L. Margetts

The 'Goldilocks' effect: preservation bias in vertebrate track assemblages

Finite-element analysis was used to investigate the extent of bias in the ichnological fossil record attributable to body mass. Virtual tracks were simulated for four dinosaur taxa of different sizes (Struthiomimus, Tyrannosaurus, Brachiosaurus and Edmontosaurus), in a range of substrate conditions. Outlines of autopodia were generated based upon osteology and published soft-tissue reconstructions. Loads were applied vertically to the feet equivalent to the weight of the animal, and distributed accordingly to fore- and hindlimbs where relevant. Ideal, semi-infinite elastic–plastic substrates displayed a ‘Goldilocks’ quality where only a narrow range of loads could produce tracks, given that small animals failed to indent the substrate, and larger animals would be unable to traverse the area without becoming mired. If a firm subsurface layer is assumed, a more complete assemblage is possible, though there is a strong bias towards larger, heavier animals. The depths of fossil tracks within an assemblage may indicate thicknesses of mechanically distinct substrate layers at the time of track formation, even when the lithified strata appear compositionally homogeneous. This work increases the effectiveness of using vertebrate tracks as palaeoenvironmental indicators in terms of inferring substrate conditions at the time of track formation. Additionally, simulated undertracks are examined, and it is shown that complex deformation beneath the foot may not be indicative of limb kinematics as has been previously interpreted, but instead ridges and undulations at the base of a track may be a function of sediment displacement vectors and pedal morphology.

Fossil vertebrate tracks as paleopenetrometers: Confounding effects of foot morphology

Abstract The depth to which a vertebrate track is indented can provide a wealth of information, being a direct result of the weight, duty factor, and limb kinematics of the animal as well as media ( =  substrate or sediment) consistency. In order to recreate the formation of the track and elucidate media consistency at the time of track formation, such factors as animal mass, duty factor, and foot morphology must be taken into consideration. This study uses Finite Element Analysis and physical modeling to demonstrate for the first time that the shape of the foot is an important factor that influences the depth to which the sediment is penetrated. In cohesive sediment, less compact morphology allows more sediment to move vertically upwards at the edges of the foot, dissipating force at the surface, and retarding transmission of load vertically down into the sediment. The reverse of this effect is seen in noncohesive sediment. Foot morphology, therefore, has a direct impact on preservation potential, both of surface tracks and undertracks, that is irrespective of the pressure exerted on the sediment surface by the foot and independent of mass and duty factor.

March of the Titans: The Locomotor Capabilities of Sauropod Dinosaurs

Sauropod dinosaurs are the largest terrestrial vertebrate to have lived on Earth. This size must have posed special challenges for the musculoskeletal system. Scaling theory shows that body mass and hence the loads that must be overcome increases with body size more rapidly than either the ability of the muscles to generate force, or the ability of the skeleton to support these loads. Here we demonstrate how one of the very largest sauropods, Argentinosaurus huinculensis (40 metres long, weighing 83 tonnes), may have moved. A musculoskeletal model was generated using data captured by laser scanning a mounted skeleton and assigning muscle properties based on comparative data from living animals. Locomotion is generated using forward dynamic simulation to calculate the accelerations produced by the muscle forces, coupled with machine learning techniques to find a control pattern that minimises metabolic cost. The simulation demonstrates that at such vast body size, joint range of motion needs to be restricted to allow sufficient force generation for an achievable muscle mass. However when this is done, a perfectly plausible gait can be generated relatively easily. Whilst this model represents the best current simulation of the gait of these giant animals, it is likely that there are as yet unknown mechanical mechanisms, possibly based on passive elastic structures that should be incorporated to increase the efficiency of the animals locomotion. It is certainly the case that these would need to be incorporated into the model to properly assess the full locomotor capabilities of the animal.

Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones

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 computed 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 (σmin) 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 = 0.03, r2 = 0.56). Under bending, FEA values of maximum principal stress (σmax) 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 = 0.02, r2 = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τtorsion 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.

Evaluating the macroscopic yield behaviour of trabecular bone using a nonlinear homogenisation approach

Computational homogenisation approaches using high resolution images and finite element (FE) modelling have been extensively employed to evaluate the anisotropic elastic properties of trabecular bone. The aim of this study was to extend its application to characterise the macroscopic yield behaviour of trabecular bone. Twenty trabecular bone samples were scanned using a micro-computed tomography device, converted to voxelised FE meshes and subjected to 160 load cases each (to define a homogenised multiaxial yield surface which represents several possible strain combinations). Simulations were carried out using a parallel code developed in-house. The nonlinear algorithms included both geometrical and material nonlinearities. The study found that for tension-tension and compression-compression regimes in normal strain space, the yield strains have an isotropic behaviour. However, in the tension-compression quadrants, pure shear and combined normal-shear planes, the macroscopic strain norms at yield have a relatively large variation. Also, our treatment of clockwise and counter-clockwise shears as separate loading cases showed that the differences in these two directions cannot be ignored. A quadric yield surface, used to evaluate the goodness of fit, showed that an isotropic criterion adequately represents yield in strain space though errors with orthotropic and anisotropic criteria are slightly smaller. Consequently, although the isotropic yield surface presents itself as the most suitable assumption, it may not work well for all load cases. This work provides a comprehensive assessment of material symmetries of trabecular bone at the macroscale and describes in detail its macroscopic yield and its underlying microscopic mechanics.

Exploring Diagonal Gait Using a Forward Dynamic Three-Dimensional Chimpanzee Simulation

Primates are unusual among terrestrial quadrupedal mammals in that at walking speeds they prefer diagonal rather than lateral gaits. A number of reasons have been proposed for this preference in relation to the arboreal ancestry of modern primates: stability, energetic cost, neural control, skeletal loading, and limb interference avoiding. However, this is a difficult question to explore experimentally since most primates only occasionally use anything other than diagonal gaits. An alternative approach is to produce biologically realistic computer simulations of primate gait that enable the constraints of biomechanical loading and the energetics of different modes of locomotion to be explored. In this paper we describe such a model for the chimpanzee Pan troglodytes. The simulation is able to produce spontaneous quadrupedal locomotion, and the footfall sequences generated are split between lateral and diagonal footfall sequences with no obvious energetic benefit associated with either option. However, out of 10 successful simulation runs, 5 were lateral sequence/lateral couplet gaits indicating a preference for a specific lateral footfall sequence with a relatively tightly constrained phase difference between the fore- and hindlimbs. This suggests that the choice of diagonal walking gaits in chimpanzees is not a simple mechanical phenomenon and that diagonal walking gaits in primates are selected for by multiple factors.

Building a Digital Wind Farm

The purpose of this paper is to provide a high level, holistic overview of the work being undertaken in the wind energy industry. It summarises the main techniques used to simulate both aerodynamic and structural issues associated with wind turbines and farms. The motivation behind this paper is to provide new researchers with an outlook of the modelling and simulation landscape, whilst highlighting the trends and direction research is taking. Each section summarises an individual area of simulation and modelling, covering the important historical research findings and a comprehensive analysis of recent work. This segregated approach emphasises the key components of wind energy. Topics range in geometric scales and detail, ranging from atmospheric boundary layer modelling, to fatigue and fracture in the turbine blades. More recent studies have begun to combine a range of scales and physics to better approximate real systems and provide higher fidelity and accurate analyses to manufacturers and companies. This paper shows a clear trend towards coupling both scales and physics into singular models utilising high performance computing system.

Towards mechanism-based simulation of impact damage using exascale computing

Over the past 60 years, the finite element method has been very successful in modelling deformation in engineering structures. However the method requires the definition of constitutive models that represent the response of the material to applied loads. There are two issues. Firstly, the models are often difficult to define. Secondly, there is often no physical connection between the models and the mechanisms that accommodate deformation. In this paper, we present a potentially disruptive two-level strategy which couples the finite element method at the macroscale with cellular automata at the mesoscale. The cellular automata are used to simulate mechanisms, such as crack propagation. The stress-strain relationship emerges as a continuum mechanics scale interpretation of changes at the micro- and meso-scales. Iterative two-way updating between the cellular automata and finite elements drives the simulation forward as the material undergoes progressive damage at high strain rates. The strategy is particul...

Use of massively parallel computing to improve modelling accuracy within the nuclear sector

The extreme environments found within the nuclear sector impose large safety factors on modelling analyses to ensure components operate in their desired manner. Improving analysis accuracy has clear value of increasing the design space that could lead to greater efficiency and reliability. Novel materials for new reactor designs often exhibit non-linear behaviour; additionally material properties evolve due to in-service damage a combination that is difficult to model accurately. To better describe these complex behaviours a range of modelling techniques previously under-pursued due to computational expense are being developed. This work presents recent advancements in three techniques: Uncertainty quantification (UQ); Cellular automata finite element (CAFE); Image based finite element methods (IBFEM). Case studies are presented demonstrating their suitability for use in nuclear engineering made possible by advancements in parallel computing hardware that is projected to be available for industry within the next decade costing of the order of

Towards mechanism-based simulation of impact damage using Exascale computing

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