Plane models of 11 mandibles of Cingulata (
Table 1), each one corresponding to a different species, were created according to the methodology summarized by Fortuny et al. (2012) (
link). The models were created using the ANSYS FEA Package (Ansys Inc.) v.15 for Windows 7 (64-bit system) to obtain the von Mises stress distribution.
Two main masticatory muscles (i.e., temporalis and masseter) were included in the model as a vector between the centroid of the muscular attachment in the mandible and the centroid of the equivalent muscle attachment in the skull following the modelling approach used in Serrano-Fochs et al. (2015) (
link). To compare the models, a scaling of the values of the forces was applied according to a quasi-homothetic transformation in the FEA models (Marcé-Nogué et al., 2013 ) using the plane model of
Chaetophractus villosus as a reference. This method corresponds to an adaptation of the scaling methods proposed by Wroe, McHenry & Thomason (2005) (
link) and Dumont, Grosse & Slater (2009) (
link) for plane models. This procedure was performed to apply the appropriate force in each model, thus allowing the comparison of the stress results when the specimens differ in size.
The information for each analysed species regarding the area of the mandible, insertion areas, forces (musculature applied force per unit area (N/mm
2)), thickness and the scale factor in the quasi-homothetic transformation can be found in
Table 1.
The boundary conditions were defined and placed to represent the loads, displacements, and constraining anchors that the structure (i.e., mandible) experiences during its function. The mandible was constrained in the
x and
y direction at the most anterior part and fixed in the
x and
y directions on the condyle at the level of the mandibular notch (
Fig. 1) following the procedures described in Serrano-Fochs et al. (2015) (
link) and Marcé-Nogué et al. (2016) .
Isotropic and linear elastic properties were assumed for the bone. In the absence of data for Cingulata or any other closer relative, as well as lacking data for any mammalian clade with a similarly shaped jaw, we decided to apply the mandibular material properties of
Macaca rhesus:
E (Elasticity Modulus) = 21,000 MPa and
v (Poisson coefficient) = 0.45 (Dechow & Hylander, 2000 (
link)). We chose the available properties of
Macaca rhesus because it has a wide range of habitats and diet which resembles omnivorous or generalist insectivorous armadillos (Richard, Goldstein & Dewar, 1989 (
link)). In addition, it has been shown that in a comparative analysis these values are not crucial (See Gil, Marcé-Nogué & Sánchez, 2015 for discussion).
As primary data, we obtained the von Mises stress distribution of each one of the analysed species. Von Mises stress is an isotropic criterion used to predict the yielding of ductile materials determining an equivalent state of stress (Reddy, 2008 ). Considering bone as a ductile material (Dumont, Grosse & Slater, 2009 (
link)) and according to Doblaré, García & Gómez (2004) (
link) when isotropic material properties are defined in cortical bone, the von Mises criterion is the most adequate for comparing stress states.
Marcé-Nogué J., De Esteban-Trivigno S., Püschel T.A, & Fortuny J. (2017). The intervals method: a new approach to analyse finite element outputs using multivariate statistics. PeerJ, 5, e3793.