<p dir="ltr">Magnetorheological elastomers (MREs) are a type of smart material composed of ferrous particles suspended in a solid elastic matrix [5, 6]. When an external magnetic field is applied to an MRE, the ferrous particles tend to align with the field, causing either deformation and/or a change in the mechanical properties of the system. MREs are utilized in applications such as soft robotics, actuators, sensors, vibration control systems, and mechanical metamaterials[20, 19, 27, 5, 6, 13]. Recent demand for theses technologies has motivated an increasing focus on the material properties of MRE’s over the last 20 years [6]. Multiple authors have proposed a variety of hyperelastic mechanical and magnetomechanical models to describe these materials [16, 12, 15, 25, 14, 38, 2, 6, 8, 24]. The research presented in this dissertation focuses on the modeling and characterization of MRE’s using a systematic development of the conservation and balance laws, Maxwell’s equations, and constitutive equations needed to describe the MRE as a multi-constituent system. The material parameters resulting from the derived constitutive equations are estimated using data collected from a series of compression experiments coupled with an externally applied magnetic field. The multi-constituent constitutive equations predicted the stress of the MRE in these compression experiments for a variety of ferrous particle concentrations.</p>

No description available.

<p dir="ltr">This thesis investigates the large deflection behavior of cantilever beams under various configurations and loading conditions. The primary objective is to uset an analytical model using elliptic integrals to solve the second-order non-linear differential equations that govern the deflection of these beams. The analytical model is implemented in Python and compared against Finite Element Analysis (FEA) results obtained from ANSYS, ensuring the accuracy and reliability of the model. The study examines multiple beam configurations, including straight and inclined beams, with both free and fixed tip slopes. Sensitivity analysis is conducted to assess the impact of key parameters, such as Young’s modulus, beam height, width, and length, on the deflection behavior. This analysis reveals critical insights into how variations in material properties and geometric dimensions affect beam performance. A detailed error analysis using Root Mean Square Error (RMSE) is performed to compare the analytical model's predictions with the FEA results. The error analysis highlights any discrepancies, demonstrating the robustness of the analytical approach. The results show that the analytical model, based on elliptic integrals, closely matches the FEA results across a range of configurations and loading scenarios. The insights gained from this study can be applied to optimize the design of cantilever beams in various engineering applications, including prosthetics, robotics, and structural components. Overall, this research provides a comprehensive understanding of the large deflection behavior of cantilever beams and offers a reliable analytical tool for engineers to predict beam performance under different conditions. The integration of Python-based numerical methods with classical elliptic integral solutions presents a useful approach that enhances the precision and applicability of beam deflection analysis.</p>

<p dir="ltr">Stress concentration represents a considerable challenge in 2.5D/ 3D integration systems, primarily due to the inherent structural and material heterogeneities. Discontinuities at interfaces between different materials and at corners lead to the formation of localized stress regions. Furthermore, coefficients of thermal expansion mismatch among materials such as silicon, copper, and polymers exacerbate these stress concentrations, particularly at critical locations including edges, corners, and interfaces. The presence of these localized stresses from both thermal and mechanical loadings heightens the risk of mechanical failure such as crack initiation or crack propagation, thereby underscoring the necessity for meticulous design and analysis to ensure the reliability of these advanced systems.</p><p dir="ltr">Numerical modeling provides insights into the relationship between design, loading, and material behavior leading to failure. Isogeometric analysis (IGA) offers a significant advantage over traditional finite element methods (FEM) by integrating Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) using NURBS-based approximations. Enriched Isogeometric Analysis (EIGA) enhances this framework by incorporating known behaviors at critical features like crack tips or interfaces to facilitate accurate modeling of flux/stress singularities.</p><p dir="ltr">Asymptotic analysis of flux singularity is systematically studied in order to capture the local thermal behavior around crack tips or junction of multi-material wedges. The general expressions of temperature and flux in polar coordinates are derived. Formulation of EIGA around crack tips or junction of multi-material wedges then presented. A bi-material wedge model is demonstrated to show that singular flux/stress can be obtained in EIGA with a very coarse discretization compared with FEM.</p><p dir="ltr">Configurational force, a key concept in fracture mechanics, describes the energy-driven force that dictates crack propagation and helps predict crack paths and material failure under varying loads and conditions. To develop configurational force for thermoelasticity, configurational optimization problem is introduced. Configurational optimization problem is proposed for determining the optimal location, orientation, and the scaling of a finite-sized heterogeneity inserted into a homogeneous domain. The derivation leads to some important results: a generalized Eshelby energy-momentum tensor, path-independent integral forms for sensitivity, and representation of <i>J-</i>, <i>L-</i> and <i>M-</i>integrals of fracture mechanics. Several illustrative examples of fracture resistant design are solved with EIGA. </p><p dir="ltr">The generalized configurational force for thermoelasticity is derived by solving the configurational optimization problem. Using the general form of Helmholtz free energy potential for thermoelasticity, the generalized configurational force and generalized Eshelby energy-momentum tensor for thermoelasticity are obtained practically without needing the assumption of thermal displacement made in prior literature. </p><p dir="ltr"><br></p><p dir="ltr">Finally, a multiscale modeling for 2.5D/3D integration is demonstrated with all the developed techniques: asymptotic analysis of flux/stress singularities, enriched isogeometric analysis as well as configurational force in thermoelasticity. The one-way coupled multiscale modeling is applied to solve the length scale spanning of package to line. By transferring the global nodal value such as displacement or temperature to the local model as boundary conditions, the one-way coupled is achieved. In local model, a fined-mesh model with EIGA provides more details, and post-processing of configurational force computation leads to a prediction of the direction of crack driving force.</p>

<p dir="ltr">Investigating the deformation and failure of human cortical bone under altered hydration contributes to the understanding of bone fracture. Further, studying the impact of hydration on bone deformation can lead to developing fracture prevention strategies that will enhance the lives of the aging population. In addition, characterization of cortical bone water modulation effects on biomechanical behavior helps us understand how bone dynamically changes due to aging, health conditions, and therapeutic interventions.</p><p dir="ltr">The concepts in this thesis are demonstrated on bone specimens of a 75-year-old male human subject. To investigate the potential role of water in bone as modulated by selective estrogen receptor modulators, we used magnetic resonance imaging to characterize bound water in human samples. The behavior of human cortical bone under mechanical loading protocols was tested to analyze the bone failure surface. Bone microstructure, microdamage, and fractures were observed from progressive bending experiments. Earlier evidence suggests that treating human cortical bone with Raloxifene (RAL) toughens bone but does not affect strength.</p><p dir="ltr">Questions remain about how RAL treatment affects bone biomechanics with the consideration of size effects. In this research, experiments were conducted on samples mimicking the thickness of cortical bone. Smaller thickness samples investigated in prior work were also considered, and intrinsic strength and tissue damage were introduced. Additionally, ultra-short echo-time magnetic resonance images were employed to observe 3D spatial information of bound and free water in the bone.</p><p dir="ltr">This research seeks to combine methods in bone biology and the mechanics of materials to solve problems of bone fragility. Linear strength concepts do not distinguish between treatments. However, treatment effects are detected with a nonlinear approach. Furthermore, this study provides valuable insights into quantifying bound water content within in-vitro specimen samples. These findings pave the way for further research into continued advancements addressing skeletal health challenges.</p>

A Natural nEighbours Method (NEM) based on the FRAEIJS de VEUBEKE (FdV) variational principle is developed in the domain of 2D infinitesimal transformations. This method is firstly applied to linear elastic problems and then is extended to materially nonlinear problems and problems of linear elastic fracture mechanics (LEFM). In all these developments, thanks to the FdV variational principle, the displacement field, the stress field, the strain field and the support reaction field are discretized independently. In the spirit of the NEM, nodes are distributed in the domain and on its contour and the corresponding Voronoi cells are constructed. In linear elastic problems the following discretization hypotheses are used: 1. The assumed displacements are interpolated between the nodes with Laplace functions. 2. The assumed support reactions are constant over each edge of Voronoi cells on which displacements are imposed. 3. The assumed stresses are constant over each Voronoi cell. 4. The assumed strains are constant over each Voronoi cell. The degrees of freedom linked with the assumed stresses and strains can be eliminated at the level of the Voronoi cells so that the final equation system only involves the nodal displacements and the assumed support reactions. The support reactions can be further eliminated from the equation system if the imposed support conditions only involve constant imposed displacements (in particular displacements imposed to zero) on a part of the solid contour, finally leading to a system of equations of the same size as in a classical displacement-based method. For the extension to materially non linear problems, similar hypotheses are used. In particular, the velocities are interpolated by Laplace functions and the strain rates are assumed to be constant in each Voronoi cell. The final equations system only involves the nodal velocities. It can be solved step by step by time integration and Newton-Raphson iterations at the level of the different time steps. In the extension of this method for LEFM, a node is located on each crack tip. In the Voronoi cells containing the crack tip, the stress and the strain discretization includes not only a constant term but also additional terms corresponding to the solutions of LEFM for modes 1 and 2. In this approach, the stress intensity coefficients are obtained as primary variables of the solution. The final equations system only involves the nodal displacements and the stress intensity coefficients. Finally, an eXtended Natural nEighbours Method (XNEM) is proposed in which the crack is represented by a line that does not conform to the nodes or the edges of the cells. Based on the hypotheses used in linear elastic domain, the discretization of the displacement field is enriched with Heaviside functions allowing a displacement discontinuity at the level of the crack. In the cells containing a crack tip, the stress and strain fields are also enriched with additional terms corresponding to the solutions of LEFM for modes 1 and 2. The stress intensity coefficients are also obtained as primary variables of the solution. A set of applications are performed to evaluate these developments. The following conclusions can be drawn for all cases (linear elastic, nonlinear, fracture mechanics). In the absence of body forces, the numerical calculation of integrals over the area of the domain is avoided: only integrations on the edges of the Voronoi cells are required, for which classical Gauss numerical integration with 2 integration points is sufficient to pass the patch test. The derivatives of the nodal shape functions are not required in the resulting formulation. The patch test can be successfully passed. Problems involving nearly incompressible materials can be solved without incompressibility locking in all cases. The numerical applications show that the solutions provided by the present approach converge to the exact solutions and compare favourably with the classical finite element method. / Une méthode des éléments naturels (NEM) basée sur le principe variationnel de FRAEIJS de VEUBEKE (FdV) est développée dans le domaine des transformations infinitésimales 2D. Cette méthode est dabord appliquée aux problèmes élastiques linéaires puis est étendue aux problèmes matériellement non linéaires ainsi quà ceux de la mécanique de la rupture élastique linéaire (LEFM). Dans tous ces développements, grâce au principe variationnel de FdV, les champs de déplacements, contraintes, réformations et réactions dappui sont discrétisés de façon indépendante. Dans lesprit de la NEM, des noeuds sont distribués dans le domaine et sur son contour et les cellules de Voronoi associées sont construites. En domaine élastique linéaire, les hypothèses de discrétisation sont les suivantes : 1. Les déplacements sont interpolés entre les noeuds par des fonctions de Laplace. 2. Les réactions dappui sont supposées constantes sur chaque côté des polygones de Voronoi le long desquels des déplacements sont imposés. 3. Les contraintes sont supposées constantes sur chaque cellule de Voronoi. 4. Les déformations sont supposées constantes sur chaque cellule de Voronoi. Les degrés de liberté associés aux hypothèses sur les contraintes et les déformations peuvent être éliminées au niveau des cellules de Voronoi de sorte que le système déquations final nimplique que les déplacement nodaux et les réactions dappui supposées. Ces dernières peuvent également être éliminées de ce système déquations si les conditions dappui nimposent que des déplacements constants (en particulier égaux à zéro) sur une partie du contour du domaine étudié, ce qui conduit à un système déquations de même taille que dans une approche basée sur la discrétisation des seuls déplacements. Pour lextension aux problèmes matériellement non linéaires, des hypothèses similaires sont utilisées. En particulier, les vitesses sont interpolées par des fonctions de Laplace et déformations sont supposées constantes sur chaque cellule de Voronoi. Le système déquations final nimplique que les vitesses nodales. Il peut être résolu pas à pas par intégration temporelle et itérations de Newton-Raphson à chaque pas de temps. Pour lextension de cette méthode aux problèmes de LEFM, un noeud est localisé à chaque pointe de fissure. Dans les cellules de Voronoi correspondantes, la discrétisation des contraintes et des déformations contient non seulement un terme constant mais aussi des termes additionnels correspondant aux solutions de la LEFM pour les modes 1 et 2. Avec cette approche, les coefficients dintensité de contraintes constituent des variables primaires de la solution. Le système déquations final ne contient que les déplacements nodaux et les coefficients dintensité de contraintes. Finalement, une méthode des éléments naturels étendue (XNEM) est proposée dans laquelle la fissure est représentée par une ligne indépendante des noeuds ou des côtés des cellules de Voronoi. La discrétisation utilisée en domaine élastique linéaire est enrichie par des fonctions de Heaviside qui autorisent une discontinuité des déplacements au niveau de la fissure. Dans les cellules contenant une pointe de fissure, les contraintes et les déformations sont aussi enrichies par des termes additionnels correspondant aux solutions de la LEFM pour les modes 1 et 2. Ici aussi, les coefficients dintensité de contraintes constituent des variables primaires de la solution. Une série dapplications numériques sont réalisées afin dévaluer ces développements. Les conclusions suivantes peuvent être tirées. Elles sappliquent à tous les cas (élastique linéaire, non linéaire, mécanique de la rupture) : En labsence de force volumique, le calcul numérique dintégrales sur laire du domaine est évité : seules sont nécessaires des intégrales numériques sur les côtés des cellules de Voronoi. Lutilisation de 2 points de Gauss suffit pour passer le patch test. Les dérivées des fonctions dinterpolation nodales ne sont pas nécessaires dans cette formulation. La formulation passe le patch test. Les problèmes impliquant des matériaux quasi incompressibles sont résolus sans verrouillage. Les applications numériques montrent que les solutions fournies par lapproche développée convergent vers les solutions exactes et se comparent favorablement avec celles de la méthode des éléments finis.

<p>Injection to the subcutaneous (SC) tissue is one of the preferred methods for drug delivery of pharmaceuticals, from small molecules to monoclonal antibodies. Delivery to SC has become widely popular in part thanks to the low cost, ease of use, and effectiveness of drug delivery through the use of auto-injector devices. However, injection physiology, from initial plume formation to the eventual uptake of the drug in the lymphatics, is highly dependent on SC mechanics, poroelastic properties in particular. Yet, the poroelastic properties of SC have been understudied. In this thesis, I present a two-pronged approach to understanding the poroelastic properties of SC. Experimentally, mechanical and fluid transport properties of SC were measured with confined compression experiments and compared against gelatin hydrogels used as SC-phantoms. It was found that SC tissue is a highly non-linear material that has viscoelastic and porohyperelastic dissipation mechanisms. Gelatin hydrogels showed a similar, albeit more linear response, suggesting a micromechanical mechanism may underline the nonlinear behavior. The second part of the thesis focuses on the multiscale modeling of SC to gain a fundamental understanding of how geometry and material properties of the microstructure drive the macroscale response. SC is composed of adipocytes (fat cells) embedded in a collagen network. The geometry can be characterized with Voroni-like tessellations. Adipocytes are fluid-packed, highly deformable and capable of volume change through fluid transport. Collagen is highly nonlinear and nearly incompressible. Representative volume element (RVE) simulations with different Voroni tesselations shows that the different materials, coupled with the geometry of the packing, can contribute to different material response under the different kinds of loading. Further investigation of the effect of geometry showed that cell packing density nonlinearly contributes to the macroscale response. The RVE models can be homogenized to obtain macroscale models useful in large scale finite element simulations of injection physiology. Two types of homogenization were explored: fitting to analytical constitutive models, namely the Blatz-Ko material model, or use of Gaussian process surrogates, a data-driven non-parametric approach to interpolate the macroscale response.</p>

<p dir="ltr">Our current constitutive models of material behavior fall short of being able to describe the mechanics of soft tissues. This is because soft tissues like skin and rubber, unlike traditional engineering materials, exhibit extremely nonlinear mechanical behavior and usually undergo large deformations. Developing accurate constitutive models for such materials requires using flexible tools at the forefront of science, such as machine learning methods. However, our past experiences show that it is crucial to incorporate physical knowledge in models of physical phenomena. The past few years has witnessed the rise of physics-informed models where the goal is to impose governing physical laws by incorporating them in the loss function. However, we argue that such "soft" constraints are not enough. This "persuasion" method has no theoretical guarantees on the satisfaction of physics and result in overly complicated loss functions that make training of the models cumbersome. </p><p dir="ltr">We propose imposing the relevant physical laws as "hard" constraints. In this approach the physics of the problem are "baked in" into the structure of the model preventing it from ever violating them. We demonstrate the power of this paradigm on a number of constitutive models of soft tissue, including hyperelasticity, viscoelasticity and continuum damage models. </p><p dir="ltr">We also argue that new uncertainty quantification strategies have to be developed to address the rise in dimensionality and the inherent symmetries present in most machine learning models compared to traditional constitutive models. We demonstrate that diffusion models can be used to construct a generative framework for physics-constrained hyperelastic constitutive models.</p>

<p dir="ltr">Microelectronic packaging plays a vital role in semiconductor devices. With Moore’s Law nearing its limits, packaging is gaining interest to overcome the challenge. Wire bonding and solder joints are two major interconnections in electronic packaging. They are both widely used based on the requirement of the packaging. Here provides mechanical models to understand the failure in both interconnections.</p><p dir="ltr">Cu (copper) wire-bonding technology is attracting attention in the electronics industry due to its low cost and high electrical and mechanical properties. However, Cu wire bonding is known for its susceptibility to corrosion. The lifetime of Cu wires is shorter than its gold (Au) counterpart. To enhance the use of Cu wires in microelectronic packages, here presents a new mechano-chemical model that couples corrosion, mechanical response, and fracture. The model is used to understand the failure of Cu wires on Al pads in microelectronic packages using a multi-phase field approach. Under high humidity environments, the Cu- rich intermetallic compound (IMC), Cu₉Al₄, formed at the interface between Cu and Al, undergoes a corrosion degradation process. The IMC expands while undergoing corrosion-inducing interface stresses that nucleate and propagate cracks along the Cu-rich IMC/Cu. The model predicts failure due to corrosion and cracking. The model developed can be extended to other systems and applications.</p><p dir="ltr">Sn (tin)-based solder joints are widely used to provide high-density interconnections in microelectronic packaging. However, under repetitive temperature cycling, Sn forms subgrains in high-strain regions, eventually leading to damage. Moreover, Sn’s highly anisotropic material properties can contribute to the subgrain formation. A crystal plasticity model incorporating Sn's anisotropic and temperature-dependent properties is utilized to study the deformation and subgrain formation in Sn solder joints. Lattice rotations are calculated to show subgrain structure. The model developed here aims to predict the reliability of Sn solder joints subjected to temperature cycling.</p>

This thesis concerns optimization of structures considering various uncertainties. The overall objective is to find methods to create solutions that are optimal both in the sense of handling the typical load case and minimising the variability of the response, i.e. robust optimal designs. Traditionally optimized structures may show a tendency of being sensitive to small perturbations in the design or loading conditions, which of course are inevitable. To create robust designs, it is necessary to account for all conceivable variations (or at least the influencing ones) in the design process. The thesis is divided in two parts. The first part serves as a theoretical background to the second part, the two appended articles. This first part includes the concept of robust design, basic statistics, optimization theory and meta modelling. The first appended paper is an application of existing methods on a large industrial example problem. A sensitivity analysis is performed on a Scania truck cab subjected to impact loading in order to identify the most influencing variables on the crash responses. The second paper presents a new method that may be used in robust optimizations, that is, optimizations that account for variations and uncertainties. The method is demonstrated on both an analytical example and a Finite Element example of an aluminium extrusion subjected to axial crushing. / ROBDES