Computational mechanics are able to reconstruct deformation, strain and stress in a digital structure after simulating a loading scenario by means of the finite element method and is has been extensively used in testing biomechanical hypothesis in functional morphology (Richmond et al., 2005). In particular, there are several different approaches that have been applied to analyse the results derived from mandibular mechanics to test theses hypotheses. While some works analyze stress results (Tseng et al., 2017) other focus on strain results (Panagiotopoulou et al., 2017). When using linear and elastic properties, it has been shown that both values are proportional and that the results of the distributions along the mandible are the same. This is due to the application of Hooke’s Law, which establishes a proportional relation between stress and strain. In fact, when linear and elastic material properties are assumed in a comparative analysis -comparing the performance of different mandibles from different taxa-, the effect of the elastic modulus of the material is irrelevant over stress patterns and strain patterns and comparative studies are allowed to be done without considering the real elastic materials properties (Gil et al., 2015). Therefore, most of the debate between the use of stress and strain is sterile when we are comparing the performance in different elastic models.
In this case, both stress and strain are accepted when comparing models below the fracture point, but, when we want to extrapolate these models to study fracture mechanics, a new debate is triggered: Is it stress or strain that causes failure? Probably the longest standing issue regarding failure criteria is whether they should be expressed in terms of stresses or in strains. In engineering, the most used form is the von Mises criterion expressed in terms of stress. Other criteria that are used are the maximum shear stress criterion (Tresca), the maximum normal stress criterion (Rankine) or the maximum normal strain criterion (Rankine). Despite the von Mises stress being a stress-designed criterion based on the maximum distortion of the strain energy, the stress-strain relations for isotropy can be used to convert the von Mises criterion in terms of stresses into a metric expressed in terms of strains. Therefore, it is usual to find in the literature the so-called “von Mises strain”. The transformation from stress to strain can be easily done using a simple mathematical procedure, but this does not eradicate the incontrovertible assumption that considers that all criteria can be switched from stress to strain (and vice versa). This is not always possible, especially when considering anisotropic material properties, but equally so for some isotropic cases. As an example, the maximum normal stress criterion and the maximum normal strain criterion take different forms when interconverted.
In my works, stress is taken as the fundamental form to be used when focusing on failure criteria. It is done because stress must be used if one wishes to have compatibility with fracture mechanics in the brittle range and with dislocation dynamics in the ductile range. Both theories require formulations in terms of stress. Moreover, in my comparative works in mandibles (Marcé‐Nogué, 2020), I understand that under equivalent loads, these stress patterns as a sign of the relative strength. According to the definition of strength in the Collins Dictionary “The strength of an object or material is its ability to be treated roughly, or to carry heavy weights, without being damaged or destroyed”. Therefore, it has sense that if we assume that more robust or stronger mandibles would be needed for processing harder food items, these mandibles should be expected to be weaker and, as a sign of strength, we use stress instead of strain to evaluate them, with higher stress indicating a weaker mandible.
On the other hand, strain has been shown valuable when comparing simulations results with experimental data (Bright and Rayfield, 2011), since strain gauges are commonly used in experimental settings. These electrical components experience changes in length as changes in resistance and this property can be used to measure strain on a bone surface and compare it with the FEA results obtained. Therefore, strain is the appropriate metric to compare in-vivo and in-silico data.
Text modified from “Marcé-Nogué, J. (2020) Mandibular biomechanics as a key factor to understand diet in mammals”.
Bright, J.A., Rayfield, E.J., 2011. Sensitivity and ex vivo validation of finite element models of the domestic pig cranium. Journal of Anatomy. 219, 456–471. https://doi.org/10.1111/j.1469-7580.2011.01408.x
Gil, L., Marcé‐Nogué, J., Sánchez, M., 2015. Insights into the controversy over materials data for the comparison of biomechanical performance in vertebrate. Palaeontologia Electronica. 287. https://doi.org/10.26879/509
Marcé‐Nogué, J., 2020. Mandibular biomechanics as a key factor to understand diet in mammals. In: Martin, T., W.V. Koenigswald (Eds.), Mammalian Teeth – Form and Function. Verlag Dr. Friedrich Pfeil, München, pp. 54–80. https://doi.org/10.23788/mammteeth.04
Panagiotopoulou, O., Iriarte-Diaz, J., Wilshin, S., Dechow, P.C., Taylor, A.B., Mehari Abraha, H., Aljunid, S.F., Ross, C.F., 2017. In vivo bone strain and finite element modeling of a rhesus macaque mandible during mastication. Zoology. 124, 13–29. https://doi.org/10.1016/j.zool.2017.08.010
Richmond, B.G., Wright, B.W., Grosse, I., Dechow, P.C., Ross, C.F., Spencer, M.A., Strait, D.S., 2005. Finite element analysis in functional morphology. The Anatomical Record Part A: Discoveries in Molecular, Cellular, and Evolutionary Biology. 283A, 259–274. https://doi.org/10.1002/ar.a.20169
Tseng, Z.J., Su, D.F., Wang, X., White, S.C., Ji, X., 2017. Feeding capability in the extinct giant Siamogale melilutra and comparative mandibular biomechanics of living Lutrinae. Scientific Reports. 7, 15225. https://doi.org/10.1038/s41598-017-15391-9
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