Objects interacting with fluid are of high interest to visually present in three-dimensional applications, such as computer games and virtual environments. For presenting the interactions with high correctness, dynamic rigid body simulation may be used. This paper presents methods for efficient, physics-based real-time simulation of fluid-immersed rigid bodies, where the correctness of the simulation is maintained. Simulated forces include gravity, buoyancy, thrust, drag, and lift. To have the simulation run efficiently in real-time, discretization of the simulated rigid body is made by applying mentioned forces to a user-defined number of particles, sampled pseudo-randomly within the rigid body.

Visual effects for film and animation often require simulated granular materials, such as sand, wheat, or dirt, to meet a director's needs. Simulating granular materials can be time consuming, in both computation and labor, as these particulate materials have complex behavior and an enormous amount of small-scale detail. Furthermore, a single cubic meter of granular material, where each grain is a cubic millimeter, would contain a billion granules, and simulating all such interacting granules would take an impractical amount of time for productions. This calls for a simplified model for granular materials that retains high surface detail and granular behavior yet requires significantly less computational time. Our proposed method simulates a minimal number of individual granules while retaining particulate detail on the surface by supporting surface particles with simplified interior granular models. We introduce a multi-state model where, depending on the material state of the interior granules, we replace interior granules with a simplified simulation model for the state they are in and automate the transitions between those states. The majority of simulation time can thus be focused on visible portions of the material, reducing the time spent on non-visible portions, while maintaining the appearance and behavior of the mass as a whole.

Advancements in computational capabilities have allowed researchers to turn towards modeling as an efficient tool to replicate and predict outcomes of complex systems. Computational models of the musculoskeletal system have gone through various iterations with early versions employing dramatic simplifications. In this work, a three-dimensional computational model of the wrist joint was developed. It accurately recreated the skeletal structures of the hand and wrist and represented the constraints imposed by soft tissue structures like ligaments, tendons, and other surrounding tissues. It was developed to function as a tool to investigate the biomechanical contributions of structures and the kinematic response of the wrist joint. The model was created with the use of a commercially available computer-aided design software employing the rigid body modeling methodology. It was validated against three different cadaveric experimental studies which investigated changes in biomechanical response following radioscapholunate fusion and proximal row carpectomy procedures. The kinematic simulations performed by the model demonstrated quantitatively accurate responses for the range of motions for both surgical procedures. It also provided some understanding to the trends in carpal bone contact force changes observed in surgically altered specimens. The model provided additional insight into the importance of structures like the triangular fibrocartilage and the capsular retinacular structures, both of which are currently not very well understood. As better understanding of components of the wrist joint is achieved, this model could function as an important tool in preoperative planning and generating individualized treatment regiments.

Musculoskeletal computational modeling is a versatile and effective tool which may be used to study joint mechanics, examine muscle and ligament function, and simulate surgical reconstructive procedures. While injury to the elbow joint can be significantly debilitating, questions still remain regarding its normal, pathologic, and repaired behavior. Biomechanical models of the elbow have been developed, but all have assumed fixed joint axes of rotation and ignored the effects of ligaments. Therefore, the objective of this thesis was to develop and validate a computational model of the elbow joint whereby joint kinematics are dictated by three-dimensional bony geometry contact, ligamentous constraints, and muscle loading.Accurate three-dimensional bone geometry was generated by acquiring CT scans, segmenting the images to isolate skeletal features, and fitting surfaces to the segmented data. Ligaments were modeled as tension-only linear springs, and muscle were represented as force vectors with discrete attachment points. Bone contact was modeled by a routine which applied a normal force at points of penetration, with a force magnitude being a function of penetration depth. A rigid body dynamics simulator was used to predict the model's behavior under particular external loading conditions.The computational model was validated by simulating past experimental investigations and comparing results. Passive flexion-extension range of motion predicted by the model correlated exceptionally well with reported values. Bony and ligamentous structures responsible for enforcing motion limits also agreed with past observations. The model's varus stability as a function of elbow flexion and coronoid process resection was also investigated. The trends predicted by the model matched those of the associated cadaver study.This thesis successfully developed an accurate musculoskeletal computational model of the elbow joint complex. While the model may now be used in a predictive manner, further refinements may expand its applicability. These include accounting for the interference between soft tissue and bone, and representing the dynamic behavior of muscles.

O presente trabalho tem por objetivo desenvolver uma formulação numérica baseada em Análise Isogeométrica para o estudo de problemas de interação fluido-estrutura (IFE) em aplicações envolvendo corpos rígidos submersos, onde escoamentos incompressíveis de fluidos Newtonianos com superfície livre são considerados. Propõe-se o emprego da Análise Isogeométrica por permitir a unificação entre os procedimentos de pré-processamento e análise, melhorando assim as condições de continuidade das funções de base empregadas tanto na discretização espacial do problema como na aproximação das variáveis do sistema de equações. O sistema de equações fundamentais do escoamento é formado pelas equações de Navier-Stokes e pela equação da conservação de massa, descrita segundo a hipótese de pseudo-compressibilidade, em uma formulação cinemática ALE (Arbitrary Lagrangean- Eulerian). A consideração da superfície livre no escoamento se dá tratando o fluido como um meio bifásico, através do método Level Set. O corpo rígido apresenta não linearidade na rotação e restrições representadas por vínculos elásticos e amortecedores viscosos, sendo a equação de equilíbrio dinâmico resolvida através do método de Newmark. O esquema de acoplamento sólido-fluido adotado é o particionado convencional, que impõe condições de compatibilidade cinemáticas e de equilíbrio sobre a interface sólido-fluido, analisando ambos os meios de maneira sequencial. A discretização das equações governantes é realizada através do esquema explícito de dois passos de Taylor-Galerkin, aplicado no contexto da Análise Isogeométrica. Por fim, são analisados alguns problemas da Dinâmica de Fluidos Computacional, de onde se concluiu que os resultados obtidos são bastante consistentes com os fenômenos envolvidos, com as ferramentas exclusivas da Análise Isogeométrica, como o refinamento k, melhorando a convergência dos resultados. Para escoamentos bifásicos, verificou-se que o método Level Set obteve resultados bastante promissores apresentando, entretanto, uma dissipação numérica excessiva. Propõe-se, para estudos futuros, a elaboração de esquemas numéricos que conservem melhor o volume da fase líquida do escoamento. / The present work aims to development of a numerical formulation based on Isogeometric Analysis for the study of Fluid-Structure Interaction problems in applications involving rigid bodies submerged, considering incompressible Newtonian flows with free surface. The use of the Isogeometric Analysis allows unification between the preprocessing and analysis steps, improving then the continuity of the base functions employed, both in the spatial discretization and approximation of the variables in the system of equations. The fundamental flow equations are formed by the Navier-Stokes and the mass conservation, described by de pseudo-compressibility hypothesis, in an ALE (Arbitrary Lagrangean-Eulerian) kinematic formulation. The free surface consideration of the flow is handled treating the fluid like a two- phase medium, using the Level Set method. The rigid body considers nonlinearity in rotation, and restrictions represented by elastic springs and viscous dampers, with the dynamic equilibrium equation being resolved using the Newmark’s method. The solid-fluid coupling scheme is the conventional partitioned, which imposes kinematics and equilibrium compatibility conditions on the solid-fluid interface, analyzing both mediums in a sequential manner. The governing equations are discretized using the explicit two step Taylor-Galerkin method, applied in an Isogeometric Analisys context. Finally, some Computational Fluid Dinamics problems are analysed, from which it was concluded that the results obtained are quite consistent with phenomena involved, with the unique tools of Isogeometric Analysis, such as k-refinement, improving the convergence of the results. For biphasic flows, it was verified that the Level Set method obtained very promising results, presenting, however, an excessive numerical dissipation. For future studies, it is proposed the elaboration of numerical schemes that better preserve the volume of the liquid phase of the flow.

The dynamics of rigid body motion are dependent on the inertial properties of the body - that is, the mass and moment of inertia. For complex systems, it may be necessary to derive these results empirically. Such is the case for manual wheelchairs, which can be modeled as a rigid body frame connected to four wheels. While 3D modeling software is capable of estimating inertial parameters, modeling inaccuracies and ill-defined material properties may introduce significant errors in this estimation technique and necessitate experimental measurements. To that end, this thesis discusses the design of a device called the iMachine that empirically determines the mass, location of the center of mass, and moment of inertia about the vertical (yaw) axis passing through the center of mass of the wheelchair. The iMachine is a spring-loaded rotating platform that freely oscillates about an axis passing through its center due to an initial angular velocity. The mass and location of the center of mass can be determined using a static analysis of a triangular configuration of load cells. An optical encoder records the dynamic angular displacement of the platform, and the natural frequency of free vibration is calculated using several techniques. Finally, the moment of inertia is determined from the natural frequency of the system. In this thesis, test results are presented for the calibration of the load cells and spring rate. In addition, objects with known mass properties were tested and comparisons are made between the analytical and empirical inertia results. In general, the mass measurement of the test object had greater than 99% accuracy. The average relative error for the x and y-coordinates of the center of mass was 0.891% and 1.99%, respectively. For the moment of inertia, a relationship was established between relative error and the ratio of the test object inertia to the inertia of the system. The results suggest that 95% accuracy can be achieved if the test object accounts for at least 25% of the total inertia of the system. Finally, the moment of inertia of a manual wheelchair is determined using the device (I = 1.213 kg-m²), and conclusions are made regarding the reliability and validity of results. The results of this project will feed into energy calculations for the Anatomical Model Propulsion System (AMPS), a wheelchair-propelling robot used to measure the mechanical efficiency of manual wheelchairs.

O presente trabalho tem por objetivo desenvolver uma formulação numérica baseada em Análise Isogeométrica para o estudo de problemas de interação fluido-estrutura (IFE) em aplicações envolvendo corpos rígidos submersos, onde escoamentos incompressíveis de fluidos Newtonianos com superfície livre são considerados. Propõe-se o emprego da Análise Isogeométrica por permitir a unificação entre os procedimentos de pré-processamento e análise, melhorando assim as condições de continuidade das funções de base empregadas tanto na discretização espacial do problema como na aproximação das variáveis do sistema de equações. O sistema de equações fundamentais do escoamento é formado pelas equações de Navier-Stokes e pela equação da conservação de massa, descrita segundo a hipótese de pseudo-compressibilidade, em uma formulação cinemática ALE (Arbitrary Lagrangean- Eulerian). A consideração da superfície livre no escoamento se dá tratando o fluido como um meio bifásico, através do método Level Set. O corpo rígido apresenta não linearidade na rotação e restrições representadas por vínculos elásticos e amortecedores viscosos, sendo a equação de equilíbrio dinâmico resolvida através do método de Newmark. O esquema de acoplamento sólido-fluido adotado é o particionado convencional, que impõe condições de compatibilidade cinemáticas e de equilíbrio sobre a interface sólido-fluido, analisando ambos os meios de maneira sequencial. A discretização das equações governantes é realizada através do esquema explícito de dois passos de Taylor-Galerkin, aplicado no contexto da Análise Isogeométrica. Por fim, são analisados alguns problemas da Dinâmica de Fluidos Computacional, de onde se concluiu que os resultados obtidos são bastante consistentes com os fenômenos envolvidos, com as ferramentas exclusivas da Análise Isogeométrica, como o refinamento k, melhorando a convergência dos resultados. Para escoamentos bifásicos, verificou-se que o método Level Set obteve resultados bastante promissores apresentando, entretanto, uma dissipação numérica excessiva. Propõe-se, para estudos futuros, a elaboração de esquemas numéricos que conservem melhor o volume da fase líquida do escoamento. / The present work aims to development of a numerical formulation based on Isogeometric Analysis for the study of Fluid-Structure Interaction problems in applications involving rigid bodies submerged, considering incompressible Newtonian flows with free surface. The use of the Isogeometric Analysis allows unification between the preprocessing and analysis steps, improving then the continuity of the base functions employed, both in the spatial discretization and approximation of the variables in the system of equations. The fundamental flow equations are formed by the Navier-Stokes and the mass conservation, described by de pseudo-compressibility hypothesis, in an ALE (Arbitrary Lagrangean-Eulerian) kinematic formulation. The free surface consideration of the flow is handled treating the fluid like a two- phase medium, using the Level Set method. The rigid body considers nonlinearity in rotation, and restrictions represented by elastic springs and viscous dampers, with the dynamic equilibrium equation being resolved using the Newmark’s method. The solid-fluid coupling scheme is the conventional partitioned, which imposes kinematics and equilibrium compatibility conditions on the solid-fluid interface, analyzing both mediums in a sequential manner. The governing equations are discretized using the explicit two step Taylor-Galerkin method, applied in an Isogeometric Analisys context. Finally, some Computational Fluid Dinamics problems are analysed, from which it was concluded that the results obtained are quite consistent with phenomena involved, with the unique tools of Isogeometric Analysis, such as k-refinement, improving the convergence of the results. For biphasic flows, it was verified that the Level Set method obtained very promising results, presenting, however, an excessive numerical dissipation. For future studies, it is proposed the elaboration of numerical schemes that better preserve the volume of the liquid phase of the flow.

O presente trabalho tem por objetivo desenvolver uma formulação numérica baseada em Análise Isogeométrica para o estudo de problemas de interação fluido-estrutura (IFE) em aplicações envolvendo corpos rígidos submersos, onde escoamentos incompressíveis de fluidos Newtonianos com superfície livre são considerados. Propõe-se o emprego da Análise Isogeométrica por permitir a unificação entre os procedimentos de pré-processamento e análise, melhorando assim as condições de continuidade das funções de base empregadas tanto na discretização espacial do problema como na aproximação das variáveis do sistema de equações. O sistema de equações fundamentais do escoamento é formado pelas equações de Navier-Stokes e pela equação da conservação de massa, descrita segundo a hipótese de pseudo-compressibilidade, em uma formulação cinemática ALE (Arbitrary Lagrangean- Eulerian). A consideração da superfície livre no escoamento se dá tratando o fluido como um meio bifásico, através do método Level Set. O corpo rígido apresenta não linearidade na rotação e restrições representadas por vínculos elásticos e amortecedores viscosos, sendo a equação de equilíbrio dinâmico resolvida através do método de Newmark. O esquema de acoplamento sólido-fluido adotado é o particionado convencional, que impõe condições de compatibilidade cinemáticas e de equilíbrio sobre a interface sólido-fluido, analisando ambos os meios de maneira sequencial. A discretização das equações governantes é realizada através do esquema explícito de dois passos de Taylor-Galerkin, aplicado no contexto da Análise Isogeométrica. Por fim, são analisados alguns problemas da Dinâmica de Fluidos Computacional, de onde se concluiu que os resultados obtidos são bastante consistentes com os fenômenos envolvidos, com as ferramentas exclusivas da Análise Isogeométrica, como o refinamento k, melhorando a convergência dos resultados. Para escoamentos bifásicos, verificou-se que o método Level Set obteve resultados bastante promissores apresentando, entretanto, uma dissipação numérica excessiva. Propõe-se, para estudos futuros, a elaboração de esquemas numéricos que conservem melhor o volume da fase líquida do escoamento. / The present work aims to development of a numerical formulation based on Isogeometric Analysis for the study of Fluid-Structure Interaction problems in applications involving rigid bodies submerged, considering incompressible Newtonian flows with free surface. The use of the Isogeometric Analysis allows unification between the preprocessing and analysis steps, improving then the continuity of the base functions employed, both in the spatial discretization and approximation of the variables in the system of equations. The fundamental flow equations are formed by the Navier-Stokes and the mass conservation, described by de pseudo-compressibility hypothesis, in an ALE (Arbitrary Lagrangean-Eulerian) kinematic formulation. The free surface consideration of the flow is handled treating the fluid like a two- phase medium, using the Level Set method. The rigid body considers nonlinearity in rotation, and restrictions represented by elastic springs and viscous dampers, with the dynamic equilibrium equation being resolved using the Newmark’s method. The solid-fluid coupling scheme is the conventional partitioned, which imposes kinematics and equilibrium compatibility conditions on the solid-fluid interface, analyzing both mediums in a sequential manner. The governing equations are discretized using the explicit two step Taylor-Galerkin method, applied in an Isogeometric Analisys context. Finally, some Computational Fluid Dinamics problems are analysed, from which it was concluded that the results obtained are quite consistent with phenomena involved, with the unique tools of Isogeometric Analysis, such as k-refinement, improving the convergence of the results. For biphasic flows, it was verified that the Level Set method obtained very promising results, presenting, however, an excessive numerical dissipation. For future studies, it is proposed the elaboration of numerical schemes that better preserve the volume of the liquid phase of the flow.

Developmental Dysplasia of the Hip (DDH) is an abnormal condition where hip joint dislocation, misalignment, or instability is present in infants. Rates of incidence of DDH in newborn infants have been reported to vary between 1 and 20 per 1000 births, making it the most common congenital malformation of the musculoskeletal system. DDH early detection and treatment is critical to avoid the use of surgical treatment in infants and to prevent future complications such as osteoarthritis in adult life. To this day several non-surgical treatments involving the use of harnesses and braces have been proposed to treat DDH in infants, with the Pavlik harness being the current non-surgical standard used to treat DDH at early stages. Although the Pavlik harness has been proven to be successful treating subtle dislocations, severe dislocations do not always reduce. Until now the use of the harness remains an empirical method, and its effectiveness often depends on physician expertise or trial-error procedures; thus a clear guideline has not been established to determine the best optimal harness configuration to treat both subtle and severe dislocations. The goal of this dissertation is to understand the connection between reductions for subtle and severe dislocations and passive muscle forces and moments generated while the harness is used during treatment. While the understanding of DDH biomechanics will provide a valuable clinically applicable approach to optimize and increase harness success rate, it is not without its difficulties. This research has created and developed a three-dimensional based on patient-specific geometry of an infant lower limb. The kinematics and dynamics of the lower limb were defined by modeling the hip, femur, tibia, fibula, ankle, foot, and toe bones. The lines of action of five (5) adductor muscles, namely, the Adductor Brevis, Adductor Longus, Adductor Magnus, Pectineus, and Gracilis were identified as mediators of reduction and its mechanical behavior was characterized using a passive response. Four grades (1-4) of dislocation as specified by the International Hip Dysplasia Institute (IHDI) were considered, and the computer model was computationally manipulated to represent physiological dislocations. To account for proper harness modeling, the femur was restrained to move in an envelope consistent with its constraints. The model of the infant lower limb has been used to analyze subtle and severe dislocations. Results are consistent with previous studies based on a simplified anatomically-consistent synthetic model and clinical reports of very low success of the Pavlik harness for severe dislocations. Furthermore the findings on this work suggest that for severe dislocations, the use of the harness could be optimized to achieve hyperflexion of the lower limb leading to successful reduction for cases where the harness fails. This approach provides three main advantages and innovations: 1) the used of patient-specific geometry to elucidate the biomechanics of DDH; 2) the ability to computationally dislocate the model to represent dislocation severity; and 3) the quantification of external forces needed to accomplish reduction for severe dislocations. This study aims to offer a practical solution to effective treatment that draws from engineering expertise and modeling capabilities and also draws upon medical input. The findings of this work will lay the foundation for future optimization of non-surgical methods critical for the treatment of DDH.

The use of computational modeling is an effective and inexpensive way to predict the response of complex systems to various perturbations. However, not until the early 1990s had this technology been used to predict the behavior of physiological systems, specifically the human skeletal system. To that end, a computational model of the human elbow joint was developed using computed topography (CT) scans of cadaveric donor tissue, as well as the commercially available software package SolidWorks™. The kinematic function of the joint model was then defined through 3D reconstructions of the osteoarticular surfaces and various soft-tissue constraints. The model was validated against cadaveric experiments performed by Hull et al and Fern et al that measured the significance of coronoid process fractures, lateral ulnar collateral ligament ruptures, and radial head resection in elbow joint resistance to varus displacement of the forearm. Kinematic simulations showed that the computational model was able to mimic the physiological movements of the joint throughout various ranges of motion including flexion/extension and pronation/supination. Quantitatively, the model was able to accurately reproduce the trends, as well as the magnitudes, of varus resistance observed in the cadaveric specimens. Additionally, magnitudes of ligament tension and joint contact force predicted by the model were able to further elucidate the complex soft-tissue and osseous contributions to varus elbow stability.