Exegesis of Sect. III.B from “Fundamentals of the Mechanics of Continua” by E. Hellinger

This is our third and last exegetic essay on the fundamental review article DIE ALLGEMEINEN ANSÄTZE DER MECHANIK DER KONTINUA in the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. IV-4, Hft. 5 (1913) by Ernst Hellinger which contains the translation and the commentary of the remaining text starting from p. 663. The six subsections, No. 9–15, deal with the applications of the previously developed conceptual tools to formulate: an effective theory of elasticity, the dynamics of ideal fluids, models for internal friction and elastic hysteresis, a theory of capillarity, optics, the fundamental equations of electrodynamics, an introduction of the thermodynamical foundations and the relationship between the theory of continua and the theory of relativity. Hellinger refers to relevant literature while consolidating in an effective way the contemporary knowledge in 1913. Considering notational differences as being irrelevant for the characterization of the presented scientific content, Hellinger's article shows that an effective compendium of a large part of the insights given in Truesdell and Toupin and Truesdell and Noll has already been available in 1913. We include in this paper an assessment of the different roles played by pioneers, who are innovating their scientific discipline, and by erudite scholars whose role consists in re-ordering existent knowledge and advertising to a wider audience the most important technical results already obtained in a given discipline

A computational neuromuscular model of the human upper airway with application to the study of obstructive sleep apnoea

Includes bibliographical references.Numerous challenges are faced in investigations aimed at developing a better understanding of the pathophysiology of obstructive sleep apnoea. The anatomy of the tongue and other upper airway tissues, and the ability to model their behaviour, is central to such investigations. In this thesis, details of the construction and development of a three-dimensional finite element model of soft tissues of the human upper airway, as well as a simplified fluid model of the airway, are provided. The anatomical data was obtained from the Visible Human Project, and its underlying micro-histological data describing tongue musculature were also extracted from the same source and incorporated into the model. An overview of the mathematical models used to describe tissue behaviour, both at a macro- and microscopic level, is given. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group to a priori unknown external forces was determined through the use of a genetic algorithm-based neural control model. The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. The response of the various muscles of the tongue to the complex loading developed during breathing is determined, with a particular focus being placed to that of the genioglossus. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus. A comparison is then made to the response determined under quasi-static conditions using the pressure distribution extracted from computational fluid-dynamics results. An analytical model describing the time-dependent response of the components of the tongue musculature most active during oral breathing is developed and validated. It is then modified to simulate the activity of the tongue during sleep and under conditions relating to various possible neural and physiological pathologies. The retroglossal movement of the tongue resulting from the pathologies is quantified and their role in the potential to induce airway collapse is discussed

A variational model of fracture for tearing brittle thin sheets

Tearing of brittle thin elastic sheets, possibly adhered to a substrate, involves a rich interplay between nonlinear elasticity, geometry, adhesion, and fracture mechanics. In addition to its intrinsic and practical interest, tearing of thin sheets has helped elucidate fundamental aspects of fracture mechanics including the mechanism of crack path selection. A wealth of experimental observations in different experimental setups is available, which has been often rationalized with insightful yet simplified theoretical models based on energetic considerations. In contrast, no computational method has addressed tearing in brittle thin elastic sheets. Here, motivated by the variational nature of simplified models that successfully explain crack paths in tearing sheets, we present a variational phase-field model of fracture coupled to a nonlinear Koiter thin shell model including stretching and bending. We show that this general yet straightforward approach is able to reproduce the observed phenomenology, including spiral or power-law crack paths in free standing films, or converging/diverging cracks in thin films adhered to negatively/positively curved surfaces, a scenario not amenable to simple models. Turning to more quantitative experiments on thin sheets adhered to planar surfaces, our simulations allow us to examine the boundaries of existing theories and suggest that homogeneous damage induced by moving folds is responsible for a systematic discrepancy between theory and experiments. Thus, our computational approach to tearing provides a new tool to understand these complex processes involving fracture, geometric nonlinearity and delamination, complementing experiments and simplified theories.Fil: Li, Bin. Universidad Politécnica de Catalunya; España. Sorbonne Université; Francia. Centre National de la Recherche Scientifique; FranciaFil: Millán, Raúl Daniel. Universidad Nacional de Cuyo. Facultad de Ciencias Aplicadas a la Industria; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Politécnica de Catalunya; EspañaFil: Torres Sánchez, Alejandro. Universidad Politécnica de Catalunya; EspañaFil: Roman, Benoît. Centre National de la Recherche Scientifique; Francia. Sorbonne Université; FranciaFil: Arroyo Balaguer, Marino. Universidad Politécnica de Catalunya; Españ

Oral processing of micro-aerated chocolates: a computational mechanics, rheological and tribological study

The emerging need to reduce the calorific value of foods, while simultaneously improving the consumer perception drives the quest for food structures that satisfy both criteria. Aiming to shed light on the influence that micro-aeration has on the breakdown of chocolate during the early stages of the oral processing, this study focuses on the investigation of the effect that micro-aeration has from a computational mechanics, rheological and tribological perspective. Firstly, several constitutive models are investigated and compared in both the explicit and implicit Finite Element (FE) frameworks and are calibrated using experimental results from mechanical testing conducted in a parallel PhD study. Afterwards, a non-local damage evolution law is presented providing mesh objectivity in both microscopic and macroscopic FE calculations. The constitutive model coupled with the non-local damage model, implemented in an ABAQUS VUMAT subroutine, is then applied in a micromechanical model for the prediction of the elastic, plastic, and fracture properties of micro-aerated chocolate using as input the properties of the non-aerated solid chocolate. Different boundary conditions are employed in both monodisperse and polydisperse dispersion of pores for the estimation of a representative volume element that is used for the estimation of the macroscopic properties. Overall, micro-aeration reduces the elastic, plastic and fracture properties of the chocolate, whereas the polydisperse dispersions provide a better estimation for the equivalent fracture strain at failure. The estimated values are applied in macroscopic FE simulations of the first bite, where the force-displacement FE results match the experimental data obtained by a replicate of the first bite model with 3D printed molar teeth. The forces needed for the fragmentation of chocolate reduce with micro-aeration level as shown from the experiments and validated by the FE simulations, whereas the in-vivo and in-vitro fragmentation studies show that micro-aerated chocolate breaks into more and smaller pieces. Furthermore, the effect of the micro-aeration on the rheological properties of the molten chocolate with and without the influence of artificial saliva is investigated. Micro-aeration increases viscosity values while the storage and loss moduli decrease. From a tribological perspective, a new bench test rig to measure friction in the simulated tongue-palate contact is developed. The test was applied to molten chocolate samples with and without artificial saliva. Friction was measured over the first few rubbing cycles, simulating mechanical degradation of chocolate in the tongue-palate region. The coefficient of friction increases with cocoa solids percentage and decreases with increasing micro-aeration level. The presence of artificial saliva in the contact reduced the friction for all chocolate samples, however, the relative ranking remained the same. Finally, the link between structure, material properties and sensory perception is given through a comparison with data from sensory tests. The current study can be used as a cost efficient tool for the investigation of new food structures that reduce the calorific value while enhancing the taste perception.Open Acces

Phase Field Modeling of Cracks in Ice

Calving of iceberg at ice shelves and floating glacier tongues is a poorly understood process, hence a physically motivated calving law is not yet existing. The demands on developing appropriate models for calving is large, as calving rates are needed for large scale ice sheet models that simulate the evolution of ice sheets. Here, we present a new approach for simulating fracture in ice. Our model is based on a finite strain theory for a viscoelastic Maxwell material, as the large simulation time leads to high strains. The fracturing process is simulated using a fracture phase field model that takes into account the elastic strain energy. We conduct simulations for a typical calving front geometry, with ice rises governing the formation of cracks. To represent the stress state adequately, we first conduct a spin-up to allow the viscous contribution to develop before the fracture phase field is computed. The analysis comprises the assessment of the crack path in comparison to observations, the influence of the spin-up, as well as elastic versus viscous strain contributions based on Hencky strain. Additionally, an estimate of released energy based on high resolution optical imagery of a Greenlandic calving front is presented

Representation of sharp rifts and faults mechanics in modeling ice shelf flow dynamics: Application to Brunt/Stancomb-Wills Ice Shelf, Antarctica

Ice shelves play a major role in buttressing ice sheet flow into the ocean, hence the importance of accurate numerical modeling of their stress regime. Commonly used ice flow models assume a continuous medium and are therefore complicated by the presence of rupture features (crevasses, rifts, and faults) that significantly affect the overall flow patterns. Here we apply contact mechanics and penalty methods to develop a new ice shelf flow model that captures the impact of rifts and faults on the rheology and stress distribution of ice shelves. The model achieves a best fit solution to satellite observations of ice shelf velocities to infer the following: (1) a spatial distribution of contact and friction points along detected faults and rifts, (2) a more realistic spatial pattern of ice shelf rheology, and (3) a better representation of the stress balance in the immediate vicinity of faults and rifts. Thus, applying the model to the Brunt/Stancomb-Wills Ice Shelf, Antarctica, we quantify the state of friction inside faults and the opening rates of rifts and obtain an ice shelf rheology that remains relatively constant everywhere else on the ice shelf. We further demonstrate that better stress representation has widespread application in examining aspects affecting ice shelf structure and dynamics including the extent of ice mélange in rifts and the change in fracture configurations. All are major applications for better insight into the important question of ice shelf stability

The variational approach to brittle fracture in materials with anisotropic surface energy and in thin sheets

Fracture mechanics of brittle materials has focused on bulk materials with isotropic surface energy. In this situation different physical principles for crack path selection are very similar or even equivalent. The situation is radically different when considering crack propagation in brittle materials with anisotropic surface energy. Such materials are important in applications involving single crystals, extruded polymers, or geological and organic materials. When this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. Thus, this situation interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Similarly, tearing of brittle thin elastic sheets, ubiquitous in nature, technology and daily life, challenges our understanding of fracture. Since tearing typically involves large geometric nonlinearity, it is not clear whether the stress intensity factors are meaningful or if and how they determine crack propagation. Geometry, together with the interplay between stretching and bending deformation, leads to complex behaviors, restricting analytical approximate solutions to very simplified settings and specific parameter regimes. In both situations, a rich and nontrivial experimental record has been successfully understood in terms of simple energetic models. However, general modeling approaches to either fracture in the presence of strong surface energy anisotropy or to tearing, capable of exploring new physics, have been lacking. The success of energetic simple models suggests that variational theories of brittle fracture may provide a unifying and general framework capable of dealing with the more general situations considered here. To address fracture in materials with strongly anisotropic surface energy, we propose a variational phase-field model resorting to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture, and reproduce strikingly well recent experimental observations. To explore tearing of thin films, we develop a geometrically exact model and a computational framework coupling elasticity (stretching and bending), fracture, and adhesion to a substrate. We numerically implement the model with subdivision surface finite elements. Our simulations qualitatively and quantitatively reproduced the crack patterns observed in tearing experiments. Finally, we examine how shell geometry affects fracture. As suggested by previous results and our own phase-field simulations, shell shape dramatically affects crack evolution and the effective toughness of the shell structure. To gain insight and eventually develop new concepts for optimizing the design of thin shell structures, we derive the configurational force conjugate to crack extension for Koiter's linear thin shell theory. We identify the conservative contribution to this force through an Eshelby tensor, as well as non-conservative contributions arising from curvature.La mécanica de fractura frágil se ha centrado en materiales tridimensionales con una energía de superficie isotrópica. En esta situación, los diferentes principios para la selección del camino de la fisura son muy similares, o incluso equivalentes. La situación es radicalmente opuesta cuando se considera la propagación de fisuras en medios con energía de superficie anisótropa. Estos materiales son importantes en aplicaciones que involucran materiales cristalinos, polímeros extrudidos, o materiales orgánicos y geológicos. Cuando la anisotropía es fuerte, el fenómeno de la propagación de fisuras es muy rico, con direcciones de propagación prohibidas o complejos patrones de ruptura en dientes de sierra. Por tanto, esta situación plantea cuestiones fundamentales en la mecánica de la fractura, incluyendo los principios de selección de la dirección de propagación de la fractura. Igualmente, el proceso de rasgado de láminas delgadas y frágiles, comunes en la naturaleza, la tecnología y la vida diaria, desafía nuestro entendimiento de la fractura. Dado que el rasgado de estas láminas típicamente involucra grandes no linealidades geométricas, no está claro si los factores de intensidad de esfuerzos son válidos o si, y en tal caso cómo determinan la propagación de fisuras. La interacción entre la geometría, las deformaciones y la curvatura da lugar a comportamientos complejos, lo que restringe las soluciones analíticas aproximadas a ejemplos muy simplificados y a regímenes de parámetros limitados. En ambas situaciones, se han podido interpretar experimentos no triviales con modelos energéticos simples. Sin embargo, no se ha profundizado en modelos generales de fractura en presencia de energía de superficie fuertemente anisótropa o en láminas delgadas, ambas interesantes por su capacidad para explorar nueva física. El mencionado éxito de los modelos energéticos simplificados sugiere que las teorías variacionales de fractura en medios frágiles pueden proveer un marco unificador para considerar situaciones más generales, como las que se consideran en este trabajo. Para caracterizar la fractura en materiales con energía de superficie fuertemente anisótropa, proponemos un modelo variacional de campo de fase basado en el modelo extendido de Cahn-Hilliard. Los modelos de campo de fase existentes para la fractura anisótropa fueron formulados en un contexto que sólo admite anisotropía débil. En este trabajo, implementamos numéricamente nuestro modelo de campo de fase de alto orden con aproximantes locales de máxima entropía en un método directo de Garlerkin. Los resultados numéricos muestran todas las características de fractura con anisotropía fuerte, y reproducen llamativamente bien las últimas observaciones experimentales. Para explorar el rasgado de láminas delgadas, desarrollamos un modelo geométricamente exacto y un esquema computacional que acopla elasticidad (estiramiento y flexión), fractura, y la adhesión a un substrato. Implementamos numéricamente el modelo con elementos finitos basados en superficies de subdivisión. Nuestras simulaciones reproducen los patrones de ruptura, tanto cualitativamente como cuantitativamente, observados en los experimentos de rasgado. Finalmente, examinamos cómo la geometría de la lámina afecta la fractura. Como ha sido sugerido en resultados previos y en nuestras propias simulaciones de campo de fase, la forma de la lámina afecta dramáticamente la evolución de fisuras y la resistencia efectiva del material. Para comprender mejor estos fenómenos y con el objetivo de desarrollar nuevos conceptos para la optimización del diseño de estructuras de láminas delgadas, derivamos la fuerza configuracional conjugada a la extensión de la fractura para la teoría lineal de láminas delgadas de Koiter. Identificamos las contribuciones conservativas a esta fuerza a través del tensor de Eshelby, así como las contriuciones no conservativas que aparecen por el efecto de la curvatura

A method of using computer simulation to assess the functional performance of football boots

This thesis details the development of Finite Element Analysis (FEA) techniques to simulate assembly and functional performance of football boots within a virtual environment. With a highly competitive market and seasonal changes in boot design common, the current design process can require numerous iterations, each adding time and cost to the development cycle. Using a reliable model allows evaluation of novel design concepts without the necessity to manufacture physical prototypes, and thus has potential financial benefits as well as reducing development time. A modelling approach was developed to construct a three dimensional boot model using FEA techniques, simulating the assembly of representative boot constituent parts based on manufacturing patterns, geometries and materials. Comparison between the modelled and physical boots demonstrated good agreement. Assessment of physical boot manufacture enabled the validation of the simulated assembly techniques, with digital image correlation hardware and software used to provide experimental measurements of the surface deformation. Good agreement was reported, demonstrating the predictive capabilities of FEA. Extensive review of literature provided applicable loading conditions of the boot during game play, with bending and torsional stiffness identified as important parameters. Boundary conditions associated with the foot during these movements provided a platform from which mechanical tests were used and developed to quantify boot function. Modelling techniques were developed and applied to the assembled FEA boot model, simulating the loading conditions to verify the validity when compared with experimental measurements. Bending and torsional stiffness extracted from the model were compared with the physical equivalent, demonstrating good predictive capabilities. The model was able to represent bending stiffness of the physical equivalent within 5.6% of an accepted boot range up to 20°, with torsional stiffness represented within the accepted range between 10° inversion to 7.5° eversion, corresponding to a large proportion of match play. Two case studies proved the applicability of the FEA techniques to simulate assembly and determine mechanical functionality virtually through a combination of automated modelling methods and a bespoke framework, demonstrating how it could be implemented within the industrial design process