There are two types of structures in human body, solid organs and hollow membrane like organs. Brain, liver and other soft tissues such as tendons, muscles, cartilage etc., are examples of solid organs. Colon and blood vessels are examples of hollow organs. They greatly differ in structure and mechanical behavior. Deformation of these types of structures is an important phenomena during the process of medical simulation. The primary focus of this project is on deformation of soft tissues. These kind of soft tissues usually undergo large deformation. Deformation of an organ can be considered as mechanical response of that organ during medical simulation. This can be modeled using continuum mechanics and FEM. The primary goal of any system, irrespective of methods and models chosen, it must provide real-time response to obtain sufficient realism and accurate information. One such example is medical training system using haptic feedback. In the past two decades many models were developed and very few considered the non-linear nature in material and geometry of the solid organs. TLED is one among them. A finite element formulation proposed by Miller in 2007, known as total Lagrangian explicit dynamics (TLED) algorithm, will be discussed with respect to implementation point of view and deploying GPU acceleration (because of its parallel nature to some extent) for both pre-processing and actual computation.

Many studies have previously been done on moisture-induced strains in wood. An in- finitesimal/engineering strain model has been used for most of these studies, which is often an accurate approximation for small rotations. However, if large deformations oc- cur, then fictive strains are obtained resulting from the simplified engineering strain.  This work aims to develop a finite element formulation for problems of moisture- induced strains in orthotropic materials based on the total Lagrangian approach, where large displacements and rotations are considered. This model is then used to examine static drying deformations and their effect on dynamic vibrations. A dynamic vibration test was also done to estimate the modulus of elasticity in the fibre direction. The pur- pose is to increase the understanding of moisture-induced strains in wood and also to emphasize the advantages of using a large deformation model.  To facilitate the understanding of large deformation theory, the implementation is first done for a 2D isotropic beam where static and dynamic simulations are made. Re- sults will be compared with a standard model based on engineering strains. For the static part, two types of wooden species are studied, radiata pine and Norway spruce, and com- pared with a previous research study [32] where engineering strain theory is used. The dynamical considerations are divided into a theoretical and an experimental part. The theoretical part analyzes the vibration of radiata pine and Norway spruce samples from a study by Cown and Ormarsson 2005 [32]. In the experimental part, three Norway spruce boards were analyzed.  The results from the numerical implementation showed, among other things, that by taking moisture-induced strains into account two additional properties, the matrix Gm and the vector Emf appear in the finite element formulation. It was concluded that by using a large deformation model the accuracy will increase without causing any extra computational costs.  The transient numerical mass flow analysis showed reasonable results although the sorption exchange rate has to be slightly higher than indicated by comparable measure- ments. For the dynamic part, the performed experiment showed a difference in response between the three Norway spruce species. It was shown that the frequency increases with distance from the pith and also with lower moisture content. The difference in vibration response between Norway spruce and radiata pine was analyzed based on boards from a study by Cown and Ormarsson 2005 [32]. The response for Norway spruce tends to show a higher frequency compared to radiata pine for the test performed in this investigation. This is mainly due to a higher modulus of elasticity and lower density for Norway spruce compared to radiata pine.

<p>Computer-based surgical simulation and non-rigid medical image registration in image-guided interventions are examples of applications that would benefit from real-time deformation simulation of soft tissues. The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models which then can be discretized by the Finite Element Method (FEM) for a numerical solution. Computational complexity of nonlinear FEM-based models has limited their use in real-time applications. The data-parallel nature and intense arithmetic operations in nonlinear FEM models are suitable for massive parallelization of the computations, in order to meet the response time requirements in such applications.</p> <p>This thesis is concerned with computational aspects of complex nonlinear deformation analysis problems with an emphasis on the speed of response using a parallel computing philosophy. It proposes a fast, accurate and scalable Graphic Processing Unit (GPU)-based implementation of the total Lagrangian FEM using implicit time integration for dynamic nonlinear deformation analysis. This is a general formulation valid for large deformations and strains and can account for material nonlinearities. A penalty method is used to satisfy the physical boundary constraints due to contact between deformable objects. The proposed set of optimized GPU kernels for computing the FEM matrices achieves more than 100 GFLOPS on a GTX 470 GPU device. The use of a novel vector assembly kernel and memory optimization strategies result in a performance gain of up to 25 GFLOPS in the PCG computations.</p> / Doctor of Philosophy (PhD)

Small kinematics assumption in classical engineering has been in the center of consideration in structural analysis for decennaries. In the recent years the interest for sustainable and optimized structures, lightweight structures and new materials has grown rapidly as a consequence of desire to archive economical sustainability. These issues involve non-linear constitutive response of materials and can only be accessed on the basis of geometrically and materially non-linear analysis. Numerical simulations have become a conventional tool in modern engineering and have proven accuracy in computation and are on the verge of superseding time consuming and costly experiments.\newlineConsequently, this work presents a numerical computational framework for modeling of geometrically non-linear large deformation of isotropic and orthotropic materials under static and dynamic loading. The numerical model is applied on isotropic steel in plane strain and orthotropic wood in 3D under static and dynamic loading. In plane strain Total Lagrangian, Updated Lagrangian, Newmark-$\beta$ and Energy Conserving Algorithm time-integration methods are compared and evaluated. In 3D, a Total Lagrangian static approach and a Total Lagrangian based dynamic approach with Newmark-$\beta$ time-integration method is proposed to numerically predict deformation of wood under static and dynamic loading. The numerical model's accuracy is validated through an experiment where a knot-free pine wood board under large deformation is studied. The results indicate accuracy and capability of the numerical model in predicting static and dynamic behaviour of wood under large deformation. Contrastingly, classical engineering solution proves its inaccuracy and incapability of predicting kinematics of the wood board under studied conditions. / Små kinematikantaganden inom klassisk ingenjörsteknik har varit centralt för konstruktionslösningar under decennier. Under de senaste åren har intresset för hållbara och optimerade strukturer, lättviktskonstruktioner och nya material ökat kraftigt till följd av önskan att uppnå ekonomisk hållbarhet. Dessa nya konstruktionslösningar involverar icke-linjär konstitutiv respons hos material och kan endast studeras baserad på geometriskt och materiellt olinjär analys. Numeriska simuleringar har blivit ett konventionellt verktyg inom modern ingenjörsteknik och visat sig ge noggrannhet i beräkning och kan på sikt ersätta tidskrävande och kostsamma experiment.\newlineDetta examensarbete presenterar ett numeriskt beräkningsramverk för modellering av geometrisk olinjäritet med stora deformationer hos isotropa och ortotropa material vid statisk och dynamisk belastning. Den numeriska modellen appliceras på isotropiskt stål i plantöjning och ortotropisk trä i 3D vid statisk och dynamisk belastning. I fallet med plantöjning jämförs och utvärderas den Totala Lagrangianen, Uppdaterade Lagrangianen, Newmark-$\beta$ och Energi Konserverings Algoritm metoderna. I 3D föreslås en statisk Total Lagrangian metod och en dynamisk Total Lagrangian-baserad metod med Newmark-$\beta$ tidsintegreringsmetod för att numeriskt förutse statisk och dynamisk deformation hos trä. Den numeriska modellens noggrannhet valideras genom ett experiment där en kvistfri furuplanka studeras under stora deformationer. Resultaten bekräftar noggrannhet och förmåga hos den numeriska modellen att förutse statiska och dynamiska processer hos trä vid stora deformationer. Däremot, visar klassisk ingenjörslösning brist på förmåga att förutse trä plankans kinematik under studerade förhållanden.