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The distribution of von Mises stress in finite element models of the skulls of Artibeus jamaicensis (top) and Cynopterus brachyotis (bottom). Models are scaled to the same surface area (189.4 mm 2 ) and loaded with the same total muscle force (100 N). Warm colors indicate high stress and cool colors indicate regions of low stress. Areas shown in white exceed the stress scale.
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In this contribution we present a method to directly compute asymptotic expansion of invariant manifolds of large finite element models from physical coordinates and their reduced-order dynamics on the manifold. We show the accuracy of the reduction on selected models, exhibiting large rotations and internal resonances. The results obtained with th...
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... We used finite-element analysis (FEA) to determine the mechanical consequences of mandible shape variation among power-amplified and non-power-amplified ants. FEA simulates in silico how three-dimensional structures respond to applied forces [22][23][24][25]. Models for FEA were based on three-dimensional surface renderings of ant mandibles generated by X-ray microtomography (microCT) (figure 2). ...
... Von Mises stress can be used to predict failure and is a good measure of structural strength. For comparison of stress between models, the ratio of force to cross-sectional area was kept constant by scaling all models to the same surface area [22]. Total strain energy is an estimate of work done deforming a structure and is related to the elastic energy stored in the structure (i.e. ...
What is the limit of animal speed and what mechanisms produce the fastest movements? More than natural history trivia, the answer provides key insight into the form-function relationship of musculoskeletal movement and can determine the outcome of predator-prey interactions. The fastest known animal movements belong to arthropods, including trap-jaw ants, mantis shrimp and froghoppers, that have incorporated latches and springs into their appendage systems to overcome the limits of muscle power. In contrast to these examples of power amplification, where separate structures act as latch and spring to accelerate an appendage, some animals use a 'snap-jaw' mechanism that incorporates the latch and spring on the accelerating appendage itself. We examined the kinematics and functional morphology of the Dracula ant, Mystrium camillae, who use a snap-jaw mechanism to quickly slide their mandibles across each other similar to a finger snap. Kinematic analysis of high-speed video revealed that snap-jaw ant mandibles complete their strike in as little as 23 μsec and reach peak velocities of 90 m s⁻¹, making them the fastest known animal appendage. Finite-element analysis demonstrated that snap-jaw mandibles were less stiff than biting non-power-amplified mandibles, consistent with their use as a flexible spring. These results extend our understanding of animal speed and demonstrate how small changes in morphology can result in dramatic differences in performance.
... Boundary and loading conditions applied to Sidneyia inexpectans follow those applied to the Limulus polyphemus model to assess shape difference. First, the S. inexpectans model was scaled up to the same volume as the L. polyphemus coxa in GEOMAGIC STUDIO [36,54,55]. Scaling up was conducted as S. inexpectans has a maximum exoskeletal length of 13 cm [22], which is much smaller than L. polyphemus (ca 24 cm without telson [56]); furthermore, extinct taxa should be scaled to the modern analogue (e.g. by scaling models to the same volume and loading parameters [55,57], or scaling muscle forces to the size of the fossil organism using a two-thirds power relationship [38]). ...
... First, the S. inexpectans model was scaled up to the same volume as the L. polyphemus coxa in GEOMAGIC STUDIO [36,54,55]. Scaling up was conducted as S. inexpectans has a maximum exoskeletal length of 13 cm [22], which is much smaller than L. polyphemus (ca 24 cm without telson [56]); furthermore, extinct taxa should be scaled to the modern analogue (e.g. by scaling models to the same volume and loading parameters [55,57], or scaling muscle forces to the size of the fossil organism using a two-thirds power relationship [38]). A trough was constructed on the dorsal side of the protopodite for muscle origins (figure 2h,i). ...
The biology of the American horseshoe crab, Limulus polyphemus, is well documented-including its dietary habits, particularly the ability to crush shell with gnathobasic walking appendages-but virtually nothing is known about the feeding biomechanics of this iconic arthropod. Limulus polyphemus is also considered the archetypal functional analogue of various extinct groups with serial gnathobasic appendages, including eurypterids, trilobites and other early arthropods, especially Sidneyia inexpectans from the mid-Cambrian (508 Myr) Burgess Shale of Canada. Exceptionally preserved specimens of S. inexpectans show evidence suggestive of durophagous (shell-crushing) tendencies-including thick gnathobasic spine cuticle and shelly gut contents-but the masticatory capabilities of this fossil species have yet to be compared with modern durophagous arthropods. Here, we use advanced computational techniques, specifically a unique application of 3D finite-element analysis (FEA), to model the feeding mechanics of L. polyphemus and S. inexpectans: the first such analyses of a modern horseshoe crab and a fossil arthropod. Results show that mechanical performance of the feeding appendages in both arthropods is remarkably similar, suggesting that S. inexpectans had similar shell-crushing capabilities to L. polyphemus This biomechanical solution to processing shelly food therefore has a history extending over 500 Myr, arising soon after the first shell-bearing animals. Arrival of durophagous predators during the early phase of animal evolution undoubtedly fuelled the Cambrian 'arms race' that involved a rapid increase in diversity, disparity and abundance of biomineralized prey species.
... Next, attachment regions of the main jawclosing muscles (temporalis, masseter, medial pterygoid) were selected in the C. c. ultima model, with the C. crocuta model as reference, by following analogous anatomical boundaries and muscle scars that delineate the attachment regions of those muscles on the fossil specimen (Supplementary Fig. 1). Muscle input forces proportional to the surface area occupied by each muscle group were created using the BoneLoad program (Grosse et al. 2007; Dumont et al. 2009), with the lower jaw propped open at 30 degrees gape (Bourke et al. 2008). Because no associated mandible was found with the fossil skull, the mandible from the C. crocuta model was scaled linearly to fit the fossil skull and used for muscle orientation estimates. ...
A central premise of bioclimatic envelope modeling is the assumption of niche conservatism. Whereas such assumptions are testable in modern populations, it is unclear whether niche conservatism holds over deeper time spans and over very large geographic ranges. Hyaenids occupied a diversity of ecological niches over time and space, and until the end-Pleistocene they occurred in Europe and most of Asia, with Asian populations of Crocuta suggested as being genetically distinct from their closest living relatives. Further, little is known regarding whether and how the dietary ecology of extinct populations of Crocuta differed from those of their extant African counterparts. Here, we use a multiproxy approach to assess an assumption of conserved dietary ecology in late Pleistocene extant spotted hyenas via finite element analysis, dental microwear texture analysis, and a novel dental macrowear method (i.e., whether teeth are minimally, moderately, or extremely worn, as defined by degree of dentin exposure) proposed here. Results from finite element simulations of the masticatory apparatus of Chinese and African Crocuta demonstrate lower skull stiffness and higher stress in the orbital region of the former when biting with carnassial teeth, suggesting that Chinese Crocuta could not process prey with the same degree of efficiency as extant Crocuta crocuta . Dental microwear texture data further support this interpretation, as Chinese Crocuta have intermediate and indistinguishable complexity values (indicative of hard-object feeding) between the extant African lion ( Panthera leo ) and extant hyenas ( C. crocuta , Hyaena hyaena , and Parahyaena brunnea ), being most similar to the omnivorous P. brunnea . The use of dental macrowear to infer dietary behavior may also be possible in extinct taxa, as evinced by dietary correlations between extant African feliforms and dental macrowear assignments. Collectively, this multiproxy analysis suggests that Chinese Crocuta may have exhibited dietary behavior distinct from that of living C. crocuta , and assumptions of niche conservatism may mask significant dietary variation in species broadly distributed in time and space.
... Similarly, model variants of MH1 were loaded with chimpanzee forces that were scaled to the volume 2/3 of MH1 UNMOD. As shown by Dumont et al. (2009), this scaling law removes size effects for a comparative analysis of stress and strain, since volume 2/3 is proportional to surface area. ...
Australopiths exhibit a number of derived facial features that are thought to strengthen the face against high and/or repetitive loads associated with a diet that included mechanically challenging foods. Here, we use finite element analysis (FEA) to test hypotheses related to the purported strengthening role of the zygomatic root and “anterior pillar” in australopiths. We modified our previously constructed models of Sts 5 (Australopithecus africanus) and MH1 (A. sediba) to differ in the morphology of the zygomatic root, including changes to both the shape and positioning of the zygomatic root complex, in addition to creating variants of Sts 5 lacking anterior pillars. We found that both an expanded zygomatic root and the presence of “anterior pillars” reinforce the face against feeding loads. We also found that strain orientations are most compatible with the hypothesis that the pillar evolved to resist loads associated with premolar loading, and that this morphology has an ancillary effect of strengthening the face during all loading regimes. These results provide support for the functional hypotheses. However, we found that an anteriorly positioned zygomatic root increases strain magnitudes even in models with an inflated/reinforced root complex. These results suggest that an anteriorly placed zygomatic root complex evolved to enhance the efficiency of bite force production while facial reinforcement features, such as the anterior pillar and the expanded zygomatic root, may have been selected for in part to compensate for the weakening effect of this facial configuration. Anat Rec, 300:171–195, 2017.
... If two models of the same shape but of different sizes have equal loads, the larger model will exhibit less stress (as stress equals force applied over the area of the model). To consider the effect of difference in shape on stress between two models, the effect of size must be controlled for, which can be achieved by keeping the ratio of force to surface area constant between the two models [43]. As PCSA values were not available for Bathyergus, surface areas for both models were calculated in Avizo, and the ratio of the two surface areas was used to scale forces applied to the Bathyergus model. ...
... This is counter to the first hypothesis that suggested the chisel-tooth digging species would exhibit lower stresses at wider gapes. However, we urge caution in interpreting this result as, although the muscle forces were scaled to surface area to enable direct comparisons of stress values [43], it only indicates how the cranial morphology responds to forces. In reality, there are likely to be large differences in the muscle force to surface area ratio, as well as potential differences in the relative proportions of the muscles and the bone material properties between the two taxa. ...
The African mole-rats (Bathyergidae) are a family of rodents highly adapted for life underground. Previous research has shown that chisel-tooth digging mole-rats (which use their incisors to dig burrows) are clearly distinguishable from scratch diggers (which only use the forelimbs to tunnel) on the basis of morphology of the skull, and that the differences are linked to the production of high bite forces and wide gapes. We hypothesized that the skull of a chisel-tooth digging mole-rat would perform better at wider gapes than that of a scratch digging mole-rat during incisor biting. To test this hypothesis, we created finite-element models of the cranium of the scratch digging Bathyergus suillus and the chisel-tooth digging Fukomys mechowii, and loaded them to simulate incisor bites at different gapes. Muscle loads were scaled such that the ratio of force to surface area was the same in both models. We measured three performance variables: overall stress across the cranium, mechanical efficiency of biting and degree of deformation across the skull. The Fukomys model had amore efficient incisor bite at all gapes, despite having greater average stress across the skull. In addition, the Fukomys model deformed less at wider gapes, whereas the Bathyergus model deformed less at narrower gapes. These properties of the cranial morphology of Fukomys and Bathyergus are congruent with their respective chisel-tooth and scratch digging behaviours and, all other factors being equal, would enable the more efficient production of bite force at wider gapes in Fukomys. However, in vivo measurements of muscle forces and activation patterns are needed to fully understand the complex biomechanics of tooth digging.
... These unscaled forces were applied to the " average " specimen (GRGL), while the six " extreme " variants were applied forces that were either scaled up or down based on differences in model size (Table 5), with size represented by model volume (i.e., the summed volume of all tet4 elements in mm 3 ) to the two-thirds power. This muscle force scaling procedure removes the effects of differences in model size on stress, strain, and strain energy density (SED) from the mechanical results (Dumont, Grosse & Slater, 2009; Strait et al., 2010). The CHIMPED model variants were also assigned forces that were scaled dependent on their size using PCSA data from an adult female chimpanzee (Strait et al., 2009; Smith et al., 2015a; Smith et al., 2015b). ...
... Importantly, however, mean element von Mises stresses were found to be relatively high in their human FEM during the second simulation, where FEMs were scaled to the same surface area and loaded with equivalent muscle forces. This is the most similar of their three scaling procedures to the scaling performed here (scaling muscle forces to model volume 2/3 ), which we believe is the best means for removing the effects of size on comparisons of mechanical performance (e.g., Dumont, Grosse & Slater, 2009; Strait et al., 2010). Bite force production and efficiency: are humans suited to produce large biting forces? ...
The evolution of the modern human ( Homo sapiens ) cranium is characterized by a reduction in the size of the feeding system, including reductions in the size of the facial skeleton, postcanine teeth, and the muscles involved in biting and chewing. The conventional view hypothesizes that gracilization of the human feeding system is related to a shift toward eating foods that were less mechanically challenging to consume and/or foods that were processed using tools before being ingested. This hypothesis predicts that human feeding systems should not be well-configured to produce forceful bites and that the cranium should be structurally weak. An alternate hypothesis, based on the observation that humans have mechanically efficient jaw adductors, states that the modern human face is adapted to generate and withstand high biting forces. We used finite element analysis (FEA) to test two opposing mechanical hypotheses: that compared to our closest living relative, chimpanzees ( Pan troglodytes ), the modern human craniofacial skeleton is (1) less well configured, or (2) better configured to generate and withstand high magnitude bite forces. We considered intraspecific variation in our examination of human feeding biomechanics by examining a sample of geographically diverse crania that differed notably in shape. We found that our biomechanical models of human crania had broadly similar mechanical behavior despite their shape variation and were, on average, less structurally stiff than the crania of chimpanzees during unilateral biting when loaded with physiologically-scaled muscle loads. Our results also show that modern humans are efficient producers of bite force, consistent with previous analyses. However, highly tensile reaction forces were generated at the working (biting) side jaw joint during unilateral molar bites in which the chewing muscles were recruited with bilateral symmetry. In life, such a configuration would have increased the risk of joint dislocation and constrained the maximum recruitment levels of the masticatory muscles on the balancing (non-biting) side of the head. Our results do not necessarily conflict with the hypothesis that anterior tooth (incisors, canines, premolars) biting could have been selectively important in humans, although the reduced size of the premolars in humans has been shown to increase the risk of tooth crown fracture. We interpret our results to suggest that human craniofacial evolution was probably not driven by selection for high magnitude unilateral biting, and that increased masticatory muscle efficiency in humans is likely to be a secondary byproduct of selection for some function unrelated to forceful biting behaviors. These results are consistent with the hypothesis that a shift to softer foods and/or the innovation of pre-oral food processing techniques relaxed selective pressures maintaining craniofacial features that favor forceful biting and chewing behaviors, leading to the characteristically small and gracile faces of modern humans.
... The FE method is a numerical method that can be used for the structural analysis of (complex) loaded structures. These structures are subdivided into a large number of small elements (a mesh), for which stresses (Von Mises stresses), strains and displacements are calculated (Bright, 2014; Dumont et al., 2009; Rayfield, 2007). Using the same method that we used to create the surface meshes of the heads, we also made surface models of the jaw cuticle for all 16 species. ...
... In the first set of FE simulations (the 'natural loading' simulations), we implemented the real muscle force for each species, based upon calculations of the head surface area (see 'Bite muscles', above). In the second set of FE simulations (the 'same size' simulations), the input force was scaled for the difference in surface area of the jaw models, to account for the size variation of the jaws (Dumont et al., 2009). In the third set of FE simulations (the 'same jaw CSA' simulations), we scaled the input force in the FE simulations according to the average cross-sectional area of the jaw ( jaw CSA; jaw cuticle volume divided by jaw length). ...
... Nevertheless, there exists a strong positive relationship between muscle force and bite force (see Fig. 3E, Fig. 4shows the material stress distribution in the 'natural loading' simulations. The region with the highest stress has the highest potential for structural failure (Dumont et al., 2009), although exceptions may occur as a result of individual variation, material fatigue, etc. The location and amplitude of the maximal material stress differ between specimens. ...
The jaws of different species of stag beetles show a large variety of shapes and sizes. The male jaws are used as weapons in fights, and they may exert a very forceful bite in some species. We investigated in 16 species whether and how their forcefulness is reflected in their jaw morphology. We found a large range of maximal muscle forces (1.8N-33N; factor 18). Species investing in large bite muscles, also have disproportionately large jaw volumes. They use this additional jaw volume to elongate their jaws, increasing their winning chances in battles. The fact that this also decreases the mechanical advantage, is largely compensated by elongated in-levers. As a result, high muscle forces are correlated with elevated bite forces (0.27N-7.6N; factor 28). Despite the large difference in forcefulness, all investigated species experience similar Von Mises stresses in their jaws while biting (29MPa-114MPa; factor 4.0; calculated with Finite Element simulations). Hence, stag beetles have successfully adapted their jaw anatomy according to their bite force in fights.
... Cennou analýzu morfologických útvarů na lebce podává deformačně-napěťová metoda konečných prvků (Dumont et al. 2009). Zkoumaná struktura (model lebky) je zobrazena jako síť, v jejíž uzlových bodech jsou zjišťovány specifické parametry (Obr. ...
Metody zabývajici se rekonstrukci výživy předků clověka se opiraji o fosilni zaznam, nabizejici ekologicke souvislosti. Tento material lze srovnavat s recentnimi organismy a modelovými situacemi. Každa z metod osvětluje cast spektra poznani jak vlastnosti stravy, ktera se nachazela v konkretnim prostředi a byla urcitým způsobem využivana, tak vlastnosti skeletu, jenž je adaptovan na ziskavani specificke stravy. Mnoha omezeni při aplikovani metod na velmi stare a fragmentarni vzorky znesnadňuji interpretaci a vedou k mnohdy obecným zavěrům, ale přesto přinasi cenna data, ktera s postupně se zlepsujicimi technologickými možnostmi rozkrývaji historii nasich davných předků a formovani dnesnich lidi.
... These unscaled forces were applied to the " average " specimen (GRGL), while the six " extreme " variants were applied forces that were either scaled up or down based on differences in model size (Table 5), with size represented by model volume (i.e., the summed volume of all tet4 elements in mm 3 ) to the two-thirds power. This muscle force scaling procedure removes the effects of differences in model size on stress, strain, and strain energy density (SED) from the mechanical results (Dumont, Grosse & Slater, 2009; Strait et al., 2010). The CHIMPED model variants were also assigned forces that were scaled dependent on their size using PCSA data from an adult female chimpanzee (Strait et al., 2009; Smith et al., 2015a; Smith et al., 2015b). ...
... Importantly, however, mean element von Mises stresses were found to be relatively high in their human FEM during the second simulation, where FEMs were scaled to the same surface area and loaded with equivalent muscle forces. This is the most similar of their three scaling procedures to the scaling performed here (scaling muscle forces to model volume 2/3 ), which we believe is the best means for removing the effects of size on comparisons of mechanical performance (e.g., Dumont, Grosse & Slater, 2009; Strait et al., 2010). Bite force production and efficiency: are humans suited to produce large biting forces? ...
The evolution of the modern human (Homo sapiens) cranium is characterized by a reduction in the size of the feeding system, including reductions in the size of the facial skeleton, postcanine teeth, and the muscles involved in biting and chewing. The conventional view hypothesizes that gracilization of the human feeding system is related to a shift toward eating foods that were less mechanically challenging to consume and/or foods that were processed using tools before being ingested. This hypothesis predicts that human feeding systems should not be well-configured to produce forceful bites and that the cranium should be structurally weak. An alternate hypothesis states that the modern human face is adapted to generate and withstand high biting forces. We used finite element analysis (FEA) to test two opposing mechanical hypotheses: that compared to our closest living relative, chimpanzees (Pan troglodytes), the modern human craniofacial skeleton is 1) less well configured, or 2) better configured to generate and withstand high magnitude bite forces. We considered intraspecific variation in our examination of human feeding biomechanics by examining a sample of geographically diverse crania that differed notably in shape. We found that our biomechanical models of human crania had broadly similar mechanical behavior despite their shape variation and were, on average, less structurally stiff than the crania of chimpanzees during unilateral biting when loaded with physiologically-scaled muscle loads. Our results also show that modern humans are efficient producers of bite force, consistent with previous analyses. However, highly tensile reaction forces were generated at the working (biting) side jaw joint during unilateral molar bites in which the chewing muscles were recruited with bilateral symmetry. In life, such a configuration would have increased the risk of joint dislocation and constrained the maximum recruitment levels of the masticatory muscles on the balancing (non-biting) side of the head. Our results do not necessarily conflict with the hypothesis that anterior tooth (incisors, canines, premolars) biting could have been selectively important in humans, although the reduced size of the premolars in humans has been shown to increase the risk of tooth crown fracture. We interpret our results to suggest that human craniofacial evolution was probably not driven by selection for high magnitude unilateral biting, and that increased masticatory muscle efficiency in humans is likely to be a secondary byproduct of selection for some function unrelated to forceful biting behaviors. These results are consistent with the hypothesis that a shift to softer foods and/or the innovation of pre-oral food processing techniques relaxed selective pressures maintaining craniofacial features favoring forceful biting and chewing behaviors, leading to the characteristically small and gracile faces of modern humans.
... These unscaled forces were applied to the " average " specimen (GRGL), while the six " extreme " variants were applied forces that were either scaled up or down based on differences in model size (Table 5), with size represented by model volume (i.e., the summed volume of all tet4 elements in mm 3 ) to the two-thirds power. This muscle force scaling procedure removes the effects of differences in model size on stress, strain, and strain energy density (SED) from the mechanical results (Dumont, Grosse & Slater, 2009; Strait et al., 2010). The CHIMPED model variants were also assigned forces that were scaled dependent on their size using PCSA data from an adult female chimpanzee (Strait et al., 2009; Smith et al., 2015a; Smith et al., 2015b). ...
... Importantly, however, mean element von Mises stresses were found to be relatively high in their human FEM during the second simulation, where FEMs were scaled to the same surface area and loaded with equivalent muscle forces. This is the most similar of their three scaling procedures to the scaling performed here (scaling muscle forces to model volume 2/3 ), which we believe is the best means for removing the effects of size on comparisons of mechanical performance (e.g., Dumont, Grosse & Slater, 2009; Strait et al., 2010). Bite force production and efficiency: are humans suited to produce large biting forces? ...
The evolution of the modern human (Homo sapiens) cranium is characterized by a reduction in the size of the feeding system, including reductions in the size of the facial skeleton, postcanine teeth, and the muscles involved in biting and chewing. The conventional view hypothesizes that gracilization of the human feeding system is related to a shift toward eating foods that were less mechanically challenging to consume and/or foods that were processed using tools before being ingested. This hypothesis predicts that human feeding systems should not be well-configured to produce forceful bites and that the cranium should be structurally weak. An alternate hypothesis states that the modern human face is adapted to generate and withstand high biting forces. We used finite element analysis (FEA) to test two opposing mechanical hypotheses: that compared to our closest living relative, chimpanzees (Pan troglodytes), the modern human craniofacial skeleton is 1) less well configured, or 2) better configured to generate and withstand high magnitude bite forces. We considered intraspecific variation in our examination of human feeding biomechanics by examining a sample of geographically diverse crania that differed notably in shape. We found that our biomechanical models of human crania had broadly similar mechanical behavior despite their shape variation and were, on average, less structurally stiff than the crania of chimpanzees during unilateral biting when loaded with physiologically-scaled muscle loads. Our results also show that modern humans are efficient producers of bite force, consistent with previous analyses. However, highly tensile reaction forces were generated at the working (biting) side jaw joint during unilateral molar bites in which the chewing muscles were recruited with bilateral symmetry. In life, such a configuration would have increased the risk of joint dislocation and constrained the maximum recruitment levels of the masticatory muscles on the balancing (non-biting) side of the head. Our results do not necessarily conflict with the hypothesis that anterior tooth (incisors, canines, premolars) biting could have been selectively important in humans, although the reduced size of the premolars in humans has been shown to increase the risk of tooth crown fracture. We interpret our results to suggest that human craniofacial evolution was probably not driven by selection for high magnitude unilateral biting, and that increased masticatory muscle efficiency in humans is likely to be a secondary byproduct of selection for some function unrelated to forceful biting behaviors. These results are consistent with the hypothesis that a shift to softer foods and/or the innovation of pre-oral food processing techniques relaxed selective pressures maintaining craniofacial features favoring forceful biting and chewing behaviors, leading to the characteristically small and gracile faces of modern humans.
