Microstructure-based numerical modeling of the mechanical behavior of Mg alloys

Dentro de los materiales estructurales, el magnesio y sus aleaciones están siendo el foco de una de profunda investigación. Esta investigación está dirigida a comprender la relación existente entre la microestructura de las aleaciones de Mg y su comportamiento mecánico. El objetivo es optimizar las aleaciones actuales de magnesio a partir de su microestructura y diseñar nuevas aleaciones. Sin embargo, el efecto de los factores microestructurales (como la forma, el tamaño, la orientación de los precipitados y la morfología de los granos) en el comportamiento mecánico de estas aleaciones está todavía por descubrir. Para conocer mejor de la relación entre la microestructura y el comportamiento mecánico, es necesaria la combinación de técnicas avanzadas de caracterización experimental como de simulación numérica, a diferentes longitudes de escala. En lo que respecta a las técnicas de simulación numérica, la homogeneización policristalina es una herramienta muy útil para predecir la respuesta macroscópica a partir de la microestructura de un policristal (caracterizada por el tamaño, la forma y la distribución de orientaciones de los granos) y el comportamiento del monocristal. La descripción de la microestructura se lleva a cabo mediante modernas técnicas de caracterización (difracción de rayos X, difracción de electrones retrodispersados, así como con microscopia óptica y electrónica). Sin embargo, el comportamiento del cristal sigue siendo difícil de medir, especialmente en aleaciones de Mg, donde es muy complicado conocer el valor de los parámetros que controlan el comportamiento mecánico de los diferentes modos de deslizamiento y maclado. En la presente tesis se ha desarrollado una estrategia de homogeneización computacional para predecir el comportamiento de aleaciones de magnesio. El comportamiento de los policristales ha sido obtenido mediante la simulación por elementos finitos de un volumen representativo (RVE) de la microestructura, considerando la distribución real de formas y orientaciones de los granos. El comportamiento del cristal se ha simulado mediante un modelo de plasticidad cristalina que tiene en cuenta los diferentes mecanismos físicos de deformación, como el deslizamiento y el maclado. Finalmente, la obtención de los parámetros que controlan el comportamiento del cristal (tensiones críticas resueltas (CRSS) así como las tasas de endurecimiento para todos los modos de maclado y deslizamiento) se ha resuelto mediante la implementación de una metodología de optimización inversa, una de las principales aportaciones originales de este trabajo. La metodología inversa pretende, por medio del algoritmo de optimización de Levenberg-Marquardt, obtener el conjunto de parámetros que definen el comportamiento del monocristal y que mejor ajustan a un conjunto de ensayos macroscópicos independientes. Además de la implementación de la técnica, se han estudiado tanto la objetividad del metodología como la unicidad de la solución en función de la información experimental. La estrategia de optimización inversa se usó inicialmente para obtener el comportamiento cristalino de la aleación AZ31 de Mg, obtenida por laminado. Esta aleación tiene una marcada textura basal y una gran anisotropía plástica. El comportamiento de cada grano incluyó cuatro mecanismos de deformación diferentes: deslizamiento en los planos basal, prismático, piramidal hc+ai, junto con el maclado en tracción. La validez de los parámetros resultantes se validó mediante la capacidad del modelo policristalino para predecir ensayos macroscópicos independientes en diferentes direcciones. En segundo lugar se estudió mediante la misma estrategia, la influencia del contenido de Neodimio (Nd) en las propiedades de una aleación de Mg-Mn-Nd, obtenida por extrusión. Se encontró que la adición de Nd produce una progresiva isotropización del comportamiento macroscópico. El modelo mostró que este incremento de la isotropía macroscópica era debido tanto a la aleatoriedad de la textura inicial como al incremento de la isotropía del comportamiento del cristal, con valores similares de las CRSSs de los diferentes modos de deformación. Finalmente, el modelo se empleó para analizar el efecto de la temperatura en el comportamiento del cristal de la aleación de Mg-Mn-Nd. La introducción en el modelo de los efectos non-Schmid sobre el modo de deslizamiento piramidal hc+ai permitió capturar el comportamiento mecánico a temperaturas superiores a 150_C. Esta es la primera vez, de acuerdo con el conocimiento del autor, que los efectos non-Schmid han sido observados en una aleación de Magnesio. The study of Magnesium and its alloys is a hot research topic in structural materials. In particular, special attention is being paid in understanding the relationship between microstructure and mechanical behavior in order to optimize the current alloy microstructures and guide the design of new alloys. However, the particular effect of several microstructural factors (precipitate shape, size and orientation, grain morphology distribution, etc.) in the mechanical performance of a Mg alloy is still under study. The combination of advanced characterization techniques and modeling at several length scales is necessary to improve the understanding of the relation microstructure and mechanical behavior. Respect to the simulation techniques, polycrystalline homogenization is a very useful tool to predict the macroscopic response from polycrystalline microstructure (grain size, shape and orientation distributions) and crystal behavior. The microstructure description is fully covered with modern characterization techniques (X-ray diffraction, EBSD, optical and electronic microscopy). However, the mechanical behaviour of single crystals is not well-known, especially in Mg alloys where the correct parameterization of the mechanical behavior of the different slip/twin modes is a very difficult task. A computational homogenization framework for predicting the behavior of Magnesium alloys has been developed in this thesis. The polycrystalline behavior was obtained by means of the finite element simulation of a representative volume element (RVE) of the microstructure including the actual grain shape and orientation distributions. The crystal behavior for the grains was accounted for a crystal plasticity model which took into account the physical deformation mechanisms, e.g. slip and twinning. Finally, the problem of the parametrization of the crystal behavior (critical resolved shear stresses (CRSS) and strain hardening rates of all the slip and twinning modes) was obtained by the development of an inverse optimization methodology, one of the main original contributions of this thesis. The inverse methodology aims at finding, by means of the Levenberg-Marquardt optimization algorithm, the set of parameters defining crystal behavior that best fit a set of independent macroscopic tests. The objectivity of the method and the uniqueness of solution as function of the input information has been numerically studied. The inverse optimization strategy was first used to obtain the crystal behavior of a rolled polycrystalline AZ31 Mg alloy that showed a marked basal texture and a strong plastic anisotropy. Four different deformation mechanisms: basal, prismatic and pyramidal hc+ai slip, together with tensile twinning were included to characterize the single crystal behavior. The validity of the resulting parameters was proved by the ability of the polycrystalline model to predict independent macroscopic tests on different directions. Secondly, the influence of Neodymium (Nd) content on an extruded polycrystalline Mg-Mn-Nd alloy was studied using the same homogenization and optimization framework. The effect of Nd addition was a progressive isotropization of the macroscopic behavior. The model showed that this increase in the macroscopic isotropy was due to a randomization of the initial texture and also to an increase of the crystal behavior isotropy (similar values of the CRSSs of the different modes). Finally, the model was used to analyze the effect of temperature on the crystal behaviour of a Mg-Mn-Nd alloy. The introduction in the model of non-Schmid effects on the pyramidal hc+ai slip allowed to capture the inverse strength differential that appeared, between the tension and compression, above 150_C. This is the first time, to the author's knowledge, that non-Schmid effects have been reported for Mg alloys.

Effect of layer thickness on the high temperature mechanical properties of Al/SiC nanolaminates

Composite laminates on the nanoscale have shown superior hardness and toughness, but little is known about their high temperature behavior. The mechanical properties (elastic modulus and hardness) were measured as a function of temperature by means of nanoindentation in Al/SiC nanolaminates, a model metal–ceramic nanolaminate fabricated by physical vapor deposition. The influence of the Al and SiC volume fraction and layer thicknesses was determined between room temperature and 150 °C and, the deformation modes were analyzed by transmission electron microscopy, using a focused ion beam to prepare cross-sections through selected indents. It was found that ambient temperature deformation was controlled by the plastic flow of the Al layers, constrained by the SiC, and the elastic bending of the SiC layers. The reduction in hardness with temperature showed evidence of the development of interface-mediated deformation mechanisms, which led to a clear influence of layer thickness on the hardness.

Mechanical behavior and failure micromechanisms of hybrid 3D woven composites in tension

The deformation and failure micromechanisms of a hybrid 3D woven composite were studied in tension. Plain and open-hole composite coupons were tested in tension until failure in the fill and warp directions, as well as fiber tows extracted from the dry fabric and impregnated with the matrix. The macroscopic evolution of damage in the composite coupons was assessed by means of periodic unloading–reloading (to obtain the elastic modulus and the residual strain), whereas the microscopic mechanism were established by means of X-ray computed microtomography. To this end, specimens were periodically removed from the mechanical testing machine and infiltrated with ZnI-containing liquid to assess the main damage modes as a function of the applied strain. The experimental observations and the predictions of an isostrain model were used to understand the key factors controlling the elastic modulus, strength and notch sensitivity of hybrid 3D woven composites in tension. It was found that the full contribution of the glass fibers to the composite strength was not employed, due to the premature fracture of the carbon fibers, but their presence increased the fracture strain and the energy dissipated during fracture. Thus, hybridization of the 3D woven composite led to a notch-insensitive behavior as demonstrated by open-hole tests

A numerical study of the influence of microvoids in the transverse mechanical response of unidirectional composites

The effect of porosity on the transverse mechanical properties of unidirectional fiber-reinforced composites is studied by means of computational micromechanics. The composite behavior is simulated by the finite element analysis of a representative volume element of the composite microstructure in which the random distribution of fibers and the voids are explicitly included. Two types of voids – interfiber voids and matrix voids – were included in the microstructure and the actual damage mechanisms in the composite, namely matrix and interface failure, were accounted for. It was found that porosity (in the range 1–5%) led to a large reduction in the transverse strength and the influence of both types of voids in the onset and propagation of damage throughout the microstructure was studied under transverse tension and compression. Finally, the failure locus of the composite lamina under transverse tension/compression and out-of-plane shear was obtained by means of computational micromechanics and compared with the predictions of Puck’s model and with experimental data available in the literature. The results show that the strength of composites is significantly reduced by the presence of voids

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion for high strain and ballistic applications is presented. A Lode angle dependent function is added to the equivalent plastic strain to failure definition of the Johnson–Cook failure criterion. The weakening in the elastic law and in the Johnson–Cook-like constitutive relation implicitly introduces the Lode angle dependency in the elastoplastic behaviour. The material model is calibrated for precipitation hardened Inconel 718 nickel-base superalloy. The combination of a Lode angle dependent failure criterion with weakened constitutive equations is proven to predict fracture patterns of the mechanical tests performed and provide reliable results. Additionally, the mesh size dependency on the prediction of the fracture patterns was studied, showing that was crucial to predict such patterns

A computational model coupling mechanics and electrophysiology in spinal cord injury

Traumatic brain injury and spinal cord injury have recently been put under the spotlight as major causes of death and disability in the developed world. Despite the important ongoing experimental and modeling campaigns aimed at understanding the mechanics of tissue and cell damage typically observed in such events, the differentiated roles of strain, stress and their corresponding loading rates on the damage level itself remain unclear. More specifically, the direct relations between brain and spinal cord tissue or cell damage, and electrophysiological functions are still to be unraveled. Whereas mechanical modeling efforts are focusing mainly on stress distribution and mechanistic-based damage criteria, simulated function-based damage criteria are still missing. Here, we propose a new multiscale model of myelinated axon associating electrophysiological impairment to structural damage as a function of strain and strain rate. This multiscale approach provides a new framework for damage evaluation directly relating neuron mechanics and electrophysiological properties, thus providing a link between mechanical trauma and subsequent functional deficits

Vortex-induced vibrations on bridges : the interaction mechanism in complex sections and a new proposed semi-empirical model

El presente trabajo de investigación se ocupa del estudio de las vibraciones verticales inducidas por vórtices (VIV) en aquellos puentes que, por sus características geométricas y propiedades dinámicas, muestran cierta sensibilidad este tipo de fenómeno aeroelástico. El objeto principal es el análisis del mecanismo de interacción viento-estructura sobre secciones no fuseladas de geometría simple, con objeto de realizar una adecuada caracterización del problema y poder abordar posteriormente el análisis de otras secciones de geometría más compleja, representativas de los principales elementos estructurales de los puentes, como arcos, tableros, torres y pilas. Este aspecto es fundamental durante la fase de diseño del puente, donde deberán tenerse en cuenta también una serie de detalles que pueden influir significativamente su sensibilidad ante problemas aerodinámicos, como la morfología y dimensiones principales de la sección transversal del tablero, la disposición de barreras de seguridad y barreras cortaviento, o las riostras que unen diferentes elementos estructurales. La configuración de dos elementos en tándem o la construcción de un puente en las inmediaciones de otro existente son otros aspectos a considerar respecto a la sensibilidad frente a efectos aeroelásticos. El estudio se ha llevado a cabo principalmente mediante la implementación de simulaciones numéricas que reproducen la interacción entre la corriente de aire y secciones representativas de modelos estructurales, a partir de un código CFD basado en el método de las partículas de vórtices (VPM), siguiendo por tanto un esquema Lagrangiano. Los resultados han sido validados con datos experimentales existentes, valores procedentes de ensayos en túnel de viento y registros reales a partir de diferentes casos de estudio: Alconétar (2006), Niterói (1980), Trans- Tokyo Bay (1995) y Volgogrado (2010). Finalmente, se propone un modelo semi-empírico para la estimación del rango de velocidades críticas y amplitudes de oscilación basado en la utilización de las derivadas de flameo de Scanlan, y la densidad espectral de las fuerzas aerodinámicas en el dominio de la frecuencia. The present research work concerns the study of vertical vortex-induced vibrations (VIV) in bridges which show certain sensitivity to this type of aeroelastic phenomenon. It focuses on the analysis of the wind-structure interaction mechanism on bluff sections, with the objective of making a good characterisation of the problem and subsequently addressing the analysis of sections with a complex geometry, which are representative of the bridge structural elements, such as arches, decks, towers and piers. This issue is of relative importance during the bridge design phase, since minor details of the aforementioned elements can significantly influence its sensitivity to aerodynamic problems. The shape and main dimensions of the deck cross section, the addition of safety barriers and windshields, the presence of braces to enhance the structure mechanical properties, the utilisation of cross sections in tandem arrangement, or the erection of a new bridge in the vicinity of another existing one are some of the aspects to be considered regarding the sensitivity to the aeroelastic effects. The study has been carried out mainly through the implementation of numerical simulations that reproduces the interaction between the airflow and the representative cross section of a structural bridge model, by the use of a CFD code based on the vortex particle method (VPM), thus following a Lagrangian scheme. The results have been validated with existing experimental data, values from wind tunnel tests and full scale observations from the different case studies: Alconétar (2006), Niterói (1980), Trans-Tokyo Bay (1995) and Volgograd (2010). Finally, a new semi-empirical model is proposed for the estimation of the critical wind velocity ranges and oscillation amplitudes based on the use of the Scanlan’s flutter derivatives and the power spectral density of aerodynamic force time history in the frequency domain.

A study of the mechanical behaviour of the human aortic artery by means of non-linear finite element models

En la presente tesis desarrollamos una estrategia para la simulación numérica del comportamiento mecánico de la aorta humana usando modelos de elementos finitos no lineales. Prestamos especial atención a tres aspectos claves relacionados con la biomecánica de los tejidos blandos. Primero, el análisis del comportamiento anisótropo característico de los tejidos blandos debido a las familias de fibras de colágeno. Segundo, el análisis del ablandamiento presentado por los vasos sanguíneos cuando estos soportan cargas fuera del rango de funcionamiento fisiológico. Y finalmente, la inclusión de las tensiones residuales en las simulaciones en concordancia con el experimento de apertura de ángulo. El análisis del daño se aborda mediante dos aproximaciones diferentes. En la primera aproximación se presenta una formulación de daño local con regularización. Esta formulación tiene dos ingredientes principales. Por una parte, usa los principios de la teoría de la fisura difusa para garantizar la objetividad de los resultados con diferentes mallas. Por otra parte, usa el modelo bidimensional de Hodge-Petruska para describir el comportamiento mesoscópico de los fibriles. Partiendo de este modelo mesoscópico, las propiedades macroscópicas de las fibras de colágeno son obtenidas a través de un proceso de homogenización. En la segunda aproximación se presenta un modelo de daño no-local enriquecido con el gradiente de la variable de daño. El modelo se construye a partir del enriquecimiento de la función de energía con un término que contiene el gradiente material de la variable de daño no-local. La inclusión de este término asegura una regularización implícita de la implementación por elementos finitos, dando lugar a resultados de las simulaciones que no dependen de la malla. La aplicabilidad de este último modelo a problemas de biomecánica se estudia por medio de una simulación de un procedimiento quirúrgico típico conocido como angioplastia de balón. In the present thesis we develop a framework for the numerical simulation of the mechanical behaviour of the human aorta using non-linear finite element models. Special attention is paid to three key aspects related to the biomechanics of soft tissues. First, the modelling of the characteristic anisotropic behaviour of the softue due to the collagen fibre families. Secondly, the modelling of damage-related softening that blood vessels exhibit when subjected to loads beyond their physiological range. And finally, the inclusion of the residual stresses in the simulations in accordance with the opening-angle experiment The modelling of damage is addressed with two major and different approaches. In the first approach a continuum local damage formulation with regularisation is presented. This formulation has two principal ingredients. On the one hand, it makes use of the principles of the smeared crack theory to avoid the mesh size dependence of the structural response in softening. On the other hand, it uses a Hodge-Petruska bidimensional model to describe the fibrils as staggered arrays of tropocollagen molecules, and from this mesoscopic model the macroscopic material properties of the collagen fibres are obtained using an homogenisation process. In the second approach a non-local gradient-enhanced damage formulation is introduced. The model is built around the enhancement of the free energy function by means of a term that contains the referential gradient of the non-local damage variable. The inclusion of this term ensures an implicit regularisation of the finite element implementation, yielding mesh-objective results of the simulations. The applicability of the later model to biomechanically-related problems is studied by means of the simulation of a typical surgical procedure, namely, the balloon angioplasty.

Multiscale analysis of the mechanical behavior of needle-punched nonwoven fabrics

Los fieltros son una familia de materiales textiles constituidos por una red desordenada de fibras conectadas por medio de enlaces térmicos, químicos o mecánicos. Presentan menor rigidez y resistencia (al igual que un menor coste de procesado) que sus homólogos tejidos, pero mayor deformabilidad y capacidad de absorción de energía. Los fieltros se emplean en diversas aplicaciones en ingeniería tales como aislamiento térmico, geotextiles, láminas ignífugas, filtración y absorción de agua, impacto balístico, etc. En particular, los fieltros punzonados fabricados con fibras de alta resistencia presentan una excelente resistencia frente a impacto balístico, ofreciendo las mismas prestaciones que los materiales tejidos con un tercio de la densidad areal. Sin embargo, se sabe muy poco acerca de los mecanismos de deformación y fallo a nivel microscópico, ni sobre como influyen en las propiedades mecánicas del material. Esta carencia de conocimiento dificulta la optimización del comportamiento mecánico de estos materiales y también limita el desarrollo de modelos constitutivos basados en mecanismos físicos, que puedan ser útiles en el diseño de componentes estructurales. En esta tesis doctoral se ha llevado a cabo un estudio minucioso con el fin de determinar los mecanismos de deformación y las propiedades mecánicas de fieltros punzonados fabricados con fibras de polietileno de ultra alto peso molecular. Los procesos de deformación y disipación de energía se han caracterizado en detalle por medio de una combinación de técnicas experimentales (ensayos mecánicos macroscópicos a velocidades de deformación cuasi-estáticas y dinámicas, impacto balístico, ensayos de extracción de una o múltiples fibras, microscopía óptica, tomografía computarizada de rayos X y difracción de rayos X de gran ángulo) que proporcionan información de los mecanismos dominantes a distintas escalas. Los ensayos mecánicos macroscópicos muestran que el fieltro presenta una resistencia y ductilidad excepcionales. El estado inicial de las fibras es curvado, y la carga se transmite por el fieltro a través de una red aleatoria e isótropa de nudos creada por el proceso de punzonamiento, resultando en la formación de una red activa de fibra. La rotación y el estirado de las fibras activas es seguido por el deslizamiento y extracción de la fibra de los puntos de anclaje mecánico. La mayor parte de la resistencia y la energía disipada es proporcionada por la extracción de las fibras activas de los nudos, y la fractura final tiene lugar como consecuencia del desenredo total de la red en una sección dada donde la deformación macroscópica se localiza. No obstante, aunque la distribución inicial de la orientación de las fibras es isótropa, las propiedades mecánicas resultantes (en términos de rigidez, resistencia y energía absorbida) son muy anisótropas. Los ensayos de extracción de múltiples fibras en diferentes orientaciones muestran que la estructura de los nudos conecta más fibras en la dirección transversal en comparación con la dirección de la máquina. La mejor interconectividad de las fibras a lo largo de la dirección transversal da lugar a una esqueleto activo de fibras más denso, mejorando las propiedades mecánicas. En términos de afinidad, los fieltros deformados a lo largo de la dirección transversal exhiben deformación afín (la deformación macroscópica transfiere directamente a las fibras por el material circundante), mientras que el fieltro deformado a lo largo de la dirección de la máquina presenta deformación no afín, y la mayor parte de la deformación macroscópica no es transmitida a las fibras. A partir de estas observaciones experimentales, se ha desarrollado un modelo constitutivo para fieltros punzonados confinados por enlaces mecánicos. El modelo considera los efectos de la deformación no afín, la conectividad anisótropa inducida durante el punzonamiento, la curvatura y re-orientación de la fibra, así como el desenredo y extracción de la fibra de los nudos. El modelo proporciona la respuesta de un mesodominio del material correspondiente al volumen asociado a un elemento finito, y se divide en dos bloques. El primer bloque representa el comportamiento de la red y establece la relación entre el gradiente de deformación macroscópico y la respuesta microscópica, obtenido a partir de la integración de la respuesta de las fibras en el mesodominio. El segundo bloque describe el comportamiento de la fibra, teniendo en cuenta las características de la deformación de cada familia de fibras en el mesodominio, incluyendo deformación no afín, estiramiento, deslizamiento y extracción. En la medida de lo posible, se ha asignado un significado físico claro a los parámetros del modelo, por lo que se pueden identificar por medio de ensayos independientes. Las simulaciones numéricas basadas en el modelo se adecúan a los resultados experimentales de ensayos cuasi-estáticos y balísticos desde el punto de vista de la respuesta mecánica macroscópica y de los micromecanismos de deformación. Además, suministran información adicional sobre la influencia de las características microstructurales (orientación de la fibra, conectividad de la fibra anisótropa, afinidad, etc) en el comportamiento mecánico de los fieltros punzonados. Nonwoven fabrics are a class of textile material made up of a disordered fiber network linked by either thermal, chemical or mechanical bonds. They present lower stiffness and strength (as well as processing cost) than the woven counterparts but much higher deformability and energy absorption capability and are used in many different engineering applications (including thermal insulation, geotextiles, fireproof layers, filtration and water absorption, ballistic impact, etc). In particular, needle-punched nonwoven fabrics manufactured with high strength fibers present an excellent performance for ballistic protection, providing the same ballistic protection with one third of the areal weight as compared to dry woven fabrics. Nevertheless, very little is known about their deformation and fracture micromechanisms at the microscopic level and how they contribute to the macroscopic mechanical properties. This lack of knowledge hinders the optimization of their mechanical performance and also limits the development of physically-based models of the mechanical behavior that can be used in the design of structural components with these materials. In this thesis, a thorough study was carried out to ascertain the micromechanisms of deformation and the mechanical properties of a needle-punched nonwoven fabric made up by ultra high molecular weight polyethylene fibers. The deformation and energy dissipation processes were characterized in detail by a combination of experimental techniques (macroscopic mechanical tests at quasi-static and high strain rates, ballistic impact, single fiber and multi fiber pull-out tests, optical microscopy, X-ray computed tomography and wide angle X-ray diffraction) that provided information of the dominant mechanisms at different length scales. The macroscopic mechanical tests showed that the nonwoven fabric presented an outstanding strength and energy absorption capacity. It was found that fibers were initially curved and the load was transferred within the fabric through the random and isotropic network of knots created by needlepunching, leading to the formation of an active fiber network. Uncurling and stretching of the active fibers was followed by fiber sliding and pull-out from the entanglement points. Most of the strength and energy dissipation was provided by the extraction of the active fibers from the knots and final fracture occurred by the total disentanglement of the fiber network in a given section at which the macroscopic deformation was localized. However, although the initial fiber orientation distribution was isotropic, the mechanical properties (in terms of stiffness, strength and energy absorption) were highly anisotropic. Pull-out tests of multiple fibers at different orientations showed that structure of the knots connected more fibers in the transverse direction as compared with the machine direction. The better fiber interconnection along the transverse direction led to a denser active fiber skeleton, enhancing the mechanical response. In terms of affinity, fabrics deformed along the transverse direction essentially displayed affine deformation {i.e. the macroscopic strain was directly transferred to the fibers by the surrounding fabric, while fabrics deformed along the machine direction underwent non-affine deformation, and most of the macroscopic strain was not transferred to the fibers. Based on these experimental observations, a constitutive model for the mechanical behavior of the mechanically-entangled nonwoven fiber network was developed. The model accounted for the effects of non-affine deformation, anisotropic connectivity induced by the entanglement points, fiber uncurling and re-orientation as well as fiber disentanglement and pull-out from the knots. The model provided the constitutive response for a mesodomain of the fabric corresponding to the volume associated to a finite element and is divided in two blocks. The first one was the network model which established the relationship between the macroscopic deformation gradient and the microscopic response obtained by integrating the response of the fibers in the mesodomain. The second one was the fiber model, which took into account the deformation features of each set of fibers in the mesodomain, including non-affinity, uncurling, pull-out and disentanglement. As far as possible, a clear physical meaning is given to the model parameters, so they can be identified by means of independent tests. The numerical simulations based on the model were in very good agreement with the experimental results of in-plane and ballistic mechanical response of the fabrics in terms of the macroscopic mechanical response and of the micromechanisms of deformation. In addition, it provided additional information about the influence of the microstructural features (fiber orientation, anisotropic fiber connectivity, affinity) on the mechanical performance of mechanically-entangled nonwoven fabrics.

Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation

The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

Topographical and mechanical characterization of living eukaryotic cells on opaque substrates: development of a general procedure and its application to the study of non-adherent lymphocytes

The mechanical behavior of living murine T-lymphocytes was assessed by atomic force microscopy (AFM). A robust experimental procedure was developed to overcome some features of lymphocytes, in particular their spherical shape and non-adherent character. The procedure included the immobilization of the lymphocytes on amine-functionalized substrates, the use of hydrodynamic effects on the deflection of the AFM cantilever to monitor the approaching, and the use of the jumping mode for obtaining the images. Indentation curves were analyzed according to Hertz's model for contact mechanics. The calculated values of the elastic modulus are consistent both when considering the results obtained from a single lymphocyte and when comparing the curves recorded from cells of different specimens

A regularised continuum damage model based on the mesoscopic scale for soft tissue

Material properties of soft fibrous tissues are highly conditioned by the hierarchical structure of this kind of composites. Collagen based tissues present, at decreasing length scales, a complex framework of fibres, fibrils, tropocollagen molecules and amino-acids. Understanding the mechanical behaviour at nano-scale level is critical to accurately incorporate this structural information in phenomenological damage models. In this work we derive a relationship between the mechanical and geometrical properties of the fibril constituents and the soft tissue material parameters at macroscopic scale. A Hodge–Petruska two-dimensional model has been used to describe the fibrils as staggered arrays of tropocollagen molecules. After a mechanical characterisation of each of the fibril components, two fibril failures modes have been defined related with two planes of weakness. A phenomenological continuous damage model with regularised softening was presented along with meso-structurally based definitions for its material parameters. Finally, numerical analysis at fibril, fibre and tissue levels are presented to show the capabilities of the model