi-homothetic concept is a new and interesting proposal to be used in plane elasticity models of biological, and specifically of vertebrate, structures which can be modelled as two-dimensional finite element models.Peer ReviewedPostprint (published version

Accounting for differences in element size and homogeneity when comparing finite element models : armadillos as a case study

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

Quasi-homothetic transformation for comparing the mechanical performance of planar models in biological research

The potential of Finite Element Analysis (FEA) as an analytical technique in biological research has been widely highlighted in recent years. In spite of its great power, only in the best of circumstances one can compare the behaviour of models that differ in size and shape. Here, a new and easy procedure to scale FE models of plane elasticity is presented for several species of extant bovids that significantly differ in size and morphology. The method is based on the modification of the values of the forces applied by taking into account the particularities of the elasticity plane models (plane strain and plane stress equations) using quasi-homothetic transformations. This approach is shown to be extremely useful when exploring the effect of the shape in front of the strength and the stiffness of vertebrate bone structures. Thus, the quasihomothetic concept is a new and interesting proposal to be used in plane elasticity models of biological, and specifically of vertebrate, structures which can be modelled as two-dimensional finite element models

Finite element analysis of the Cingulata jaw: an ecomorphological approach to Armadillo's diets

Finite element analyses (FEA) were applied to assess the lower jaw biomechanics of cingulate xenarthrans: 14 species of armadillos as well as one Pleistocene pampathere (11 extant taxa and the extinct forms Vassallia, Eutatus and Macroeuphractus). The principal goal of this work is to comparatively assess the biomechanical capabilities of the mandible based on FEA and to relate the obtained stress patterns with diet preferences and variability, in extant and extinct species through an ecomorphology approach. The results of FEA showed that omnivorous species have stronger mandibles than insectivorous species. Moreover, this latter group of species showed high variability, including some similar biomechanical features of the insectivorous Tolypeutes matacus and Chlamyphorus truncatus to those of omnivorous species, in agreement with reported diets that include items other than insects. It remains unclear the reasons behind the stronger than expected lower jaw of Dasypus kappleri. On the other hand, the very strong mandible of the fossil taxon Vassallia maxima agrees well with the proposed herbivorous diet. Moreover, Eutatus seguini yielded a stress pattern similar to Vassalia in the posterior part of the lower jaw, but resembling that of the stoutly built Macroeuphractus outesi in the anterior part. The results highlight the need for more detailed studies on the natural history of extant armadillos. FEA proved a powerful tool for biomechanical studies in a comparative framework.Peer ReviewedPostprint (published version

Accounting for differences in element size and homogeneity when comparing finite element models : armadillos as a case study

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

The intervals method : a new approach to analyse finite element outputs using multivariate statistics

Background. In this paper, we propose a new method, named the intervals' method, to analyse data from finite element models in a comparative multivariate framework. As a case study, several armadillo mandibles are analysed, showing that the proposed method is useful to distinguish and characterise biomechanical differences related to diet/ecomorphology. - Methods. The intervals' method consists of generating a set of variables, each one defined by an interval of stress values. Each variable is expressed as a percentage of the area of the mandible occupied by those stress values. Afterwards these newly generated variables can be analysed using multivariate methods. - Results. Applying this novel method to the biological case study of whether armadillo mandibles differ according to dietary groups, we show that the intervals' method is a powerful tool to characterize biomechanical performance and how this relates to different diets. This allows us to positively discriminate between specialist and generalist species. - Discussion. We show that the proposed approach is a useful methodology not affected by the characteristics of the finite element mesh. Additionally, the positive discriminating results obtained when analysing a difficult case study suggest that the proposed method could be a very useful tool for comparative studies in finite element analysis using multivariate statistical approaches