Differences in the structural response of 'granny-smith' apples under mechanical impact and compression

Apple fruits, cv. Granny Smith, were subjected to mechanical impact and compression loads utilizing a steel rod with a spherical tip 19 mm diameter, 50.6 g mass. Energies applied were low enough to produce enzymatic reaction: 0.0120 J for impact, and 0.0199 J for compression. Bruised material was cut and examined with a transmission electron microscope. In both compression and impact, bruises showed a central region located in the flesh parenchyma, at a distance that approximately equalled the indentor tip radius. The parenchyma cells of this region were more altered than cells from the epidermis and hypodermis. Tissues under compression presented numerous deformed parenchyma cells with broken tonoplasts and tissue degradation as predicted by several investigators. The impacted cells supported different kinds of stresses than compressed cells, resulting in the formation of intensive vesiculation, either in the vacuole or in the middle lamella region between cell walls of adjacent cells. A large proportion of parenchyma cells completely split or had initiated splitting at the middle lamella. Bruising may develop with or without cell rupture. Therefore, cell wall rupture is not essential for the development of a bruise, at least the smallest one, as predicted previously

Woolliness assessment in peaches. Comparison between human and instrumental procedures and results

Woolliness, a negative attribute of sensory texture, is characterised by the lack of juiciness without variation of the tissue water content an incapacity of ripening although there is external ripe appearance. In this study, peaches cv Springcrest (early and soft flesh peaches) and Miraflores (late and hard flesh peaches) corresponding to three different maturity stages at harvest, stored 0, 1, 2, 3 and 4 weeks at 1 and 5°C have been tested by instrumental and sensory means. A Instrumental classification of woolliness has been compared to the sensory assessment. For Springcrest peaches the sensory results match with those found for the instrumental procedure. In this case , Woolliness appears after 2 weeks of storage at 5°C, changing abruptly from crispy to woolly. Miraflores peaches did not develop woolliness during storage. After comparing with sensory results, it is shown that a common instrumental scale may be appropriate to classify for woolliness all peach varieties.

Effect of the temperature, strain rate and microstructure on flow and fracture characteristics of Ti-45Al-2Nb-2Mn+0.8vol.% TiB2 XD alloy

A series of quasi-static and dynamic tensile tests at varying temperatures were carried out to determine the mechanical behaviour of Ti-45Al-2Nb-2Mn+0.8vol.% TiB2 XD as-HIPed alloy. The temperature for the tests ranged from room temperature to 850  ∘C. The effect of the temperature on the ultimate tensile strength, as expected, was almost negligible within the selected temperature range. Nevertheless, the plastic flow suffered some softening because of the temperature. This alloy presents a relatively low ductility; thus, a low tensile strain to failure. The dynamic tests were performed in a Split Hopkinson Tension Bar, showing an increase of the ultimate tensile strength due to the strain rate hardening effect. Johnson-Cook constitutive relation was used to model the plastic flow. A post-testing microstructural of the specimens revealed an inhomogeneous structure, consisting of lamellar α2 + γ structure and γ phase equiaxed grains in the centre, and a fully lamellar structure on the rest. The assessment of the duplex-fully lamellar area ratio showed a clear relationship between the microstructure and the fracture behaviour.

A robust numerical framework to the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

Damage Mechanisms in the Handling of fruits.

Recent findings on the importance of losses due to damage incidence, on causes and on mechanisms of damage in fruits are reviewed and discussed. Incidence of damage in different fruits in some European markets has been -proved to be very high. Structure of fruit flesh and skin (hystology) is of foremost importance in the response of fruits to impacts and to compression. Continuous variation of fruit compositional and structural characteristics during maturation has to be taken into consideration when studying damage susceptibility.

Mealiness assessment in apples and peaches using MRI techniques.

Since Januarv 1946 a wade EC Project entitled "Mealiness in fruits Consumers perception and means for detection is being carried out. Mealiness is a sensory attribute that cannot be defined by a single parameter but through a combination of variables (multidimensional structure) Previous studies propose the definition of mealiness as the lack of crispiness of hardness and of juiciness. A destructive instrumental procedure combined with a integration technique has been already developed enabling to identify mealy fruits by destructive instrumental means use other contributions of Barreiro and Ortiz to this Ag Eng 98. Current aims .are focused on establishing non destructive tests for mealiness assessment. Magnetic resonance Imaging (MRI) makes use of the magnetic properties that some atomic nuclei have. especially hidrogen nuclei from water molecules to obtain high quality images in the field of internal quality evaluation the MRI has been used to assess internal injury due to conservation as o treatments as chilling injury un Persimmons Clark&Forbes (1994) and water-core in apples (Wang et al. 1998. In the case of persimmons the chilling injury is described as an initial tissue breakdown and lack of cohesion between cells followed by formation of a firm gel and by a lack of juiciness without changes in the total amount ol water content. Also a browning of the flesh is indicated (Clark&Forhes 1994). This definition fits into the previous description of mealiness.

Lateral impact sensor for measuring firmness of fruits in an experimental packing line.

Different parameters are used to quantify the maturity of fruits at or near harvest (shape, color, flesh texture and internal composition). Flesh firmness is a critical handling parameter for fruits such as peach, pear and apple. Results of previous studies conducted by different researchers have shown that impact techniques can be used to evaluate firmness of fruits. A prototype impact system for firmness sorting of fruits was developed by Chen and Ruiz-Altisent (Chen et al, 1996). This sensor was mounted and tested successfully on a 3 m section of a commercial conveyor belt (Chen et al, 1998). This is a further development of the on-line impact system for firmness sorting of fruits. The design of the sensor has been improved and it has been mounted on a experimental fruit packing line (Ortiz-Cañavate et al 1999).

Statistical characterization of soft tissue inelastic parameters and application to the material failure of the aortic ach

Caracterización de los procesos de disipación mecánica basándose en la microestructura de los tejidos blandos. We present a continuous damage model with regularized softening (smeared crack models) for fiber reinforced soft tissues. Material parameters of the continuous model derive from the mesoscopic scale. In the mesoscopic scale continuum is considered as a collagenous fibrilreinforced composite. We want to study the continnumlevel response as a function of the nanoscale properties of the collagen and the adherent forces between the tropocollagen molecules.

Storage stability of SBS/sulfur modified bitumens at high temperature: influence of bitumen composition and structure

Polymer modified bitumens, PMBs, are usually prepared at high temperature and subsequently stored for a period of time, also at high temperature. The stability of PMBs, in these conditions, has a decisive influence in order to obtain the adequate performances for practical applications. In this article the attention is focused in the analysis of the factors that determine the stability of styrene–butadiene–styrene copolymer (SBS)/sulfur modified bitumens when the mixtures are maintained at high temperature. Bitumens from different crude oil sources were used to prepare SBS/sulfur modified bitumens. Changes in the values of viscosity, softening point, as well as in the morphology of PMB samples, stored at 160 °C, were related to the bitumen chemical composition and to the amount of asphaltene micelles present in the neat bitumen used in their preparation El trabajo se centra en el estudio de la influencia de la estructura /composición del betún sobre la compatibilidad del sistema betún/SBS. Cuatro betunes provenientes de dos crudos distintos se seleccionaron y sus mezclas se utilizaron para preparar betunes modificados con contenidos de SBS del 3% en peso

Efecto de la adición de ingredientes funcionales en el comportamiento reológico y la textura de puré de patata (Cv. Kennebec) fresco y congelado

El interés creciente en encontrar alimentos precocinados congelados que se asemejen a productos naturales, capaces de superar un procesado con el menor daño, ha generado un aumento en el estudio de nuevos productos en este campo de la investigación. Las características de cada matriz alimentaria, la composición y estructura de los ingredientes, así como el efecto de las interacciones entre ellos, modifica la textura, estructura y las propiedades físicas y sensoriales del alimento, así como su aceptación por el consumidor. En este contexto, la investigación realizada en esta tesis doctoral se ha llevado a cabo en puré de patata considerado como una matriz alimentaria semisólida y se ha centrado en analizar los efectos de la concentración y modificación de la composición en las propiedades reológicas y de textura, en las propiedades físico-químicas y estructurales, así como en los atributos sensoriales de los purés de patata cuando a estos se le añaden diferentes ingredientes funcionales como fibra de guisante, inulina, aceite de oliva, aislado de proteína de soja, ácidos grasos omega 3 y/o sus mezclas. Para ello, se han realizado cuatro estudios donde se determinan las propiedades reológicas mediante ensayos dinámicos oscilatorios y en estado estacionario, los parámetros instrumentales de textura mediante ensayos de extrusión inversa y de penetración cónica, además de los cambios estructurales a través de cromatografía iónica con detector de pulsos amperométrico, cromatografía de gases con detector de ionización de llama y microscopía electrónica de barrido. Conjuntamente, se han evaluado los atributos sensoriales de los diferentes purés generando los descriptores que mejor definen la calidad sensorial del producto, utilizando un panel de jueces entrenados y valorándose la aceptación global de los nuevos productos mediante un panel de consumidores. En un primer estudio, el puré de patata natural congelado elaborado con crioprotectores se enriqueció con fibra dietética insoluble (fibra de guisante), fibra dietética soluble (inulina) y sus mezclas. La fibra de guisante influyó significativa y negativamente en la textura del puré de patata, percibiéndose en el producto un incremento de la dureza y de la arenosidad, mientras que la inulina produjo un ablandamiento del sistema. En un segundo estudio, el puré de patata natural fresco y congelado/descongelado elaborado con y sin crioprotectores, se enriqueció con fibra dietética soluble (inulina), aceite de oliva virgen extra y sus mezclas. La adición de estos dos ingredientes generó un ablandamiento de la matriz del sistema, produciéndose, sin embargo, un efecto sinérgico entre ambos ingredientes funcionales. La inulina tuvo un efecto más significativo en la viscosidad aparente del producto, mientras que el aceite de oliva virgen extra afectó más significativamente a la pseudoplasticidad, al índice de consistencia y a la viscosidad plástica del mismo. El proceso de congelación y descongelación utilizado favoreció la reducción del tamaño de las partículas de inulina haciéndolas imperceptibles al paladar, obteniéndose productos más cremosos y con mayor aceptabilidad global que sus homólogos frescos. En un tercer estudio, el puré de patata natural fresco y congelado/descongelado elaborado con crioprotectores se enriqueció con mezclas de fibra dietética soluble (inulina) y aislado de proteína de soja. Los resultados demostraron que el ciclo de congelación y descongelación realizado no afecta el grado de polimerización de la inulina. La estructura química de la inulina tampoco se vio afectada por la incorporación de la soja. El proceso de congelación/descongelación, así como la adición de concentraciones altas de inulina y bajas de aislado de proteína de soja, favorecen la disminución de la contribución de la componente viscosa en las propiedades viscoelásticas del puré de patata. La cremosidad fue el único atributo sensorial que presentó una correlación lineal significativa entre las puntuaciones otorgadas por panelistas entrenados y no entrenados. Por último, se elaboró un puré de patata natural fresco y congelado/descongelado optimizado con crioprotectores y enriquecido con la suma de ácido docosahexaenoico (DHA, C22:6 n-3) y ácido eicosapentaenoico (EPA, C20:5 n-3) y con ácido α-linolénico (ALA, C18:3 n-3) microencapsulados. El ciclo de congelación y descongelación no afectó al perfil de ácidos grasos del puré de patata. La adición de omega 3 procedente de aceites de lino y pescado microencapsulados mejora los indicadores nutricionales que definen la calidad de la grasa, obteniéndose un producto más saludable. ABSTRACT The growing interest in finding frozen precooked products that are like a natural product and capable of withstanding initial processing with minimum damage and remaining stable during preservation and reheating prior to consumption has generated an increase in studies of new products in this field of research. The characteristics of each food matrix, the composition and structure of the ingredients and the effect of interactions between them alter the texture, structure and physical and sensory properties of the food product and its acceptance by the consumer. In this context, the research conducted in this doctoral thesis was carried out on mashed potato, considered as a semi-solid food matrix, and focused on analysing the effects of concentration and modification of the composition of the mashed potato matrix on the rheological and textural properties, physicochemical and structural properties and sensory attributes of mashed potato when various functional ingredients are added to it, such as pea fibre, inulin, olive oil, soy protein isolate, omega 3 fatty acids and/or mixtures of these ingredients. Four studies were conducted for this purpose. Rheological properties were determined by oscillatory dynamic tests and stationary state tests, and instrumental texture parameters by backward extrusion and cone penetration tests. Structural changes were studied by ion chromatography with pulsed amperometric detector, gas chromatography with flame ionisation detector and scanning electron microscopy. The sensory attributes of the various mashed potato mixtures were evaluated by generating the descriptors that best defined the sensory quality of the products and using a panel of trained judges, and overall acceptance of the new products was evaluated by a panel of consumers. In the first study, frozen natural mashed potato incorporating cryoprotectants was enriched with insoluble dietary fibre (pea fibre), soluble dietary fibre (inulin) and mixtures of the two. Pea fibre had a significant negative influence on the texture of the mashed potato, producing an increase in hardness and granularity, whereas inulin produced a softening of the system. In the second study, fresh and frozen/thawed natural mashed potato prepared with and without cryoprotectants was enriched with soluble dietary fibre (inulin), extra virgin olive oil and mixtures of the two. The addition of these two ingredients generated softening of the matrix of the system, but a synergic effect between the two functional ingredients was produced. Inulin had a more significant effect on the apparent viscosity of the product, whereas extra virgin olive oil had a more significant effect on its pseudoplasticity, consistency index and plastic viscosity. The freezing and thawing process that was used contributed to a reduction in the size of the inulin particles, making them imperceptible to the palate and producing creamier products with greater overall acceptability than their fresh equivalents. In the third study, the fresh and frozen/thawed natural mashed potato incorporating cryoprotectants was enriched with mixtures of soluble dietary fibre (inulin) and soy protein isolate. The results showed that the freezing and thawing process that was performed did not affect the degree of polymerisation of the inulin. The chemical structure of the inulin was also not affected by the incorporation of soy. The freezing and thawing process and the addition of high concentrations of inulin and low concentrations of soy protein isolate favoured a decrease in the contribution of the viscous component to the viscoelastic properties of the mashed potato. Creaminess was the only sensory attribute that presented a significant linear correlation between the scores given by trained and untrained panellists. Lastly, fresh and frozen/thawed natural mashed potato optimised with cryoprotectants was prepared and enriched with the sum of docosahexaenoic acid (DHA, C22:6 n-3) and eicosapentaenoic acid (EPA, C20:5 n-3) and with α-linolenic acid (ALA, C18:3 n-3), microencapsulated. The freezing and thawing process did not affect the fatty acid profile of the mashed potato. The addition of omega 3 obtained from microencapsulated linseed and fish oils improved the nutritional indicators that define the quality of the fat, producing a healthier product.

Study of the effect of four warm mix asphalt additives on bitumen modified with 15% crumb rubber

Due to a growing concern over global warming, the bituminous mixture industry is making a constant effort to diminish its emissions by reducing manufacturing and installation temperatures without compromising the mechanical properties of the bituminous mixtures. The use of mixtures with tyre rubber has demonstrated that these mixtures can be economical and ecological and that they improve the behaviour of the pavements. However, bituminous mixtures with a high rubber content present one major drawback: they require higher mixing and installation temperatures due to the elevated viscosity caused by the high rubber content and thus they produce larger amounts of greenhouse gas emissions than conventional bituminous mixtures. This article presents a study of the effect of four viscosity-reducing additives (Sasobit®, Asphaltan A®, Asphaltan B® and Licomont BS 100®) on a bitumen modified with 15% rubber. The results of this study indicate that these additives successfully reduce viscosity, increase the softening temperature and reduce penetration. However, they do not have a clear effect on the test for elastic recovery and ductility at 25 °C.

Modelización tridimensional de ensayos de adherencia tipo viga del refuerzo NSM-FRP en hormigón

El uso de refuerzos NSM‐FRP en estructuras de hormigón armado se ha incrementado considerablemente en los últimos años como método de refuerzo estructural. Los ensayos de arrancamiento en viga de los refuerzos NSM‐FRP permiten el estudio del comportamiento de la unión pegada. El principal objetivo del presente trabajo aborda la simulación numérica de este tipo de ensayos, con el propósito de caracterizar correctamente la adherencia entre las barras de NSM‐FRP y el hormigón. En una fase inicial se simuló un modelo bidimensional para conseguir evaluar y verificar el comportamiento de los elementos cohesivos y ver su comportamiento primero ante diferentes modelos de material y segundo ante un modo mixto de fallo, debido a la aplicación simultanea de carga axial y carga cortante. En una segunda fase se creó un modelo tridimensional para estudiar el arrancamiento de una barra de material compuesto insertada en hormigón, creando un modelo de material de hormigón y viendo el comportamiento cualitativo del sistema ante variaciones en los parámetros de los diferentes materiales. En la tercera fase, la más importante del presente trabajo, se abordó la simulación numérica del ensayo de arrancamiento en viga. Se simularon todos los componentes del ensayo y se evaluaron diferentes alternativas para representar la interfase NSM‐FRP ‐ hormigón, usando elementos cohesivos y diferentes distribuciones de los mismos en la interfase. Para conseguir representar lo más fielmente posible las condiciones del ensayo, se diseñó también un controlador PID que permite realizar las simulaciones numéricas mediante un control en desplazamientos, lo cual permite capturar más correctamente el comportamiento de reblandecimiento de la unión pegada. El controlador PID aplica técnicas de ingeniería de control para conseguir calcular a priori la amplitud necesaria del desplazamiento impuesto que provoque una evolución establecida en una variable interna del sistema. La variable usada para correlacionar los ensayos es la diferencia en desplazamientos entre dos puntos y se escoge una evolución lineal de la misma, pero en la tesis también se exponen los resultados de escoger otras posibles variables internas con diferentes evoluciones. Se compararon las simulaciones numéricas con resultados de mediciones experimentales previamente publicadas. Los resultados carga‐deslizamiento obtenidos encajan bien con los datos experimentales. El modelo propuesto es también capaz de predecir el modo de fallo en la interfase NSM‐FRP ‐ hormigón. Finalmente, también se han llevado a cabo estudios paramétricos, para evaluar la influencia de cada parámetro en los resultados. También se realizó un estudio cualitativo de cómo se comporta la unión pegada en cada momento de la simulación, mediante el uso macros y gráficas tridimensionales, para conseguir una mejor visualización y facilitar el análisis de los resultados. ABSTRACT The use of near‐surface mounted FRP reinforcement in reinforced concrete structures has seen a considerable increase in recent years as a strengthening method. Beam pull‐out tests for near‐surface reinforcement allow obtaining the local bond‐slip behavior of a bonded joint. The main objective of the current work deals with the three‐dimensional modeling of this kind of test with the purpose of characterizing suitably the mechanics of bond between FRP rods and concrete. In an initial stage, a two bidimensional in order to evaluate and to verify the behavior of the cohesive elements. Its behavior was evaluated first testing different material models and second testing the behavior when mixed mode failure appears, due to simultaneous axial and shear load. In a second stage a tridimensional model was created in order to study the pull‐out of an inserted beam of composite material in concrete. A concrete material model was created and the influence of each material parameter was studied qualitatively. The third part, the most relevant of the present work, the numerical simulation of the Beam Pull‐Out test was faced. All the parts of the Beam Pull‐Out test were included inthe simulation and different alternatives to represent the FRP bar – concrete interface have been evaluated, using cohesive elements and different distributions of them. In order to reproduce the test conditions more reliably, a PID controller has also been designed to conduct suitably the numerical tests in order to properly capture the softening branch of the load‐slip behaviour. The PID controller applies control techniques to calculate a priori the necessary amplitude of the load in order to achieve a given evolution through the simulation of an internal variable previously chosen. The variable used in order to correlate the simulation with the test results is the difference in displacements between two points and a linear evolution was chosen, but in the thesis the results of choosing other possible internal variables with different evolutions are also shown. The numerical FE simulations were compared with experimental measurements previously published. Load‐slip predictions compare well with the corresponding experimental data. The proposed model is also able to predict the failure mode at the FRP‐concrete interface. Some parametric studies have also been carried out, in order to evaluate the influence of each material parameter in the results. A qualitative study of the behaviour of the joint was also performed, using the results of the numeric simulations and through the use of macros and 3D graphs, the tensional state of each point of the joint can be visualized in each moment of the simulation.

Limit load instabilities in structural elements

Este trabajo analiza distintas inestabilidades en estructuras formadas por distintos materiales. En particular, se capturan y se modelan las inestabilidades usando el método de Riks. Inicialmente, se analiza la bifurcación en depósitos cilíndricos formados por material anisótropo sometidos a carga axial y presión interna. El análisis de bifurcación y post-bifurcación asociados con cilindros de pared gruesa se formula para un material incompresible reforzado con dos fibras que son mecánicamente equivalentes y están dispuestas simétricamente. Consideramos dos casos en la naturaleza de la anisotropía: (i) Fibras refuerzo que tienen una influencia particular sobre la respuesta a cortante del material y (ii) Fibras refuerzo que influyen sólo si la fibra cambia de longitud con la deformación. Se analiza la propagación de las inestabilidades. En concreto, se diferencia en el abultamiento (bulging) entre la propagación axial y la propagación radial de la inestabilidad. Distintos modelos sufren una u otra propagación. Por último, distintas inestabilidades asociadas al mecanismo de ablandamiento del material (material softening) en contraposición al de endurecimiento (hardening) en una estructura (viga) de a: hormigón y b: hormigón reforzado son modeladas utilizando una metodología paralela a la desarrollada en el análisis de inestabilidades en tubos sometidos a presión interna. This present work deals with the instability of structures made of various materials. It captures and models different types of instabilities using numerical analysis. Firstly, we consider bifurcation for anisotropic cylindrical shells subject to axial loading and internal pressure. Analysis of bifurcation and post bifurcation of inflated hyperelastic thick-walled cylinder is formulated using a numerical procedure based on the modified Riks method for an incompressible material with two preferred directions which are mechanically equivalent and are symmetrically disposed. Secondly, bulging/necking motion in doubly fiber-reinforced incompressible nonlinearly elastic cylindrical shells is captured and we consider two cases for the nature of the anisotropy: (i) reinforcing models that have a particular influence on the shear response of the material and (ii) reinforcing models that depend only on the stretch in the fiber direction. The different instability motions are considered. Axial propagation of the bulging instability mode in thin-walled cylinders under inflation is analyzed. We present the analytical solution for this particular motion as well as for radial expansion during bulging evolution. For illustration, cylinders that are made of either isotropic incompressible non-linearly elastic materials or doubly fiber reinforced incompressible non-linearly elastic materials are considered. Finally, strain-softening constitutive models are considered to analyze two concrete structures: a reinforced concrete beam and an unreinforced notch beam. The bifurcation point is captured using the Riks method used previously to analyze bifurcation of a pressurized cylinder.

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.

Coupled Nonlinear Ginzburg-Landau and Mechanics Model for Martensitic Transformations in Polycrystals

Las transformaciones martensíticas (MT) se definen como un cambio en la estructura del cristal para formar una fase coherente o estructuras de dominio multivariante, a partir de la fase inicial con la misma composición, debido a pequeños intercambios o movimientos atómicos cooperativos. En el siglo pasado se han descubierto MT en diferentes materiales partiendo desde los aceros hasta las aleaciones con memoria de forma, materiales cerámicos y materiales inteligentes. Todos muestran propiedades destacables como alta resistencia mecánica, memoria de forma, efectos de superelasticidad o funcionalidades ferroicas como la piezoelectricidad, electro y magneto-estricción etc. Varios modelos/teorías se han desarrollado en sinergia con el desarrollo de la física del estado sólido para entender por qué las MT generan microstructuras muy variadas y ricas que muestran propiedades muy interesantes. Entre las teorías mejor aceptadas se encuentra la Teoría Fenomenológica de la Cristalografía Martensítica (PTMC, por sus siglas en inglés) que predice el plano de hábito y las relaciones de orientación entre la austenita y la martensita. La reinterpretación de la teoría PTMC en un entorno de mecánica del continuo (CM-PTMC) explica la formación de los dominios de estructuras multivariantes, mientras que la teoría de Landau con dinámica de inercia desentraña los mecanismos físicos de los precursores y otros comportamientos dinámicos. La dinámica de red cristalina desvela la reducción de la dureza acústica de las ondas de tensión de red que da lugar a transformaciones débiles de primer orden en el desplazamiento. A pesar de las diferencias entre las teorías estáticas y dinámicas dado su origen en diversas ramas de la física (por ejemplo mecánica continua o dinámica de la red cristalina), estas teorías deben estar inherentemente conectadas entre sí y mostrar ciertos elementos en común en una perspectiva unificada de la física. No obstante las conexiones físicas y diferencias entre las teorías/modelos no se han tratado hasta la fecha, aun siendo de importancia crítica para la mejora de modelos de MT y para el desarrollo integrado de modelos de transformaciones acopladas de desplazamiento-difusión. Por lo tanto, esta tesis comenzó con dos objetivos claros. El primero fue encontrar las conexiones físicas y las diferencias entre los modelos de MT mediante un análisis teórico detallado y simulaciones numéricas. El segundo objetivo fue expandir el modelo de Landau para ser capaz de estudiar MT en policristales, en el caso de transformaciones acopladas de desplazamiento-difusión, y en presencia de dislocaciones. Comenzando con un resumen de los antecedente, en este trabajo se presentan las bases físicas de los modelos actuales de MT. Su capacidad para predecir MT se clarifica mediante el ansis teórico y las simulaciones de la evolución microstructural de MT de cúbicoatetragonal y cúbicoatrigonal en 3D. Este análisis revela que el modelo de Landau con representación irreducible de la deformación transformada es equivalente a la teoría CM-PTMC y al modelo de microelasticidad para predecir los rasgos estáticos durante la MT, pero proporciona una mejor interpretación de los comportamientos dinámicos. Sin embargo, las aplicaciones del modelo de Landau en materiales estructurales están limitadas por su complejidad. Por tanto, el primer resultado de esta tesis es el desarrollo del modelo de Landau nolineal con representación irreducible de deformaciones y de la dinámica de inercia para policristales. La simulación demuestra que el modelo propuesto es consistente fcamente con el CM-PTMC en la descripción estática, y también permite una predicción del diagrama de fases con la clásica forma ’en C’ de los modos de nucleación martensítica activados por la combinación de temperaturas de enfriamiento y las condiciones de tensión aplicada correlacionadas con la transformación de energía de Landau. Posteriomente, el modelo de Landau de MT es integrado con un modelo de transformación de difusión cuantitativa para elucidar la relajación atómica y la difusión de corto alcance de los elementos durante la MT en acero. El modelo de transformaciones de desplazamiento y difusión incluye los efectos de la relajación en borde de grano para la nucleación heterogenea y la evolución espacio-temporal de potenciales de difusión y movilidades químicas mediante el acoplamiento de herramientas de cálculo y bases de datos termo-cinéticos de tipo CALPHAD. El modelo se aplica para estudiar la evolución microstructural de aceros al carbono policristalinos procesados por enfriamiento y partición (Q&P) en 2D. La microstructura y la composición obtenida mediante la simulación se comparan con los datos experimentales disponibles. Los resultados muestran el importante papel jugado por las diferencias en movilidad de difusión entre la fase austenita y martensita en la distibución de carbono en las aceros. Finalmente, un modelo multi-campo es propuesto mediante la incorporación del modelo de dislocación en grano-grueso al modelo desarrollado de Landau para incluir las diferencias morfológicas entre aceros y aleaciones con memoria de forma con la misma ruptura de simetría. La nucleación de dislocaciones, la formación de la martensita ’butterfly’, y la redistribución del carbono después del revenido son bien representadas en las simulaciones 2D del estudio de la evolución de la microstructura en aceros representativos. Con dicha simulación demostramos que incluyendo las dislocaciones obtenemos para dichos aceros, una buena comparación frente a los datos experimentales de la morfología de los bordes de macla, la existencia de austenita retenida dentro de la martensita, etc. Por tanto, basado en un modelo integral y en el desarrollo de códigos durante esta tesis, se ha creado una herramienta de modelización multiescala y multi-campo. Dicha herramienta acopla la termodinámica y la mecánica del continuo en la macroescala con la cinética de difusión y los modelos de campo de fase/Landau en la mesoescala, y también incluye los principios de la cristalografía y de la dinámica de red cristalina en la microescala. ABSTRACT Martensitic transformation (MT), in a narrow sense, is defined as the change of the crystal structure to form a coherent phase, or multi-variant domain structures out from a parent phase with the same composition, by small shuffles or co-operative movements of atoms. Over the past century, MTs have been discovered in different materials from steels to shape memory alloys, ceramics, and smart materials. They lead to remarkable properties such as high strength, shape memory/superelasticity effects or ferroic functionalities including piezoelectricity, electro- and magneto-striction, etc. Various theories/models have been developed, in synergy with development of solid state physics, to understand why MT can generate these rich microstructures and give rise to intriguing properties. Among the well-established theories, the Phenomenological Theory of Martensitic Crystallography (PTMC) is able to predict the habit plane and the orientation relationship between austenite and martensite. The re-interpretation of the PTMC theory within a continuum mechanics framework (CM-PTMC) explains the formation of the multivariant domain structures, while the Landau theory with inertial dynamics unravels the physical origins of precursors and other dynamic behaviors. The crystal lattice dynamics unveils the acoustic softening of the lattice strain waves leading to the weak first-order displacive transformation, etc. Though differing in statics or dynamics due to their origins in different branches of physics (e.g. continuum mechanics or crystal lattice dynamics), these theories should be inherently connected with each other and show certain elements in common within a unified perspective of physics. However, the physical connections and distinctions among the theories/models have not been addressed yet, although they are critical to further improving the models of MTs and to develop integrated models for more complex displacivediffusive coupled transformations. Therefore, this thesis started with two objectives. The first one was to reveal the physical connections and distinctions among the models of MT by means of detailed theoretical analyses and numerical simulations. The second objective was to expand the Landau model to be able to study MTs in polycrystals, in the case of displacive-diffusive coupled transformations, and in the presence of the dislocations. Starting with a comprehensive review, the physical kernels of the current models of MTs are presented. Their ability to predict MTs is clarified by means of theoretical analyses and simulations of the microstructure evolution of cubic-to-tetragonal and cubic-to-trigonal MTs in 3D. This analysis reveals that the Landau model with irreducible representation of the transformed strain is equivalent to the CM-PTMC theory and microelasticity model to predict the static features during MTs but provides better interpretation of the dynamic behaviors. However, the applications of the Landau model in structural materials are limited due its the complexity. Thus, the first result of this thesis is the development of a nonlinear Landau model with irreducible representation of strains and the inertial dynamics for polycrystals. The simulation demonstrates that the updated model is physically consistent with the CM-PTMC in statics, and also permits a prediction of a classical ’C shaped’ phase diagram of martensitic nucleation modes activated by the combination of quenching temperature and applied stress conditions interplaying with Landau transformation energy. Next, the Landau model of MT is further integrated with a quantitative diffusional transformation model to elucidate atomic relaxation and short range diffusion of elements during the MT in steel. The model for displacive-diffusive transformations includes the effects of grain boundary relaxation for heterogeneous nucleation and the spatio-temporal evolution of diffusion potentials and chemical mobility by means of coupling with a CALPHAD-type thermo-kinetic calculation engine and database. The model is applied to study for the microstructure evolution of polycrystalline carbon steels processed by the Quenching and Partitioning (Q&P) process in 2D. The simulated mixed microstructure and composition distribution are compared with available experimental data. The results show that the important role played by the differences in diffusion mobility between austenite and martensite to the partitioning in carbon steels. Finally, a multi-field model is proposed by incorporating the coarse-grained dislocation model to the developed Landau model to account for the morphological difference between steels and shape memory alloys with same symmetry breaking. The dislocation nucleation, the formation of the ’butterfly’ martensite, and the redistribution of carbon after tempering are well represented in the 2D simulations for the microstructure evolution of the representative steels. With the simulation, we demonstrate that the dislocations account for the experimental observation of rough twin boundaries, retained austenite within martensite, etc. in steels. Thus, based on the integrated model and the in-house codes developed in thesis, a preliminary multi-field, multiscale modeling tool is built up. The new tool couples thermodynamics and continuum mechanics at the macroscale with diffusion kinetics and phase field/Landau model at the mesoscale, and also includes the essentials of crystallography and crystal lattice dynamics at microscale.