Finite element analysis (FEA) is a technique that reconstructs stress, strain, and deformation in a digital structure. Although commonplace in engineering and orthopedic science for more than 30 years, only recently has it begun to be adopted in the zoological and paleontological sciences to address questions of organismal morphology, function, and evolution. Current research tends to focus on either deductive studies that assume a close relationship between form and function or inductive studies that aim to test this relationship, although explicit hypothesis-testing bridges these two standpoints. Validation studies have shown congruence between in vivo or in vitro strain and FE-inferred strain. Future validation work on a broad range of taxa will assist in phylogenetically bracketing our extinct animal FE-models to increase confidence in our input parameters, although currently, FEA has much potential in addressing questions of form-function relationships, providing appropriate questions are asked of the existing data.

Mechanical comparison of different species is performed with the help of computational tools like Finite Element Analysis FEA. In palaeobiology it is common to consider bone like an isotropic material for simulations but often real data of bone materials is impossible to know. This work investigates the influence of choice of bone materials properties over the results of simulations, showing when and why the materials data are relevant and when the selection of these data becomes irrelevant. With a theoretical approach from continuum mechanics and with a practical example the relationship between material data and comparative metrics like stress, strains and displacements is discussed. When linear and elastic material properties are assumed in a comparative analysis, the effect of the elastic modulus of the material is irrelevant over stress patterns. This statement is true for homogeneous and inhomogeneous materials, in this last case the proportion between the different materials properties must kept constant. In the case of the strains and displacements, there is an inverse proportionality kept constant, between the values of the metrics and the changes in the elastic modulus. These properties allow comparative studies without considering the real elastic materials properties.

In recent years finite element analysis (FEA) has emerged as a useful tool for the analysis of skeletal form-function relationships. While this approach has obvious appeal for the study of fossil specimens, such material is often fragmentary with disrupted internal architecture and can contain matrix that leads to errors in accurate segmentation. Here we examine the effects of varying the detail of segmentation and material properties of teeth on the performance of a finite element model of a Macaca fascicularis cranium within a comparative functional framework. Cranial deformations were compared using strain maps to assess differences in strain contours and Procrustes size and shape analyses, from geometric morphometrics, were employed to compare large scale deformations. We show that a macaque model subjected to biting can be made solid, and teeth altered in material properties, with minimal impact on large scale modes of deformation. The models clustered tightly by bite point rather than by modeling simplification approach, and fell out as being distinct from another species. However localized fluctuations in predicted strain magnitudes were recorded with different modeling approaches, particularly over the alveolar region. This study indicates that, while any model simplification should be undertaken with care and attention to its effects, future applications of FEA to fossils with unknown internal architecture may produce reliable results with regard to general modes of deformation, even when detail of internal bone architecture cannot be reliably modeled.

During the last ten years, techniques from Computational Mechanics, as the Finite Element Analysis, has been started to be used in Biology and Palaeontology. Here we summarize how the utilization of these engineering techniques has helped in the paleoecological and paleobiological study of vertebrates and how the creation of multidisciplinary research groups from Palaeontology and Engineering has importantly contributed to the study of vertebrate alaeontology and to the apparition of new challenges in this field.

Finite-element (FE) analysis has been used in palaeobiology to assess the mechanical performance of the jaw. It uses two types of models: tomography-based three-dimensional (3D) models (very accurate, not always accessible) and two-dimensional (2D) models (quick and easy to build, good for broad-scale studies, cannot obtain absolute stress and strain values). Here, we introduce extruded FE models, which provide fairly accurate mechanical performance results, while remaining low-cost, quick and easy to build. These are simplified 3D models built from lateral outlines of a relatively flat jaw and extruded to its average width. There are two types: extruded (flat mediolaterally) and enhanced extruded (accounts for width differences in the ascending ramus). Here, we compare mechanical performance values resulting from four types of FE models (i.e. tomography-based 3D, extruded, enhanced extruded and 2D) in Morganucodon and Kuehneotherium . In terms of absolute values, both types of extr...

 Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution com- puted tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (smin) were on average 142 per cent (+28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two- tailed p 1⁄4 0.03, r2 1⁄4 0.56). Under bending, FEA values of maximum principal stress (smax) and beam theory values differed on average by 12 per cent (+4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p 1⁄4 0.02, r2 1⁄4 0.62). In torsion, assuming maximum stress values occurred at the location of mini- mum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of ttorsion were on average 14 per cent (+5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.

Finite element (FE) analysis is becoming a frequently used tool for exploring the craniofacial biomechanics of extant and extinct vertebrates. Crucial to the application of the FE analysis is the knowledge of how well FE results replicate reality. Here I present a study investigating how accurately FE models can predict experimentally derived strain in the mandible of the ostrich Struthio camelus, when both the model and the jaw are subject to identical conditions in an in-vitro loading environment. Three isolated ostrich mandibles were loaded hydraulically at the beak tip with forces similar to those measured during force transducer pecking experiments. Strains were recorded at four gauge sites at the dorsal and ventral dentary, and medial and lateral surangular. Specimen-specific FE models were created from computed tomography scans of each ostrich and loaded in an identical fashion as in the in-vitro test. The results show that the strain magnitudes, orientation, patterns and maximum : minimum principal strain ratios are predicted very closely at the dentary gauge sites, even though the FE models have isotropic and homogeneous material properties and solid internal geometry. Although the strain magnitudes are predicted at the postdentary sites, the strain orientations and ratios are inaccurate. This mismatch between the dentary and postdentary predictions may be due to the presence of intramandibular sutures or the greater amount of cancellous bone present in the postdentary region of the mandible and requires further study. This study highlights the predictive potential of even simple FE models for studies in extant and extinct vertebrates, but also emphasizes the importance of geometry and sutures. It raises the question of whether different parameters are of lesser or greater importance to FE validation for different taxonomic groups.