Finite-element modelling reveals force modulation of jaw adductors in stag beetles

Abstract

Male stag beetles carry large and heavy mandibles that arose through sexual selection over mating rights. Although the mandibles of Cyclommatus metallifer males are used in pugnacious fights, they are surprisingly slender. Our bite force measurements show a muscle force reduction of 18% for tip biting when compared with bites with the teeth located halfway along the mandibles. This suggests a behavioural adaptation to prevent failure. We confirmed this by constructing finite-element (FE) models that mimic both natural bite situations as well as the hypothetical situation of tip biting without muscle force modulation. These models, based on micro-CT images, investigate the material stresses in the mandibles for different combinations of bite location and muscle force. Young's modulus of the cuticle was experimentally determined to be 5.1 GPa with the double indentation method, and the model was validated by digital image correlation on living beetles. FE analysis proves to be a valuable tool in the investigation of the trade-offs of (animal) weapon morphology and usage. Furthermore, the demonstrated bite force modulation in male stag beetles suggests the presence of mechanosensors inside the armature.

Jaw morphology and fighting forces in stag beetles

“…The jaw material was modelled to be linearly elastic and isotropic, with a Young's modulus of 5.1 GPa and a Poisson ratio of 0.3. These material properties are the same as those measured for C. metallifer (Goyens et al, 2014b). The FE model of C. metallifer was previously successfully validated with an experimental measurement of the jaw deformation during biting using an optical technique (digital image correlation; Goyens et al, 2014b).…”

“…These material properties are the same as those measured for C. metallifer (Goyens et al, 2014b). The FE model of C. metallifer was previously successfully validated with an experimental measurement of the jaw deformation during biting using an optical technique (digital image correlation; Goyens et al, 2014b). This ensures that the model accurately reproduces the biological reality (Bright, 2014;Rayfield, 2007).…”

“…5A-C, respectively). Alternatively, they may reduce their failure risk by modulating their bite muscle force (as C. metallifer is capable of doing; Goyens et al, 2014b) or by enhanced material properties. Further, it can of course not be excluded that our assumptions regarding the size and stress of the bite muscles are less appropriate for these species.…”

“…The size and stress of the bite muscle and the Young's modulus of the jaw exoskeleton are only known for C. metallifer (Goyens et al, 2014b). Based on the finding that these properties do not differ between sexes (i.e.…”

“…This ensures that the model accurately reproduces the biological reality (Bright, 2014;Rayfield, 2007). For a detailed description of the model and its validation, see Goyens et al (2014b). A muscle force was applied at the muscle attachment site, which caused a moment about the jaw hinge.…”