<p>A thermodynamically consistent coarsed-grained phase field model was developed to find the conditions under which a heterogeneous porous electrode can be treated as homogeneous in the description of Lithium-ions in rechargeable batteries. Four regimes of behavior under which the transport phenomena can be homogenized to describe porous LIBs were identied: regime (a), where the model is inaccurate, for physically accessible particle packings of aspect ratios smaller than c/a = 0.5 and electrode porosities between 0.34 to 0.45; regime (b), where the model is valid, for particles of aspect ratios greater than c/a = 0.7 and electrode porosities greater than 0.35; regime (c), where the model is valid, but the microstructures are physically inaccessible, and correspond to particles with aspect ratios greater than c/a = 0.7 and electrode porosities smaller than 0.34; and regime (d), where the model is invalid and the porous microstructures are physically inaccessible, and correspond to particles with aspect ratios smaller than c/a = 1 and electrode porosities smaller than 0.34.</p> <p>The developed formulation was applied to the graphite | LixNi1/3Mn1/3Co1/3O2 system to analyze the effect of microstructure and coarsed-grained long-range chemomechanical effects on the electrochemical behavior. Specically, quantiable lithium distribution populations in the cathode, as a result of long range interactions of the diffuse interface, charge effects and mechanical stresses were identified: i) diffusion limited population due to negligible composition gradients, ii) stress-induced population as a result of chemically induced stresses, and iii) lithiation-induced population, as a consequence of the electrochemical potential gradients.</p>

For some alloys martensitic transformation is responsible for the so-called shape memory effect and pseudoelasticity. These properties are used in a wide range of industry applications. Each of these materials is transformed to the shape it was manufactured in when heated to its critical temperature (austenite phase) no matter how seriously it was deformed at lower temperatures (martensite phase). Looking at the microstructure, one can observe significant change of crystalographic lattice depending on temperature and deformation. This the- sis focuses on modelling the evolution of microstructure during deformation for materials in the martensite phase. In this case, the creation of multiple variants of martensite is observed, divided by interfaces where a part of energy is stored. This behaviour can be described by the phase-field model. The numerical im- plementation of this model using the standard finite element method requires large computational costs. The aim of this thesis is to implement this model in MATLAB using a spectral method based on the fast Fourier transform, which is suitable for solving problems on a periodic domain. It is interesting to com- pare the computation using spectral method on a conventional PC with the computation written in FEniCS computed on a cluster. However, the...

Industrial development processes as well as research in physics, materials and engineering science rely on computer modelling and simulation techniques today. With increasing computer power, computations are carried out on multiple scales and involve the analysis of coupled problems. In this work, continuum modelling is therefore applied at different scales in order to facilitate a prediction of the effective material or structural behaviour based on the local morphology and the properties of the individual constituents. This provides valueable insight into the structure-property relations which are of interest for any design process. In order to obtain reasonable predictions for the effective behaviour, numerical models which capture the essential fine scale features are required. In this context, the efficient representation of discontinuities as they arise at, e.g. material interfaces or cracks, becomes more important than in purely phenomenological macroscopic approaches. In this work, two different approaches to the modelling of discontinuities are discussed: (i) a sharp interface representation which requires the localisation of interfaces by the mesh topology. Since many interesting macroscopic phenomena are related to the temporal evolution of certain microscopic features, (ii) diffuse interface models which regularise the interface in terms of an additional field variable and therefore avoid topological mesh updates are considered as an alternative. With the two combinations (i) Extended Finite Elemente Method (XFEM) + sharp interface model, and (ii) Isogeometric Analysis (IGA) + diffuse interface model, two fundamentally different approaches to the modelling of discontinuities are investigated in this work. XFEM reduces the continuity of the approximation by introducing suitable enrichment functions according to the discontinuity to be modelled. Instead, diffuse models regularise the interface which in many cases requires even an increased continuity that is provided by the spline-based approximation. To further increase the efficiency of isogeometric discretisations of diffuse interfaces, adaptive mesh refinement and coarsening techniques based on hierarchical splines are presented. The adaptive meshes are found to reduce the number of degrees of freedom required for a certain accuracy of the approximation significantly. Selected discretisation techniques are applied to solve a coupled magneto-mechanical problem for particulate microstructures of Magnetorheological Elastomers (MRE). In combination with a computational homogenisation approach, these microscopic models allow for the prediction of the effective coupled magneto-mechanical response of MRE. Moreover, finite element models of generic MRE microstructures are coupled with a BEM domain that represents the surrounding free space in order to take into account finite sample geometries. The macroscopic behaviour is analysed in terms of actuation stresses, magnetostrictive deformations, and magnetorheological effects. The results obtained for different microstructures and various loadings have been found to be in qualitative agreement with experiments on MRE as well as analytical results. / Industrielle Entwicklungsprozesse und die Forschung in Physik, Material- und Ingenieurwissenschaft greifen in einem immer stärkeren Umfang auf rechnergestützte Modellierungs- und Simulationsverfahren zurück. Die ständig steigende Rechenleistung ermöglicht dabei auch die Analyse mehrskaliger und gekoppelter Probleme. In dieser Arbeit kommt daher ein kontinuumsmechanischer Modellierungsansatz auf verschiedenen Skalen zum Einsatz. Das Ziel der Berechnungen ist dabei die Vorhersage des effektiven Material- bzw. Strukturverhaltens auf der Grundlage der lokalen Werkstoffstruktur und der Eigenschafen der konstitutiven Bestandteile. Derartige Simulationen liefern interessante Aussagen zu den Struktur-Eigenschaftsbeziehungen, deren Verständnis entscheidend für das Material- und Strukturdesign ist. Um aussagekräftige Vorhersagen des effektiven Verhaltens zu erhalten, sind numerische Modelle erforderlich, die wesentliche Eigenschaften der lokalen Materialstruktur abbilden. Dabei kommt der effizienten Modellierung von Diskontinuitäten, beispielsweise Materialgrenzen oder Rissen, eine deutlich größere Bedeutung zu als bei einer makroskopischen Betrachtung. In der vorliegenden Arbeit werden zwei unterschiedliche Modellierungsansätze für Unstetigkeiten diskutiert: (i) eine scharfe Abbildung, die üblicherweise konforme Berechnungsnetze erfordert. Da eine Evolution der Mikrostruktur bei einer derartigen Modellierung eine Topologieänderung bzw. eine aufwendige Neuvernetzung nach sich zieht, werden alternativ (ii) diffuse Modelle, die eine zusätzliche Feldvariable zur Regularisierung der Grenzfläche verwenden, betrachtet. Mit der Kombination von (i) Erweiterter Finite-Elemente-Methode (XFEM) + scharfem Grenzflächenmodell sowie (ii) Isogeometrischer Analyse (IGA) + diffuser Grenzflächenmodellierung werden in der vorliegenden Arbeit zwei fundamental verschiedene Zugänge zur Modellierung von Unstetigkeiten betrachtet. Bei der Diskretisierung mit XFEM wird die Kontinuität der Approximation durch eine Anreicherung der Ansatzfunktionen gemäß der abzubildenden Unstetigkeit reduziert. Demgegenüber erfolgt bei einer diffusen Grenzflächenmodellierung eine Regularisierung. Die dazu erforderliche zusätzliche Feldvariable führt oft zu Feldgleichungen mit partiellen Ableitungen höherer Ordnung und weist in ihrem Verlauf starke Gradienten auf. Die daraus resultierenden Anforderungen an den Ansatz werden durch eine Spline-basierte Approximation erfüllt. Um die Effizienz dieser isogeometrischen Diskretisierung weiter zu erhöhen, werden auf der Grundlage hierarchischer Splines adaptive Verfeinerungs- und Vergröberungstechniken entwickelt. Ausgewählte Diskretisierungsverfahren werden zur mehrskaligen Modellierung des gekoppelten magnetomechanischen Verhaltens von Magnetorheologischen Elastomeren (MRE) angewendet. In Kombination mit numerischen Homogenisierungsverfahren, ermöglichen die Mikrostrukturmodelle eine Vorhersage des effektiven magnetomechanischen Verhaltens von MRE. Außerderm wurden Verfahren zur Kopplung von FE-Modellen der MRE-Mikrostruktur mit einem Randelement-Modell der Umgebung vorgestellt. Mit Hilfe der entwickelten Verfahren kann das Verhalten von MRE in Form von Aktuatorspannungen, magnetostriktiven Deformationen und magnetischen Steifigkeitsänderungen vorhergesagt werden. Im Gegensatz zu zahlreichen anderen Modellierungsansätzen, stimmen die mit den hier vorgestellten Methoden für unterschiedliche Mikrostrukturen erzielten Vorhersagen sowohl mit analytischen als auch experimentellen Ergebnissen überein.

Title: Studies of Relaxor Ferroelectrics with Spontaneous Polar Nanoregions Author: Petr Ondrejkovič Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: Ing. Jiří Hlinka, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: The thesis is devoted to relaxor ferroelectrics with spontaneous polar nanoregions. We have investigated one of the canonical representatives, uniaxial strontium barium niobate, by means of neutron scattering, and also performed computer simulations with a model of a uniaxial ferroelectric with point defects. Neutron scattering studies of strontium barium niobate single crystals under a defined sequence of thermal and electric field treatments elucidate nature of distinct components of its transverse diffuse scattering. These components are associated mainly with the static ferroelectric nanodomain structure and the dynamic order-parameter (polarization) fluctuations. Moreover, high-resolution neutron backscattering experiments allowed us to resolve characteristic frequencies of the order-parameter fluctuations and prove that this component is caused by the same polar fluctuations that are responsible for the Vogel-Fulcher dielectric relaxation, the hallmark of relaxor ferroelectrics. The model system of a uniaxial ferroelectric with point...

Anticiper l’évolution de la microstructure d’un matériau en condition d’usage est d’une importance cruciale pour l’industrie. Cette maîtrise du vieillissement nécessite une compréhension claire des mécanismes sous-jacents, qui agissent sur une large gamme d’échelles spatiales et temporelles. Dans cette optique, ce travail de thèse a choisi d’appliquer la méthode de champ de phase qui, en raison du saut d’échelle qu’elle réalise naturellement, est un outil intensivement employé dans le domaine des matériaux, pour prédire l’évolution en temps long de la microstructure. L’enjeu de l’étude a été d’étendre cette méthode à un système porté loin de l’équilibre thermodynamique, en particulier en présence d’irradiation. Nous avons ainsi adopté le formalisme du mélange ionique, introduit par Gras-Marti pour décrire le mélange balistique au sein d’une cascade de déplacements. Par l’utilisation conjointe d’un schéma numérique et d’une approche analytique, il nous a été possible d’établir le diagramme de phase générique d’un matériau irradié. Nous avons ensuite étudié le vieillissement de l’alliage binaire test AgCu sous irradiation, par l’utilisation conjointe de la méthode du champ de phase et d’approches atomistiques, dans une démarche multi-échelles. En fixant les paramètres de contrôle que sont le flux d’irradiation et la température, il nous a ainsi été possible de prédire la taille,la concentration ainsi que la distribution spatiale des nodules de cuivre produits sous irradiation dans cet alliage. La connaissance de ces informations a permis de simuler un diagramme de diffraction en incidence rasante, directement comparable aux diagrammes expérimentaux. / It is of dramatic matter for industry to be able to predict the evolution of material microstructure under working conditions. This requires a clear understanding of the underlying mechanisms, which act on numerous space and time scales. Because it intrinsically performs a scale jump, we chose to use a phase field approach, which is widely used amidst the condensed matter community to study the aging of materials. The first challenge of this work was to extend this formalism beyond its thermodynamic scope and embrace the case of far from equilibrium systems when subjected to irradiation. For that purpose, we adopted the model of ion mixing, developed by Gras Marti to account for ballistic exchanges within a displacements cascade. Based on a numerical scheme and ananalytical method, we were able to describe the generic microstructure signature for materials under irradiation.We then applied this formalism to the particular case of the immiscible binary alloy AgCu.With the joined use of the phase field approach and atomistic methods, we managed to predict how the temperature and the irradiation flux tailor the main microstructure features such as the size, the concentration and the distribution of copper precipitates. This eventually allowed us to simulate a diffraction pattern in grazing incidence, which is directly comparable to experimental ones.

Une bonne tenue mécanique des structures du génie civil en béton armé sous chargements dynamiques sévères est primordiale pour la sécurité et nécessite une évaluation précise de leur comportement en présence de propagation dynamique de fissures. Dans ce travail, on se focalise sur la modélisation constitutive du béton assimilé à un matériau élastique-fragile endommageable. La localisation des déformations sera régie par un modèle d'endommagement à gradient où un champ scalaire réalise une description régularisée des phénomènes de rupture dynamique. La contribution de cette étude est à la fois théorique et numérique. On propose une formulation variationnelle des modèles d'endommagement à gradient en dynamique. Une définition rigoureuse de plusieurs taux de restitution d'énergie dans le modèle d'endommagement est donnée et on démontre que la propagation dynamique de fissures est régie par un critère de Griffith généralisé. On décrit ensuite une implémentation numérique efficace basée sur une discrétisation par éléments finis standards en espace et la méthode de Newmark en temps dans un cadre de calcul parallèle. Les résultats de simulation de plusieurs problèmes modèles sont discutés d'un point de vue numérique et physique. Les lois constitutives d'endommagement et les formulations d'asymétrie en traction et compression sont comparées par rapport à leur aptitude à modéliser la rupture fragile. Les propriétés spécifiques du modèle d'endommagement à gradient en dynamique sont analysées pour différentes phases de l'évolution de fissures : nucléation, initiation, propagation, arrêt, branchement et bifurcation. Des comparaisons avec les résultats expérimentaux sont aussi réalisées afin de valider le modèle et proposer des axes d'amélioration. / In civil engineering, mechanical integrity of the reinforced concrete structures under severe transient dynamic loading conditions is of paramount importance for safety and calls for an accurate assessment of structural behaviors in presence of dynamic crack propagation. In this work, we focus on the constitutive modeling of concrete regarded as an elastic-damage brittle material. The strain localization evolution is governed by a gradient-damage approach where a scalar field achieves a smeared description of dynamic fracture phenomena. The contribution of the present work is both theoretical and numerical. We propose a variationally consistent formulation of dynamic gradient damage models. A formal definition of several energy release rate concepts in the gradient damage model is given and we show that the dynamic crack tip equation of motion is governed by a generalized Griffith criterion. We then give an efficient numerical implementation of the model based on a standard finite-element spatial discretization and the Newmark time-stepping methods in a parallel computing framework. Simulation results of several problems are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture. Specific properties of the dynamic gradient damage model are investigated for different phases of the crack evolution: nucleation, initiation, propagation, arrest, kinking and branching. Comparisons with experimental results are also performed in order to validate the model and indicate its further improvement.

Active matter describes systems that convert energy from their environment into directed motion. Therefore, these systems are in intrinsic nonequilibrium, unlike their passive counterparts. From a theoretical point of view, such active systems have been modeled by agent-based models, as well as hydrodynamic approaches, which allowed for the investigation of a wide range of observed collective phenomena characterizing active matter. In this thesis we develop a microscopic field-theoretical approach to describe generic properties of active systems. This description combines the phase field crystal model with a polar order parameter and a self-propulsion term. First, we validate this approach by reproducing results obtained with corresponding agent-based models, such as binary collisions, collective migration and vortex formation. We also perform a direct comparison between our model and a microscopic phase field description of active matter. Next, we use this continuum approach to simulate some larger active systems and to analyze the coarsening process in active crystals, as well as the mechanisms leading to mobile clusters. We show the generality of our approach by extending it to binary mixtures of interacting active and passive particles. Also in this case, we first validate the model by reproducing known results, such as enhanced crystallization via active doping and the suppression of collective migration in an active bath in the presence of fixed obstacles. Interestingly, for the regime of mobile passive particles in an active bath a laning state is found, which is characterized by an alignment of the active particles that is globally nematic, but polar within each lane. This state represents a theoretical prediction feasible to be validated experimentally. Finally, we explore the field of topological active matter. We develop an agent-based model to describe self-propelled particles on curved surfaces and study the complex spatiotemporal patterns that emerge. / Aktive Materie beschreibt Systeme, die Energie aus ihrer Umgebung in gerichtete bewegung umwandeln. Im Gegensatz zur passiven Materie befinden sich diese Systeme nie im physikalischen Gleichgewicht und offenbaren dadurch interessante physikalische Phänomene. Vom theoretischen Standpunkt her wurde aktive Materie bereits simuliert, typischerweise durch agenten-basierte Modelle oder hydrodynamische Ansätze, die es ermöglichen eine Vielzahl der auftretenden kollektiven Bewegungsprinzipien zu untersuchen. In dieser Doktorarbeit entwickeln wir einen mikroskopischen Kontinuumsansatz um die generischen Eigenschaften von aktiven Systemen zu untersuchen. Unsere Beschreibung kombiniert das Phasenfeld-Kristall Modell mit einem polaren Ordnungsparameter und einem Antriebsterm. Zuerst validieren wir den Ansatz durch Reproduktion bekannter Ergebnisse agenten-basierter Modelle, wie binäre Kollisionen, kollektive Bewegung und Wirbelformationen. Des Weiteren führen wir einen direkten Vergleich zwischen unserem Modell und einer mikroskopischen Phasenfeldbeschreibung aktiver Materie durch. Danach nutzen wir den kontinuierlichen Ansatz um große aktive Systeme zu simulieren und analysieren den Vergröberungsprozess in aktiven Kristallen und Mechanismen der mobilen Aggregatbildung. Wir illustrieren die Allgemeingültigkeit unseres Simulationsansatzes durch die Erweiterung auf binäre Systeme, in denen sowohl aktive als auch passive Partikel enthalten sind. Auch in diesem Fall validieren wir das Modell durch Vergleiche mit bekannten Resultaten, wie zum Beispiel die verstärkte Kristallisation durch aktives Doping oder die Unterdrückung kollektiver Bewegung durch die Einführung von Hindernissen in einem aktiven Bad. Interessanterweise finden wir bei der Präsenz mobiler passiver Partikel in einem aktiven Bad einen Fahrspur-Zustand, in welchem die aktiven Partikel nematische Fahrspuren bilden und sich nur jeweils innerhalb einer Fahrspur nematisch polar anordnen. Dieser bisher unbekannte Zustand stellt eine theoretische Vorhersage dar, die experimentell geprüft werden kann. Schließlich begeben wir uns auf das Gebiet der topologischen aktiven Materie. Wir entwickeln ein agenten-basiertes Modell um selbst-angetriebene Partikel auf gekrümmten Oberflächen zu beschreiben und untersuchen die dabei auftretenden zeitlich und räumlich komplexen Muster.%, die dabei auftreten.

<p>A wide variety of phase evolution phenomena observed in solids such as intermetallic growth at the junction between two metals subjected to high temperature, growth of oxide on metal surfaces due to atmospheric exposure and void evolution induced by electromigration in microelectronic devices for example, can be classified as being driven by reaction-diffusion processes. These phase evolution phenomena have a significant impact on material reliability for critical applications, and therefore, there is a requirement for modeling such reaction-diffusion driven phase evolution phenomena. It is difficult to analyze these due to the complexity of modeling the evolving interface between solid phases. Additional complexity is  due to the multi-physics nature of the diffusive and reactive processes. Diffusion in solids is driven by a variety of stimuli such as current, temperature and stress, in addition to the chemical potential. Therefore, there is a need for a model that accounts for the influence of such factors on phase evolution. In this thesis,  a generalized continuum based reaction-diffusion theory for phase and void evolution in solid state is developed. The derivation starts off with generalized interface balance laws for mass, momentum and energy. The thermodynamic entropy inequality for irreversible phase growth is derived for arbitrary anisotropic and inhomogeneous surface stress. These interface relations are combined with governing relations in the material bulk for the temperature, stress, electrical and concentration fields, to develop a general model capable of analyzing and describing phase evolution in solids. This theory is then applied to a variety of intermetallic phase and void evolution phenomena observed in microelectronics.</p> <p><br></p> <p>Electromigration induced voiding in thin metal films is an example of phase evolution that is an important reliability concern in microelectronics. Studies have reported that the electromigration induced void growth rate is inversely related to the adhesion of metal thin films with the base and capping layers. Electromigration experiments are performed on fabricated test devices with Cu thin films with SiNx and TiN capping layers. The observations from electromigration experiments on thin Cu metal films at a range of temperatures indicate that the contribution of interface adhesion strength to electromigration resistance decreases with an increase in temperature. The generalized reaction-diffusion theory developed here is modified to develop an expression to account for the effect of base and passivation layer adhesion and temperature on electromigration resistance of metal thin films. The void growth rates measured in the experiments are analyzed with the expression for void growth rate to estimate the interface adhesion strength for the Cu-TiN and Cu-SiNx interfaces. </p> <p><br></p> <p>Demand for increased bandwidth, power efficiency and performance requirements have resulted in a trend of reduction in size and pitch of Cu pillar-Solder micro-bump interconnects used in heterogeneously integrated packages. As the size of micro-bumps reduce, reliability challenges due to voiding in the solder joint and the growth of Cu-Sn intermetallics are observed. The underlying reaction-diffusion mechanisms responsible for Cu-Sn intermetallic growth and voiding in solder joints are unclear at this stage and require further investigation. The current practice of material characterization in micro-bumps involve destructive cross-sectioning and polishing of the micro-bumps after testing. These processes result in loss of continuity in the samples used for the experiments, and material removal due to abrasive polishing might result in a loss of critical information. Therefore, a novel test device capable of non-destructive characterization of Cu-Sn intermetallic growth and voiding in sub-30 micron size micro-bumps is designed and fabricated in this work. The fabricated test devices are subjected to thermal aging for over 1000 h and the underlying reaction-diffusion mechanisms behind the intermetallic phase and void evolution are investigated. </p> <p><br></p> <p>A reaction-diffusion mechanism is proposed explaining the evolution of  various Cu-Sn intermetallic phases and solder joint void observed from experiments. Using the reaction-diffusion mechanism inferred from the thermal aging experiments and the generalized reaction-diffusion theory for phase evolution developed in this thesis, a sharp interface model is developed for the evolution of Cu-Sn intermetallic phases and solder joint void. The diffuse interface phase field equivalent equations for the sharp interface model governing equations are developed using matched formal asymptotic analysis. The evolution of Cu-Sn intermetallic phase and voids in the solder joint are simulated for different temperatures and current density to demonstrate the validity of the phase field and sharp interface models.  </p> <p><br></p>

<p>    </p> <p>In this thesis, a thermodynamically consistent phase field formulation was developed to identify the physical origin of interfacial transitions that drive macroscopic phenomena, start- ing at the single-particle length scale and building up to the polycrystalline length scale. At the single-particle length scale, the framework identified two interfacial phases that are stable at the surface of Sn nanoparticles: 1) a disordered interfacial phase, i.e., the experimentally observed premelted surface layer; and 2) an ordered surficial phase displaying a remnant de- gree of order in fully melted particles. Regimes of melting behavior as a function of particle size and temperature are discussed. To bridge the gap between single-particle and densified polycrystals, an analytical model was developed to capture the physical driving forces for densification during electric field-assisted sintering. Here, the model acknowledges the struc- tural contributions of particle-particle interfaces to the strength of mechanical, electrical, and surficial driving forces for densification, and shows good agreement with experimental flash sintering data. Finally, the theory was applied to polycrystalline LiCoO₂ (LCO) and shows that the experimentally observed metal-insulator transition is driven by grain bound- ary lithium segregation, the interfacial misorientation, and the size of the abutting grains. A critical misorientation as a function of the macroscopic lithium content exists above which the grain boundaries undergo a metal-insulating transition, suggesting that the fabrication of textured LCO microstructures will delay the metal-insulator transition. </p>

In this thesis, micro computed tomography (μ−CT) scans of a bio-glass scaffold produced by the robocasting technique was used to create finite element method (FEM) models with the purpose of determining its mechanical strength. Prior to this, a Matlab script was used to create several simplified geometries of the scaffold in an effort to determine the importance of scaffold design parameters (such as the fiber compenetration between two adjacent printing planes) on the strength of the scaffold. Furthermore, to assess the influence of micro-structural defects such as voids and micro-cracks that are intrinsic to the robocasting manufacturing process, the total number of voids and their respective volume was calculated using the μ-CT scan imagery and fitted to a statistical distribution. The distribution of voids was then used to create several scaffold models in Matlab with either spherical or ellipsoidal voids present. In the final two models, one scaled-down and one scaled-up FEM based on μ-CT scans were investigated.To model the crack initiation, propagation and final failure, the phase-field method was used. The method was implemented by the use of a publicly available Fortran user subroutine and was edited to account for asymmetric tension/compression energy degradation. The resulting strength of the produced models have been presented as non-dimensional values. The finite element analysis (FEA) of the Matlab produced scaffolds showed that the fiber shifting between two adjacent layers, porosity, and voids of ellipsoidal shape that were perpendicular to the loading direction had the highest effect on the strength of the scaffold. The resulting normalized strength values obtained from the μ-CT models was partially validated through a comparison with the literature available.The different failure modes and overall architectural arrangement of cracks also showed promising results. / I den här uppsatsen så användes mikrotomografi (μ-CT) skanning av en bio-glas stödstruktur tillverkad av robocasting tekniken för att skapa finita element modeller med syftet att bestämma dess mekaniska styrka. Innan detta så användes ett Matlab-skript för att skapa flera förenklade geometrier av stödstrukturen i ett försök att fastställa betydelsen av viktiga designparametrar (som t.ex fiberpenetrering mellan två intilliggande plan) på stödstrukturens styrka. Vidare, för att bedöma påverkan av mikrostrukturella defekter som tomrum och mikrosprickor som är naturligt förekommande i robocasting-tillverkningsprocessen så uppmättes det totala antal hålrum och deras respektive volym med hjälp av μ-CT-skannade bilder. Denna data blev anpassad till en statistisk fördelning. Fördelningen av tomrum och mikcrosprickor användes sedan för att skapa flera modeller av stödstrukturerna i Matlab med antingen sfäriska eller ellipsoida hålrum närvarande. I de sista två modellerna undersöktes en en nedskalad och en uppskalad finita elementmodell baserad på μ-CT-skanning.För att modellera sprickinitiering, sprickpropagering och slutligen brott användes fasfältsmetoden. Fasfältsmetoden implementerades med hjälp av en för allmänheten tillgänglig Fortran användarrutin som redigerades för att ta hänsyn till en asymmetrisk energidegradering i drag-och tryck. Den resulterande styrkan hos alla modeller har presenterats som icke-dimensionella värden. Finita elementanalysen av Matlab modellerna visade att fiberskiftningen mellan två intilliggande plan, porositet och hålrum med ellipsoid form som var vinkelräta mot belastningsriktningen hade störst effekt på stödstrukturens styrka. De resulterande normaliserade styrkevärdena erhållna från μ-CTmodeller validerades delvis genom en jämförelse med tillgänglig litteratur. Dom olika felmoderna och övergripande strukturella fördelningen av sprickor visade också lovande resultat.