Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work presents the Cauchy's theorem in its classical form, and aims to weaken their hypotheses, providing a more advantageous use in continuum mechanics. The methodology is axiomatic, that is, basic concepts are presented aiming to triggering logical statements that were made in the main theorems to achieve the objectives of this dissertation. The main result is Theorem 14, where a law of balance is folowed necessary and suficient condition for a Cauchy Flow be Weakly Balanced. / Neste trabalho é apresentado o Teorema de Cauchy em sua forma clássica e tem por objetivo enfraquecer suas hipóteses, proporcionando uma aplicação mais vantajosa na mecânica do contínuo. A metodologia empregada é axiomática, ou seja, são apresentados conceitos básicos com vistas ao desencadeamento lógico das demonstrações que foram realizadas nos teoremas principais para atingir os objetivos dessa dissertação. O resultado principal é o teorema 14, onde obedecer a uma lei de balanço, é condições necessária e suficiente para que um Fluxo de Cauchy seja Fracamente Balanceado.

This doctoral thesis deals with the description of the mechanical behavior of arterial walls under supra-physiological loading conditions. After a brief description of the continuum mechanical basis, the focus is first set to continuum damage mechanics (CDM) formulations for soft biological tissues. Thereby, different phenomenological damage equations are introduced yielding smooth and non-smooth material tangent moduli at the induction of initial damage, respectively. The performance of the latter formulations is investigated in numerical calculations of inhomogeneous boundary value problems. Afterwards, a micromechanically motivated damage approach for arterial tissues is derived in the CDM framework, taking into account statistically distributed microscopical parameters. The model response is adjusted to experimental data of human arteries and used in a numerical simulation of a simplified atherosclerotic artery model showing the applicability of the proposed formulation in a finite element framework. Moreover, a relaxed incremental variational formulation from the literature, which in contrast to the CDM formulations avoids a potential loss of convexity, is extended in this work to account for arterial tissues by the inclusion of fiber dispersion and hysteresis behavior. A framework denoted as ’Optimal Uncertainty Quantification’ is utilized to compute bounds on the probability of failure in a simplified diseased artery model after several overexpansions. Therefore, a virtual experimental data set and two different rupture criteria are considered, which are based on fiber stretch and fiber damage, respectively. / Diese Dissertation behandelt die Beschreibung des mechanischen Verhaltens von Arterienwänden unter supraphysiologischen Belastungszuständen. Nach einer kurzen Beschreibung der kontinuumsmechanischen Grundlagen, wird der Schwerpunkt zunächst auf Formulierungen im Rahmen der Kontinuumsschädigungsmechanik (KSM) für biologische Weichgewebe gelegt. Dabei werden unterschiedliche phänomenologische Schädigungsfunktionen eingeführt, die zu stetigen bzw. unstetigen Tangentenmoduln bei Schädigungsiniziierung führen. Das Verhalten dieser Formulierungen wird in numerischen Berechnungen inhomogener Randwertprobleme untersucht. Danach wird ein mikromechanisch motivierter Schädigungsansatz im Rahmen der KSM unter Berücksichtigung statistisch verteilter mikroskopischer Parameter hergeleitet. Die Modellantwort wird an experimentelle Daten menschlicher Arterien angepasst und in einer numerischen Simulation eines vereinfachten atherosklerotischen Arterienmodells verwendet, wobei die Anwendbarkeit der vorgeschlagenen Formulierung im Rahmen der Finite-Elemente-Methode gezeigt wird. Zusätzlich wird eine inkrementelle Variationsformulierung für Schädigung aus der Literatur, die im Vergleich zu den KSM-Formulierungen einen möglichen Konvexitätsverlust vermeidet, durch Einbindung von Faserstreuung und Hystere-Verhalten für die Beschreibung arteriellen Gewebes erweitert. Im Rahmen einer Methode, die als ’Optimale Unsicherheitsquantifizierung’ bezeichnet wird, werden Grenzwerte für die Versagenswahrscheinlichkeit an einem vereinfachten Modell einer erkrankten Arterie nach mehreren Überdehnungen berechnet. Dafür werden ein virtueller experimenteller Datensatz und zwei unterschiedliche Versagenskriterien berücksichtigt, die auf der Faserdehnung bzw. auf der Faserschädigung basieren.

Continuum mechanics is used to model the mechanical behaviour of concrete structures subjected to high rates of loading in defence applications. Large deformation theory is used and an isotropic elastic-plastic constitutive equation with isotropic hardening, damage and strain rate dependent loading surface. The hydrostatic pressure is governed by an equation of state. Numerical analysis is performed using the finite element method and the central difference method for the time integration. Projectile penetration is studied and it is concluded that it is not suitable to use material description of the motion of both the target and the projectile together with an erosion criterion. Instead, the material description should be used only for the projectile and the spatial description for the target. In this way the need for an erosion criterion is eliminated. Also, in the constitutive model used it is necessary to introduce a scaling of the softening phase in relation to the finite element size, in order to avoid strain localization. Drop weight testing of reinforced concrete beams are analysed, where a regularisation is introduced that renders mesh objectivity regarding fracture energy release. The resulting model can accurately reproduce results from material testing but the regularisation is not sufficient to avoid strain localization when applied to an impact loaded structure. It is finally proposed that a non-local measure of deformation could be a solution to attain convergence. The third study presents the behaviour of a concrete constitutive model in a splitting test and a simplified non-local theory applied in a tensile test. The splitting test model exhibits mesh dependency due to a singularity. In the tensile test the non-local theory is shown to give a convergent solution. The report https://www.diva-portal.org/liu/webform/form.jsp#paper0is concluded with a discussion on how to better model concrete materials.

Almost all animal cells maintain a thin layer of actin filaments and associated proteins underneath the cell membrane. The actomyosin cortex is subject to internal stress patterns which result from the spatiotemporally regulated activity of non-muscle myosin II motors in the actin network. We study how these active stresses drive changes in cell shape and flows within the cortical layer, and how these cytoskeletal deformations and flows govern processes such as cell migration, cell division and organelle transport. Following a continuum mechanics approach, we develop theoretical descriptions for three different cellular processes, to obtain - in collaboration with experimental groups - a detailed and quantitative understanding of the underlying cytoskeletal mechanics. We investigate the forces and cortex flows involved in adhesion-independent cell migration in confinement. Many types of cell migration rely on the extension of protrusions at the leading edge, where the cells attach to the substrate with specific focal adhesions, and pull themselves forward, exerting stresses in the kPa range. In confined environments however, cells exhibit migration modes which are independent of specific adhesions. Combining hydrodynamic theory, microfluidics and quantitative imaging of motile, non-adherent carcinosarcoma cells, we analyze the mechanical behavior of cells during adhesion-independent migration. We find that the accumulation of active myosin motors in the rear part of these cells results in a retrograde cortical flow as well as the contraction of the cell body in the rear and expansion in the front, and we describe how both processes contribute to the translocation of the cells, depending on the geometric and mechanical parameters of the system. Importantly, we find that the involved propulsive forces are several orders of magnitude lower than during adhesive motility while the achieved migration velocities are similar. Moreover, the distribution of forces on the substrate during non-adhesive migration is fundamentally different, giving rise to a positive force dipole. In contrast to adhesive migration modes, non-adhesive cells move by exerting pushing forces at the rear, acting to expand rather than contract their substrate as they move. These differences may strongly affect hydrodynamic and/or deformational interactions between collectively migrating cells. In addition to the work outlined above, we study contractile ring formation in the actin cytoskeleton before and during cell division. While in disordered actin networks, myosin motor activity gives rise to isotropic stresses, the alignment of actin filaments in the cortex during cell division introduces a preferred direction for motor-filament interactions, resulting in anisotropies in the cortical stress. Actin filaments align in myosin-dependent shear flows, resulting in possible feedback between motor activity, cortical flows and actin organization. We investigate how the mechanical interplay of these different cortical properties gives rise to the formation of a cleavage furrow during cell division, describing the level of actin filament alignment at different points on the cortex with a nematic order parameter, in analogy to liquid crystal physics. We show that cortical anisotropies arising from shear-flow induced alignment patterns are sufficient to drive the ingression of cellular furrows, even in the absence of localized biochemical myosin up-regulation. This mechanism explains the characteristic appearance of pseudocleavage furrows in polarizing cells. Finally, we study the characteristic nuclear movements in pseudostratified epithelia during development. These tissues consist of highly proliferative, tightly packed and elongated cells, with nuclei actively travelling to the apical side of the epithelium before each cell division. We explore how cytoskeletal properties act together with the mechanics of the surrounding tissue to control the shape of single cells embedded in the epithelium, and investigate potential mechanisms underlying the observed nuclear movements. These findings form a theoretical basis for a more detailed characterization of processes in pseudostratified epithelia. Taken together, we present a continuum mechanics description of the actomyosin cell cortex, and successfully apply it to several different cell biological processes. Combining our theory with experimental work from collaborating groups, we provide new insights into different aspects of cell mechanics.

Les matériaux nanostructurés suscitent un intérêt qui va croissant en raison de leurs propriétés chimiques et physiquesexceptionnelles. A cause de la complexité et du coût des développements expérimentaux à l’échelle nano, la simulationnumérique devient une alternative de plus en plus populaire aux études expérimentales. Dans ce travail de thèse, nous avons essayé de combiner des simulations à l’échelle atomique avec de la modélisation en milieu continu pour évaluer la conductivité thermique et la réponse élastique de matériaux nanostructurés. Nous avons utilisé des simulations de dynamique moléculaire pour calculer la réponse mécanique et thermique des matériaux sur des volumes à l’échelle nano. Des méthodes de micromécanique et la méthode des éléments finis, qui utilisent la mécanique des milieux continus, ont permis d’évaluer les propriétés mécaniques des matériaux à l'échelle macroscopique. Les résultats obtenus par ces simulations numériques ont été ensuite comparés avec ceux issus de l’expérience. / Nanostructured materials are gaining an ongoing demand because of their exceptional chemical and physical properties. Due to complexities and costs of experimental studies at nanoscale, computer simulations are getting more attractive asexperimental alternatives. In this PhD work, we tried to use combination of atomistic simulations and continuum modeling for the evaluation of thermal conductivity and elastic stiffness of nanostructured materials. We used molecular dynamics simulations to probe and investigate the thermal and mechanical response of materials at nanoscale. The finite element and micromechanics methods that are on the basis of continuum mechanics theories were used to evaluate the bulk properties of materials. The predicted properties are then compared with existing experimental results.

De nos jours, l’enjeu de la mécanobiologie ne cesse de grandir. On s’intéresse à la description des problèmes biophysiques d’un point de vue mécanique avec des approches multiéchelles. Dans ce travail, nous proposons d’étudier deux exemples mettant en évidence le rôle important de la mécanique sur des processus purement biologiques. 1) La croissance tumorale dans son stade avasculaire : nous proposons un modèle continu où le tissu tumoral est considéré capable de croître et de se déformer tout en obéissant aux lois de conservation. Nous proposons ensuite pour étudier l’effet des propriétés mécaniques du microenvironnement -où réside la tumeur- sur le développement tumoral d’intégrer certaines conditions aux interfaces tumeur/microenvironnement. 2) La reconstruction des propriétés élastiques de la cuticule d’arthropode : nous proposons un modèle multiéchelles de son comportement mécanique fondé sur la structure hiérarchique établie dans la littérature. Pour remédier à la sous-estimation du modèle des propriétés élastiques de la cuticule, nous proposons d’inclure les interfaces à certaines échelles qui pourraient améliorer la transmission des efforts aux constituants multiéchelles du composite (cuticule) et donc améliorer les propriétés élastiques macroscopiques de ce dernier. / Nowadays, the challenge of mechanobiology keeps growing. We are interested in the description of biophysical problems from a mechanical point of view with multiscale approaches.In the present study, we propose to study two examples highlighting the substantial role of mechanics on purely biological processes. 1) Tumor growth in the avascular stage: we propose a continuous model where tumor tissue is considered able to grow and to deform while obeying to conservation laws. Then, we propose to study the effect of the mechanical properties of the microenvironment- where lives the tumor- on the tumor development by integration of certain interfaces conditions tumor/microenvironment. 2) Reconstruction of the elastic properties of the arthropod cuticle: we propose a multiscale model of its mechanical behavior based on the hierarchical structure established in the literature. To remedy the under-estimation of the cuticle elastic properties of the model, we propose to include the interfaces to some scales that could improve the transmission of forces to the multiscale components of the composite (cuticle) and thus improve their macroscopic elastic properties.

Thesis (Ph. D.)--Ohio State University, 2006. / Available online via OhioLINK's ETD Center; full text release delayed at author's request until 2007 Jun 16

La present tesi investiga l'ús de la modelització amb elements finits per a l'estudi de la biomecànica lumbar per a l'avaluació clínica. Els estudis bibliogràfics del capítol 1 mostren relacions funcionals clares entre les forces externes i les estructures i formes del teixit lumbar. Els estudis clínics demostraren que independentment del seu origen, el dolor lumbar pot veure's empitjorat per sobrecàrregues dels teixits. Les mesures experimentals són insuficients per descriure la distribució de càrrega entre els diferents teixits lumbars, és així que s'han utilitzat models d'elements finits. No obstant, la fiabilitat dels models a l'hora de predir les càrregues locals en els teixits no ha estat demostrada, essent aquest un dels objectes d'estudi.En el Capítol 2 s'elaborà un model bisegment de la columna lumbar. El model inicial es completà incloent el còrtex vertebral, una definició complerta de les juntes sinovials, les plaques terminals de cartílag i una descripció millorada de l'estructura de l'anell. Es van simular càrregues simplificades per als estudis in vitro per calcular les distribucions de tensions, deformacions i energia. El model bisegment és vàlid per interpretar les distribucions de càrrega funcionals a L3-L5 en el cas d'estructures conegudes de teixit, però el conjunt de la geometria L3-L5 necessitava ser millorat.Així al Capítol 3 es creà un model geomètric bisegment precís de L3-L5. El nou model incloïa les corregides: dimensions i formes, alçades de disc, localitzacions del nucli, formes posteriors de l'os, i distribució dels lligaments. Després de comparar a nivell biomecànic l'antiga geometria amb la nova, els resultats mostraren que els rols relatius dels teixits modelats depenen de la geometria. En general, les distribucions de càrrega predites eren més fisiològiques en el nou model. En canvi, ambdós models, reprodueixen rangs experimentals de moviment, així doncs la seva validació hauria de tenir en compte les transferències de càrrega locals.El Capítol 4 es centra en la variabilitat dels angles creuats del col·lagen de l'anell. Es crearen quatre models bisegment amb organitzacions d'anell fibrós basats en la bibliografia comparant-se sota diverses càrregues. A més es proposà un paràmetre d'estabilització de l'anell per analogia a un tub de parets gruixudes. La biomecànica del model depenia en gran mesura de l'organització de l'anell fibrós, però el paràmetre d'estabilització era soviet contradictori amb les tensions i forces predites. Així, s'assumí que la geometria de la columna i l'organització de l'anell fibrós estaven lligades. Les xarxes d'anell de col·lagen adaptades es poden determinar numèricament, però els models d'anell haurien d'estar bastats en relacions mecanobiològiques.Al Capítol 5 es presenta un model de disc artificial acoblat amb el model de L3-L5. Models bisegment amb i sense implant van ser comparats amb càrregues controlades per força o desplaçament, incloent o no l'aproximació del pes del cos. La rigidesa de la pròtesi alterava generalment les distribucions de càrrega i les rotacions controlades per desplaçament conduint a grans efectes adjacents. Incloent el pes del cos les condicions de contorn semblaven més fisòlogiques que sense. Malgrat la rigidesa del nou disc, aquest sembla més prometedor que altres dispositius comercials.En aquesta tesi s'han creat sis models nous elements finits de la columna lumbar osteoligamentosa. Les simulacions han mostrat que l'ús fiable dels models requereix d'una descripció precisa de les càrregues locals i respostes mecàniques de teixits. Les prediccions locals van estar limitades qualitativament degudes al desconeixement de les estructures de teixit tou, equacions constitutives i condicions de contorn. En canvi, els models poden ser emprats com a laboratoris in silico per superar aquestes limitacions. Basat en la informació numèrica i experimental, s'ha proposat un procediment jeràrquic per al desenvolupament qualitativament fiable de models elements finits de la columna lumbar. / This PhD thesis investigated the use of finite element modelling to study lumbar spine biomechanics for clinical assessment. Bibliographic studies reported in the first Chapter showed clear functional relations between external forces and lumbar spine tissue structures and shapes. Clinical research revealed that independently of its origin, low back pain may be worsened by altered tissue mechanical environments. Experimental measurements alone cannot truly describe the load distributions between the different lumbar spine tissues. Thus, finite element models have been used in the past. But model reliability in predicting local tissue loadings is still not manifest and has been explored in this thesis as described in the following chapters.In Chapter 2, a L3-L5 lumbar spine bi-segment model was built. An initial model was completed to include the vertebral cortex, a full definition of the facet joints, the cartilage endplates, and an improved description of the annulus fibre-reinforced structure. Simplified load-cases used for in vitro studies were simulated to calculate stress and strain energy distributions. Predictions within the L3-L5 lumbar spine bi-segment model could be interpreted in terms of functional load distributions related to known tissue structures, but the overall L3-L5 bisegment model geometry needed further update.Thus, in Chapter 3, a geometrically accurate L3-L5 lumbar spine bi-segment model was created. The new model included corrected L3 and L5 body shapes and dimensions, corrected disc heights and nucleus placements, corrected posterior bone shapes, dimensions, and orientations, and corrected ligament distributions. The new and old geometries were biomechanically compared. Results showed that the relative roles of modelled tissues greatly depend on the geometry. Predicted load distributions were generally more physiological in the new model. However, new and old models could both reproduce experimental ranges of motion, meaning that their validation should take into account local load transfers.Chapter 4 focuses on the variability of the annulus collagen criss-cross angles. Four bi-segment models with literature-based annulus fibre organizations were created and compared under diverse loads. Moreover, an annulus stabilization parameter was proposed by analogy to a thick walled pipe. Model biomechanics greatly depended on the annulus fibre organization, but annulus stabilization parameter was often contradictory with the predicted stresses and strains. Spine geometry and annulus fibrous organization were hypothesized to be linked together. Adapted annulus collagen networks may be numerically determined, but annulus modelling should be based on mechano-biological relationships.In Chapter 5, a case-study of a novel artificial disc design coupled with the L3-L5 lumbar spine model is presented. Bi-segment models with and without implant were compared under load- or displacement-controlled rotations, with or without body-weight like load. Prosthesis stiffness generally altered the load distributions and displacement-controlled rotations led to strong adjacent level effects. Including body weight-like loads seemed to give more realistic results. Although the novel disc substitute is too stiff, it is more promising than other existing commercial devices.In this thesis, six new osteoligamentous lumbar spine bi-segment finite element models were created. Simulations showed that reliable use of lumbar spine finite element models requires precise descriptions of local tissue loading and response. Local predictions were qualitatively mainly limited by a lack of knowledge about soft tissue structural organisations, constitutive equations, and boundary conditions. However, models can be used as in silico laboratories to overcome such limitations. A hierarchical procedure for the development of qualitatively reliable lumbar spine finite element models was proposed based on available numerical and experimental inputs.

A suspension flow model based on the "suspension balance" approach has been developed. This work modifies the model to allow the solution of suspension flows under general flow conditions. This requires the development of a frame-invariant constitutive model for the particle stress which can take into account the spatially-varying local kinematic conditions. The mass and momentum balances for the bulk suspension and particle phase are solved numerically using a finite volume method. The particle stress is based upon the computed rate of strain and the local kinematic conditions. A nonlocal stress contribution corrects the continuum approximation of the particle phase for finite particle size effects. Local kinematic conditions are accounted through the local ratio of rotation to extension in the flow field. The coordinates for the stress definition are the local principal axes of the rate of strain field. The developed model is applied to a range of problems. (i) Axially-developing conduit flows are computed using both the full two-dimensional solution and the more computationally efficient "marching" method. The model predictions are compared to experimental results for cross-stream particle concentration profiles and axial development lengths. (ii) Model predictions are compared to experiments for wide-gap circular Couette flow of a concentrated suspension in a shear-thinning liquid. With minor modification, the suspension flow model predicts the major trends and results observed in this flow. (iii) Comparisons are made to experiments for an axisymmetric contraction-expansion. Model predictions for a two-dimensional planar contraction flow test the influence of model formulation. The variation of the magnitude of an isotropic particle normal stress with local kinematic conditions and anisotropy in the in-plane normal stresses are both explored. The formulation of the particle phase stress is found to have significant effects on the solid fraction and velocity. (iv) Finally, for a rectangular piston-driven flow and an obstructed channel flow, a "computational suspension dynamics" study explores the effect of particle migration on the bulk flow field, system pressure drop and particle phase composition.

The soil-structure interface is fundamental to the performance of many geotechnical engineering systems; including penetration test devices, deep foundations, and retaining structures. In geotechnical engineering structures, the counterface may range from a polymer in the case of a geosynthetically reinforced earth retaining structure to steel for cone penetration testing or pile foundations. Interface strength is affected by many factors, among which surface roughness is the most dominant. To date common practice has been to characterize counterface surface roughness by a roughness parameter based on only its spatial properties and soil roughness separately by various incompatible means resulting in two roughness values unrelated to each other. The vast number of analyzing methods and developed parameters reveal the general confusion regarding this concept. Rather than analyzing the particulate and continuum media separately, it is compulsory to coalesce the analysis and quantify the relative nature of interface behavior. This can be accomplished by examining the particulate and continuum media through the same powerful tools. The motive of this study is to develop a unified approach to determining the index properties of particles and surfaces in a particle-surface interface. This is accomplished by examining several particle shape and surface roughness parameters in terms of their ability to uniquely describe and distinguish particulate medium and continuum roughness, respectively. In this study, surfaces are analyzed as derived particles by wrapping surface profiles and particles are evaluated as derived surfaces via unrolling particle outlines. In addition, particle shape parameters are modified to allow surface roughness analysis and surface roughness parameters are modified to characterize particle shape. A unified approach for particulate shape and continuum roughness would ultimately lead to a better understanding of micro-scale interaction mechanism and better quantification of macro-scale mobilized resistance for soil and engineering surface interaction.