Continuum Mechanics

A method is proposed for deriving dynamical equations for systems with both rigid and flexible components. During the derivation, each flexible component of the system is represented by a ``surrogate element'''' which captures the response characteristics of that component and is easy to mathematically manipulate. The derivation proceeds essentially as if each surrogate element were a rigid body. Application of an extended form of Lagrange''s equation yields a set of simultaneous differential equations which can then be transformed to be the exact, partial differential equations for the original flexible system. This method''s use facilitates equation generation either by an analyst or through application of software-based symbolic manipulation.

This article describes a fiber-optic interrogation device based on the pulsed time-of-flight technique. The apparatus is capable of measuring time delays between wideband reflectors, such as connectors, along a fiber path with a precision of about 280 fs (rms value) and a spatial resolution of about 3 ns (0.30 m) in a measurement time of 25 ms. Potential application areas include measuring integral strain and its derivatives such as cracks, deflections, and displacements, particularly in large civil engineering and composite structures. The operation and basic blocks of the measurement system are presented in detail together with measurement results obtained in laboratory and field conditions. It is shown that by using a fiber loop sensor with a reference fiber, it is possible to achieve a strain precision below 1 microstrain and a measurement frequency of 4 Hz. System performance proved adequate for the study of both static and dynamic phenomena in a bridge deck.

On the basis of continuum mechanics, a rate dependent directional damage model for fibred materials with application to soft biological tissues is presented. The structural model is formulated using the concept of internal variables that provides a very general description of materials involving irreversible effects. Continuum damage mechanics is used to describe the softening behavior of soft tissues under large deformation. To account for the rate dependency and to regularize the localization problems associated with strain-softening, a viscous damage mechanism is presented in this paper in decoupled form for matrix and fibers. The numerical implementation in the context of the finite element method is discussed in detail. In order to show the performance of the constitutive model and its algorithmic counterpart some simple examples are included. Results show that the model is able to capture the typical stress–strain behavior observed in fibrous soft tissues and appear to confirm the soundness of the proposed formulation.

By means of computer simulation, we study the deformation of nanoscale poIymer films under the action of external bending forces. The polymer is represented by a generalized bead-spring model, intended to reproduce characterisUc features of n-alkanes. The film is loaded by the action of a prismatic blade which is pressed into the polymer bulk from above and a pair of columns which support the film from below. The interaction between blade and support columns and the polymer ~s modelled by the repulsive part of a Lennard-Jones potential. For different system sizes as well as for different chain lengths, this nanoscale experiment is simulated by molecular dynamics methods. Our results allow us to give a first characterization of deformed states for such films. We resolve the kinetic and the dynamic stage of the deformation process m time and access the length scale between discrete particle and continuum mechanics behaviour. For the chain lengths considered here, we find that the deformation process is dominated by shear. We observe strangling effects for the film and deformation fluctuauons in the steady state. © 1997 Elsevier Science S.A.

We study the shapes of human red blood cells using continuum mechanics. In particular, we model the crenated, echinocytic shapes and show how they may arise from a competition between the bending energy of the plasma membrane and the stretching/shear elastic energies of ...

Numerical simulation can provide a useful tool for investigating the dynamics of phenomena like rock avalanches, within realistic geological contexts and in the framework of a better risk assessment and decision making. Difficulties in numerical modelling of a heterogeneous moving mass are mainly linked to the simulation of the complex behaviour assumed by the mass during propagation. The numerical code RASH3D, based on a continuum mechanics approach and on the long wave approximation, is used to back-analyse two cases of rock avalanches: Frank (1903, Canada) and Val Pola (1987, Italy). The two events are characterised by approximately the same volume (about 30 Â 10 6 m 3) while the run out area morphologies are widely different. Three alternative ''rheologies'' (Frictional, Voellmy and Pouliquen) are used. Comparison among obtained results underlines that the validation of a ''rheology'' requires not only a good agreement between the numerical simulation results and the run out area boundaries but also in term of depth distribution of the mass in the deposit. In case of a Frictional rheology, the obtained calibrated dynamic friction angle values are in a range of 15 AE 1 for both the cases; while assuming a Pouliquen or a Voellmy rheology it emerges a different behaviour of rheological parameters for each of the considered events. Besides the calibration of rheological parameters to better back-analyse each of the considered events, it is investigated how the behaviour due to the assumed rheology is influenced by the geometry of the run out area (e.g. narrow or broad valley).

Using a transparent tool entrapment, compression and eventual escape of liquid lubricant in surface pockets is observed in plane strip drawing. The two mechanisms of lubricant escape, Micro Plasto HydroDynamic and Hydrostatic Lubrication (MPHDL and MPHSL), are observed and quantified experimentally with varying viscosity, speed, reduction, workpiece material, back tension and friction. The mechanisms are influenced by all these parameters in an explicable way. Theoretical models of the escape mechanisms are established combining continuum mechanic analyses of the die pressure distribution with a fluid mechanic analysis of the lubricant escape. Oscillations in the drawing force are caused by the local escape of lubricant.

A device to study the friction of two molecularly smooth surfaces separated by an ultrathin liquid film is presented along with its design, calibration, and performance. The apparatus can move one of the surfaces and measure the friction force on the other one bidimensionally for both processes. A high mechanical impedance system (10 4 N/m) measures continuous friction forces where only stick-slip was previously observed. The frequency and travel distance of the movement can be varied over a wide range ͑frequency from 10 Ϫ4 to 7 Hz and distance from 1 to 800 m͒ to provide variations of the shear rate over seven orders of magnitude. The actual movement provided by piezoelectric bimorph drive can be affected by the friction forces and is measured by strain gauges. The friction forces are measured with an accuracy of Ϯ2N with a capacitance sensor. The mechanical design prevents the surfaces from rolling under force. The apparatus is tested with hexadecane. The potential applications of this apparatus and its limitations are discussed.

Abstract The steady, laminar, non-isothermal fully developed flow of a class of non-linear viscoelastic fluids in tubes of arbitrary contour is analyzed under constant wall heat flux including viscous dissipation. Equations of motion and energy are solved analytically and velocity and temperature fields are determined through an asymptotic approach in terms of the Weissenberg number coupled with the shape factor method a one-to-one and continuous mapping taking the circular boundary into a large, continuous spectrum of non-circular tube contours. The analysis developed is general and covers all members of the family of constitutive models considered as well as a large array of non-circular tubes. The case of tubes with circular and triangular contours are discussed as specific examples for various numerical combinations of the Weissenberg, Reynolds, Peclet and Brinkman numbers and the Nusselt number variation is computed for fluids abiding by the Modified Phan-Thien-Tanner (MPTT) and Simplified Phan-Thien-Tanner (SPTT) models. Newtonian velocity and temperature fields in a large spectrum of non-circular tubes are recovered at the lowest order of the asymptotic analysis. Through a matching procedure we also extend the computation of the Nusselt number in round tubes to any desired value of the Weissenberg number.

In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by a quantitative analysis of both a biophysical agent-based and a continuum mechanical model that for densely packed aggregates the expansion of the cell population is dominated by cell proliferation controlled by mechanical stress. The biophysical agent-based model introduced earlier (Drasdo and Hoehme in Phys Biol 2:133-147, 2005) approximates each cell as an isotropic, homogeneous, elastic, spherical object parameterised by measurable biophysical and cell-biological quantities and has been shown by comparison to experimental findings to explain the growth patterns of dense monolayers and multicellular spheroids. Both models exhibit the same growth kinetics, with initial exponential growth of the population size and aggregate diameter followed by linear growth of the diameter and power-law growth of the cell population size. Very sparse monolayers can be explained by a very small or absent cell-cell adhesion and large random cell migration. In this case the expansion speed is not controlled by mechanical stress but by random cell migration and can be modelled by the Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) reaction-diffusion equation. The growth kinetics differs from that of densely packed aggregates in that the initial spread, as quantified by the radius of gyration, is

An overview of the micromechanical theoretical and numerical models of wood is presented. Different methods of analysis of the effects of wood microstructures at different scale levels on the mechanical behaviour, deformation and strength of wood are discussed and compared. Micromechanical models of deformation and strength of wood are divided into three groups: cellular models (applied most often to the mesoscale or cell scale analysis of the wood deformation), continuum micromechanics and homogenization based methods, models which consider wood as a composite and are applied mainly to the analysis of wood at the microscale (cell wall scale) level and multiscale models. Lattice and composite models, which are used to analyze the damage and fracture of wood, are considered in a separate section. The areas of applicability and strong sides of each approach are discussed.

This paper presents a study of a roll compaction process as a dry granulation method for typical food materials such as maize powder. This process is widely applied in industry as it can continuously produce large quantities of granular product at comparatively low cost. The objectives of this work were to predict the roll compaction performance from a simple measurement involving uniaxial die compaction using the classical Johanson model. This involved determination of the optimum operating conditions for the production of granules as evaluated by apparent density.

Analytical formulations are presented to predict the elastic moduli of graphene sheets and carbon nanotubes using a linkage between lattice molecular structure and equivalent discrete frame structure. The obtained results for a graphene sheet show an isotropic behavior, in contrast to limited molecular dynamic simulations. Young's modulus of CNT represents a high dependency of stiffness on tube thickness, while dependency on tube diameter is more tangible for smaller tube diameters. The presented closed-form solution provides an insight to evaluate finite element models constructed by beam elements. The results are in a good agreement with published data and experimental results.

The fracture mode of austenitic steel may feature a ductile to brittle transition (DBT), depending on alloy composition and temperature. The DBT variation can be explained in terms of the actual deformation structure evolving during cold work and the correlated internal stresses. The crucial features of microstructure causing brittle fracture are found to be the intersections of deformation twins and the total density of free dislocations. To avoid brittle fracture, the stresses of intersecting twins must be screened by dislocations. Manganese and nitrogen promote brittle fracture since they lower the stacking fault energy and thus shift the onset of twinning to low strain levels where the total dislocation density is low. Nickel additions oppose this trend. The results of the microstructural fracture model agree well with experimental results and the model is confirmed by continuum-mechanical considerations.

Preface

This book collects most of the lecture notes I have developed and I have been using in a course on Continuum Mechanics for the Master of Science Course on Computational Mechanics and the Master Course on Numerical Methods in Engineering taught at the Barcelona School of Civil Engineering, Technical University of Catalonia, UPC BarcelonaTech, in Barcelona, Spain.
When the Master of Science Course on Computational Mechanics began, the Director of the Master asked me to take charge and to develop a course on Continuum Mechanics. The course should have around 40-45 class hours and  would be scheduled to be taught in the first semester of the first year of the Master. I embarked on this path by designing and developing what has been my flagship and signature course on Continuum Mechanics.

This book has been designed as an updated and expanded version of my Continuum Mechanics lecture notes and has been structured in 10 chapters. As an introduction, Chapters 1 and 2 are devoted to Tensor Algebra and Tensor Analysis. Part I of the book includes the next 3 chapters. Chapter 3 is devoted to Nonlinear Kinematics, Chapter 4 deals with Stresses, and Chapter 5 addresses the Fundamental Conservation/Balance Laws. Part II includes the next 4 chapters. Chapter 6 is devoted to Finite Deformation Hyperelasticity, Chapter 7 to Finite Deformation Plasticity, Chapter 8 to Finite Deformation Coupled Thermoplasticity, and Chapter 9 to Finite Deformation Contact Mechanics. The last chapter, Chapter 10, deals with Variational Methods in Solid Mechanics, including coupled thermoplasticity and contact problems.

The common feature of Part I is that all the contents are always valid, regardless of the material, be it solid or fluid. At the end of Part I we should be able to set up in local spatial/material form, the fundamental governing equations and inequalities for a Continuum Mechanics problem. The fundamental governing equations and inequalities arise from the fundamental conservation/balance principles and from the constraints imposed by the second law of thermodynamics, and are valid for any material. At the end of Part I, we should be able to check how many governing equations we have, and how many unknowns are involved in those governing equations and inequalities. We will realize that we have more unknowns than equations. So, to have a well posed problem, we would need to add a number of equations, so that the final number of equations is equal to the number of unknowns. The equations we should add would depend on the material and for some particular material models will be considered in Part II of the book.

Part II of the book is devoted to presenting some nonlinear constitutive models for Nonlinear Solid Mechanics, including Finite Deformation Hyperelasticity, Finite Deformation Plasticity, Finite Deformation Coupled Thermoplasticity, and Finite Deformation Contact Mechanics. Constitutive equations are derived within a thermodynamically consistent framework. Finite deformation elastoplasticity models are based on the multiplicative decomposition of the deformation gradient and the notion of an intermediate configuration. Different formulations based on the intermediate configuration, the current or spatial configuration, and the material configuration, are considered. The last chapter is devoted to Variational Methods in Solid Mechanics, a fundamental topic in Computational Mechanics.

The book may be used as a text book for a Master’s course on Nonlinear Continuum Mechanics for graduate students in Civil, Mechanical or Aerospace Engineering, Applied Mathematics or Applied Physics, with interest in Continuum Mechanics and Computational Mechanics.

I am grateful to my colleagues and friends Jean-Philippe Ponthot at University of Liege, and Mariana Seabra at University of Porto for their careful reading of the manuscript.

I hope you enjoy reading the book as much as I have enjoyed writing it.

Carlos Agelet de Saracibar
Barcelona, Spain, 22 March 2022

ABSTRACT: A survey of secondary flows of viscoelastic liquids in straight tubes is given including recent work pointing at striking analogies with transversal deformations associated with the simple shearing of solid materials. The importance and implications of secondary flows of viscoelastic fluids in heat transfer enhancement are explored together with the difficulties in detecting weak secondary flows (dilute, weakly viscoelastic solutions) in a laboratory setting. Recent new work by the author and colleagues which explores for the first time the structure of the secondary flow field in the pulsating flow of a constitutively nonlinear simple fluid, whose structure is defined by a series of nested integrals over semi-infinite time domains, in straight tubes of arbitrary cross-sections is summarized. The transversal field arises at the second order of the perturbation of the nonlinear constitutive structure, and is driven by first order terms which define the linearly viscoelastic longitudinal flow in the hierarchy of superposed linear flows stemming from the perturbation of the constitutive structure. Arbitrary conduit contours are obtained through a novel approach to the concept of domain perturbation. Time averaged, mean secondary flow streamline contours are presented for the first time for triangular, square and hexagonal pipes.

The problem of formulating and numerically solving the equations of motion for a multibody system undergoing large motion and elasto-plastic deformations is considered here. Based on the principles of continuum mechanics and the finite element method, the equations of motion for a flexible body are derived. It is shown that the use of a lumped mass formulation and the description of thc nodal accelerations relative to a nonmoving reference frame lead to a simple form of these equations. In order to reduce the number of coordinates that describe a deformable body, a Guyan condensation technique is used. The equations of motion of the complete multibody system are then formulated in terms of joint coordinates between the rigid bodies. The kinematic constraints that involve flexible bodies are introduced in the equations of motion through the use of Lagrange multipliers,

This thesis is a pilot study, designed to test and develop methods suitable for the study of Scandinavian flint spearhead functionality. The functionality of projectile and lithic point armament has not been studied for almost 30 years in Scandinavia. Meanwhile, methods used to analyse lithic projectiles have developed considerably. However, few of these methods are precise enough to be used in conjunction with Scandinavian stone technological analyses that emphasize the societal aspect of lithic points. Consequently, two methods were chosen that could provide data for Scandinavian research issues: 3D-scanning/continuum mechanical simulations and organic residue analysis. The methods were tested on 6 experimental spearheads. The continuum mechanical simulation generated both visual and numerical data that could be used to create precise functional-morphological descriptions. The data could also potentially be used for projectile point classification. The organic residue analysis revealed promising results for the use of an artefact and activity specific analysis, with a sequential extraction protocol. In unison, the results from both analyses could be used to reveal how spearheads were functionally designed and used in Stone Age Scandinavia, even though there are methodological and technological issues that need solving.

This paper deals with the erosion rate of stainless steels due to the impact of solid particulate. These materials are used in high temperature applications. Several theoretical models have been developed for determining the erosion resistance of ductile materials. These approaches assume a failure mode (so called micro cutting) which does not seem to be adequate, as has been proved experimentally. Moreover these models derive formulas for the eroded volume of material that depend on several constants which need to be determined experimentally. The great uncertainty of the experimental results, intrinsic to the erosion tests, together with the high expense involved led the author to develop alternative methods based on numerical simulations. On the basis of theoretical models, the author developed erosion criteria for ductile materials which could be implemented as Fortran routines in commercial FEM codes. The numerical simulations concern with multiple impacts of particles on stainless steel target. The erosion criterion, which looks like the energetic criterion of the fracture mechanic , was applied to the elements of the mesh step by step during the transient. A damage indicator for each element in a tensile stress state was calculated in every time step. This indicator represents the eroded fraction of the element in each time step and permits to eliminate the dependence of the results from the mesh size. Several analyses were performed considering different plasticity criteria, the dependence of the erosion rate on the strain rate, the temperature. The numerical results were compared with experimental and theoretical results. In spite of some simplifying assumptions, there was a good agreement between the numerical and experimental results. Moreover a theoretical erosion model for ductile material, developed by the author, agreed better than the other models being examined. The described numerical method could be a powerful means of assessing the erosion resistance of components in real operating conditions.

W szczegółowy sposób omówione zostały założenia ogólnej nieliniowej teorii sprężystości i wyprowadzenia podstawowych elementów mechaniki ośrodka ciągłego, a także przytoczone zostały dowody fundamentalnych twierdzeń rozważanej teorii w ramach kinematyki, statyki i dynamiki ciał odkształcalnych. Omówiono kwestie formułowania związków konstytutywnych dla ciał izotropowych i anizotropowych zarówno o liniowej, jak i nieliniowej charakterystyce, ze szczególnym uwzględnieniem zagadnienia energetycznego sprzężenia miar naprężenia i odkształcenia oraz zastosowania rozkładu widmowego tensorów sprężystości. Osobno omówiono liniowy wariant teorii z różnymi jego sformułowaniami oraz metodami analitycznymi, m.in. zastosowaniem funkcji naprężeń, potencjałów, metod półodwrotnych oraz analizy zespolonej. Rozważania te poszerzono o opis teorii ogólniejszych – mechanikę ośrodka mikropolarnego Cosseratów oraz mechanikę ośrodka mikromorficznego Mindlina. W ramach teorii liniowej przedstawiono matematyczny opis zjawisk elastooptyki, propagacji płaskich i sferycznych fal sprężystych, a także propagacji sprężystych fal powierzchniowych. Przytoczono i udowodniono twierdzenia wariacyjne teorii liniowej oraz omówiono ich zastosowanie w ramach numerycznych metod rozwiązywania zagadnień tej teorii. Przeanalizowano rozwiązania trzynastu klasycznych zagadnień liniowej teorii sprężystości oraz zagadnień pokrewnych, ze szczególnym uwzględnieniem zagadnień dynamicznych. Całość uzupełniona została rozbudowanym dodatkiem poświęconym rachunkowi tensorowemu i absolutnemu rachunkowi różniczkowemu.

Items with a reviewer byline (coded R) are by AMR's corps of dedicated outside volunteer reviewers. AMR will attempt to get critical reviews of all relevant textbooks, reference works, and monographs. Items without a reviewer byline (coded N) are prepared by AMR in-house staff and are largely based on material such as a book's table of contents and editor's preface or foreword. In the interest of timeliness, most conference proceedings and multi-author contributed volumes will receive descriptive notes in this fashion. Books deemed to be somewhat peripheral to AMR's basic scope may simply be listed by title. Also listed by title when first received are books under review.

Continuum Mechanics [250952]
Master: Erasmus Mundus Master of Science in Computational Mechanics, Barcelona School of Civil Engineering, UPC BarcelonaTech
Master: Numerical Methods in Engineering, Barcelona School of Civil Engineering, UPC BarcelonaTech
Master: Numerical Methods in Engineering (on-line version), Barcelona School of Civil Engineering, UPC BarcelonaTech
Master: Civil Engineering, Barcelona School of Civil Engineering, UPC BarcelonaTech
Master: Structural and Construction Engineering, Barcelona School of Civil Engineering, UPC BarcelonaTech
Language: English
Credits: 5 ECTS
Topics: Tensor algebra, Nonlinear continuum mechanics, Nonlinear kinematics, Motion, Strains, Stresses, Balance laws, Thermodynamics, Linear elasticity, Plane linear elasticity, Fluid mechanics, Newtonian fluids, Variational principles
Lecture notes: Introduction Course 2016-2017, Chapter 1: Tensor Algebra, Chapter 2: Motion, Chapter 3: Strains, Chapter 4: Infinitesimal Strains, Chapter 5: Stresses, Chapter 6: Balance Laws, Chapter 7: Linear Elasticity, Chapter 8: Plasticity, Chapter 9: Fluid Mechanics, Chapter 10: Ideal Fluids, Chapter 11: Newtonian Fluids, Chapter 12: Variational Principles

In this study, flow simulation of the two-fluid system with sharp interface and soluble surfactants is performed using OpenFOAM, an object-oriented C++ library for simulations in continuum mechanics. The Finite Volume method with moving computational mesh support is used to implement an interface-tracking procedure, where each fluid phase is associated with a separate mesh which moves and deforms according to interface motion. Mathematical model governing incompressible fluid flow is solved on each moving mesh separately and coupling is accomplished by enforcing the kinematic and dynamic conditions at the interface. Surfactant adsorption/desorption at the interface is modelled using the Langmuir kinetic law, while surface tension is calculated from surfactant concentration at the interface using the nonlinear Frumkin-Langmuir equation of state. Surfactant transport along the interface is calculated using a Finite Area Method for discretisation of surface transport equation on a curved and moving unstructured surface mesh. The numerical procedure is used to simulate the effects of soluble surfactants on the motion of a free-rising air bubble in still water. The bubble of 2 mm diameter is considered, where experiments show ellipsoidal bubble shape and motion along a zig-zag and/or a helicoidal path. Calculations are performed for a clean and contaminated bubble and the results shows good agreement with available experimental data.

A computational methodology is presented for modeling the non-linear mechanical behavior of composite structures made of FRP (Fiber-Reinforced Polymers) laminates. The model is based on the appropriate combination of the constitutive models of compounding materials, considered to behave as isolated continua, together with additional "closure equations" that characterize the micro-mechanics of the composite from a morphological point of view. To

The existing motorcycle helmets are thermally uncomfortable as there is no provision for air flow inside the helmet. A new design of helmet, with grooves in the liner foam and slot in the outer shell and liner foam to improve the ventilation, is proposed. Computational fluid dynamics studies show considerable improvement in air velocities inside the helmet in the presence of grooves and slot. Impact dynamics and biomechanics studies on various motorcycle helmets with deformable and rigid head show that the proposed design meets the requirements of the standards in the drop test. The optimum size of the groove and number of grooves for a motorcycle helmet are decided on the basis of the above studies.

A computational methodology is presented for modelling the material non-linear mechanical behaviour of composite structures made of FRP (Fibre-Reinforced Polymers) laminates. The model is based on the appropriate combination of the constitutive models of component materials, considered to behave as isolated continua, together with additional 'closure equations' that characterize the micromechanics of the composite from a morphological point of view. To this end, any appropriate constitutive model may be selected for each phase. Each component is modelled separately and the global response is obtained by assembling all contributions taking into account the interactions between components in a general phenomenological way. To model the behaviour of a single unidirectional (UD) composite lamina, a Serial-Parallel continuum approach has been developed assuming that components behave as parallel materials in the fibres alignment direction and as serial materials in orthogonal directions. Taking into account the internal morphology of the composite material, it is devised a strategy for decoupling and coupling component phases. This methodology [Rastellini 2006], named "compounding of behaviours", allows to take into consideration local degradation phenomena (in the constituents materials), like plasticity, etc. in a coupled manner. It is based on the proper management of homogenous constitutive models, already available for each component. In this way, it is used all developments achieved in constitutive modelling of plain materials, what makes possible the transference of this technology to composites. A lamination theory complemented with the proposed UD model is employed to describe the mechanical behaviour of multidirectional laminates. A specific solution strategy for the general non linear case is proposed. It provides quick local and global convergences, what makes the model suitable for large scale structures. The model brings answers on the non-linear behaviour of composites, where classical micro-mechanics formulas are restricted to their linear elastic part. The methodology is validated through several numerical analyses and contrasted against experimental data and benchmark tests.

Assume that the physics on the microscale (interactions between atoms,
molecules, defects in crystals . . . ) is understood.What is the appropriate mesoscale
continuum theory for the problem? What are the assumptions involved and how do
they define the limitations of the continuum model? To answer these questions, we
begin with the definition of mesoscale continuum kinematics from the microscale
kinematics. The geometry of micro-structure (e.g., order vs. disorder) has a decisive
role in defining the continuum kinematics. We thus arrive at three kinematic
formulations: mass continuum, lattice continuum and granular continuum. Then,
upon formulating the power balance, we use the principle of virtual power to
arrive at a variety of mathematical formulations: simple continuum with moving
boundaries, phase field formulation, and, a higher order, size-dependent continuum.
The problems considered include: mixing of fluids and capillary flows, granular
flow/deformation, and, polycrystalline diffusional/dislocation creep accompanied
by dislocation plasticity.

Cette thèse a été réalisée au Laboratoire de Mécanique et Rhéologie (LMR) de l'université François Rabelais de Tours dans les locaux du Centre d'Etude et de Recherche Matériaux Elastomère (CERMEL). Je remercie Naranayaswami Ranganathan, directeur du laboratoire et également mon directeur de thèse pour m'avoir offert l'opportunité de mener à bien cette thèse dans ses locaux. Je le remercie également pour m'avoir partagé son expérience scientifique et expérimentale qui m'aura été précieuse. Je lui suis reconnaissant pour sa confiance et son soutien qu'il m'aura témoigné pendant toute la période de ma thèse, ce qui m'aura permis de vivre des expériences très enrichissantes. Je remercie les membres du jury d'avoir accepté d'évaluer mon travail de thèse. Je remercie Monsieur François Tran Van de m'avoir fait l'honneur de présider mon jury de thèse. Je remercie Messieurs André Chrysochoos et Yves Nadot d'avoir accepté de rapporter sur mon mémoire de thèse. J'ai eu l'occasion de les rencontrer avant ma soutenance, et m'ont offert un accueil chaleureux (surtout l'accueil à Montpellier avec la voiture de Police qui m'attendait à la gare ...). Ils m'ont également partagé leur point de vue extérieur, qui m'a été très précieux. Je remercie Messieurs Stéphane Lejeune et William Mars d'avoir examiné mon travail. Ils m'ont montré des perspectives d'avenir de mon travail que je n'avais pas du tout soupçonnés. Enfin, je remercie Monsieur Yves Chauvin de m'avoir fait l'honneur d'avoir assisté à ma soutenance de thèse. Je remercie Florian Lacroix, tout d'abord pour m'avoir proposé cette offre de thèse, alors que j'étais encore stagiaire au sein de Hutchinson Joué-les-Tours. Il aura été avec Stéphane Méo des encadrants de premier choix tout au long de ma thèse. Ils ont réussi à me supporter, même si parfois, j'ai pu être très difficile à encadrer, en bonne tête de lard que je suis. Ils avaient à eux deux des compétences complémentaires (Expérimental et modélisation) qui, je l'espère, reflètent l'identité de ma thèse. Ils étaient sur le terrain avec moi, à mettre les mains dans le cambouis et je leur en remercie. Leur conseil, leur expérience, et leur encadrement m'on été indispensable ; et si je suis là où j'en suis, c'est en grande partie grâce à eux. Je suis conscient de la chance que j'ai pu avoir de travailler dans de telles conditions. Je remercie Patrice Méroz, conseiller scientifique de la société Hutchinson SNC Joué-les-Tours, pour avoir su me faire profiter de sa longue longue expérience professionnelle de caoutchoutier. Comme il aime à le dire, il a su me transformer, tout au long de ma thèse en quelqu'un de meilleur. Ca n'a pas tel-00780307, version 1 -23 Jan 2013 iv été sans mal, ne nous le cachons pas. Cette transformation a du passer par des coups de sabre récurrents (Je me demande encore comment j'ai fait pour garder ma tête sur mes épaules ! !) ! ! Je le remercie également pour avoir été une interface précieuse entre la société Hutchinson SNC de Joué-les-Tours et moi.

Continuum Mechanics [250952]
Master: Erasmus Mundus Master of Science in Computational Mechanics, Barcelona School of Civil Engineering, UPC BarcelonaTech
Master: Numerical Methods in Engineering, Barcelona School of Civil Engineering, UPC BarcelonaTech
Master: Numerical Methods in Engineering (on-line version), Barcelona School of Civil Engineering, UPC BarcelonaTech
Master: Civil Engineering, Barcelona School of Civil Engineering, UPC BarcelonaTech
Master: Structural and Construction Engineering, Barcelona School of Civil Engineering, UPC BarcelonaTech
Language: English
Credits: 5 ECTS
Topics: Tensor algebra, Nonlinear continuum mechanics, Nonlinear kinematics, Motion, Strains, Stresses, Balance laws, Thermodynamics, Linear elasticity, Plane linear elasticity, Fluid mechanics, Newtonian fluids, Variational principles
Lecture notes: Introduction Course 2016-2017, Chapter 1: Tensor Algebra, Chapter 2: Motion, Chapter 3: Strains, Chapter 4: Infinitesimal Strains, Chapter 5: Stresses, Chapter 6: Balance Laws, Chapter 7: Linear Elasticity, Chapter 8: Plasticity, Chapter 9: Fluid Mechanics, Chapter 10: Ideal Fluids, Chapter 11: Newtonian Fluids, Chapter 12: Variational Principles

The generation of direct current electricity using solid oxide fuel cells (SOFCs) involves several interplaying transport phenomena. Their simulation is crucial for the design and optimization of reliable and competitive equipment, and for the eventual market deployment of this technology. An open-source library for the computational modeling of mass-transport phenomena in SOFCs is presented in this article. It includes several multicomponent mass-transport models (i.e. Fickian, Stefan-Maxwell and Dusty Gas Model), which can be applied both within porous media and in porosity-free domains, and several diffusivity models for gases. The library has been developed for its use with OpenFOAM ® , a widespread open-source code for fluid and continuum mechanics. The library can be used to model any fluid flow configuration involving multicomponent transport phenomena and it is validated in this paper against the analytical solution of one-dimensional test cases. In addition, it is applied for the simulation of a real SOFC and further validated using experimental data.

This paper starts out by recalling the basic assumptions required for the classical (Cauchy type) continuum mechanics to hold. It turns out that the micro-and nano-scale structures of many materials -such as lattice-type porous solids and two-phase composites -may not satisfy the requirement of separation of scales and/or the postulate of negligible internal couple force fields. If that is the case, the mechanics of material cannot be predicted correctly by a classical theory of a Cauchy continuum. We give a sketch of history and achievements of non-classical (Cosserat type) elastic continua, and then focus on micropolar models, their planar cases, and the somewhat enigmatic characteristic lengths. This is followed by an outline of formulation of micropolar elasticity models for three beam-type lattices of classical geometries: triangular, square, and honeycomb. Next, we review very recent studies on determination of such models for two-phase (inclusion-matrix) periodic composites, which are locally of Cauchy type. It is shown that, in cases of both lattices and composites, the micropolar moduli and the characteristic lengths can be determined from first principles. The paper also provides a summary of the pros and cons of Cauchy vis-à-vis Cosserat models, and of the outstanding challenges in this field.

Project Description: Perform a literature review on the origins and derivation of the principle of virtual power and its advantages and disadvantages as a means to find solutions to boundary value problems. Explain the meaning of the virtual motion used to obtain the virtual work and how it can lead to a framework to solve continuum mechanics problems with known boundary and initial conditions. Show examples of its use for either fluids or solids. Abstract: The Principle of Virtual Power, largely synonymous with the Principle of Virtual Work, is a useful tool for the modeling of various systems. The history of the principle and its general meaning are discussed, along with some of its advantages and drawbacks. Both the Principle of Virtual Work and Principle of Virtual Power are derived from first principles, beginning with the conservation of linear momentum, and resulting in a statement of conservation of mechanical work/energy. An example of application is also presented for deformable semiconductors, with a derivation which includes an extension of the Principle of Virtual Power.