Immersed boundary-finite element model of fluid-structure interaction in the aortic root

It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe fluid-structure interaction models of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employ a version of Peskin's immersed boundary (IB) method with a finite element (FE) description of the structural elasticity. We develop both an idealized model of the root with three-fold symmetry of the aortic sinuses and valve leaflets, and a more realistic model that accounts for the differences in the sizes of the left, right, and noncoronary sinuses and corresponding valve cusps. As in earlier work, we use fiber-based models of the valve leaflets, but this study extends earlier IB models of the aortic root by employing incompressible hyperelastic models of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backwards displacement method that determines the unloaded configurations of the root models. Our models yield realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations demonstrate that IB models of the aortic valve are able to produce essentially grid-converged dynamics at practical grid spacings for the high-Reynolds number flows of the aortic root

A generative approach for image-based modeling of tumor growth

22nd International Conference, IPMI 2011, Kloster Irsee, Germany, July 3-8, 2011. ProceedingsExtensive imaging is routinely used in brain tumor patients to monitor the state of the disease and to evaluate therapeutic options. A large number of multi-modal and multi-temporal image volumes is acquired in standard clinical cases, requiring new approaches for comprehensive integration of information from different image sources and different time points. In this work we propose a joint generative model of tumor growth and of image observation that naturally handles multi-modal and longitudinal data. We use the model for analyzing imaging data in patients with glioma. The tumor growth model is based on a reaction-diffusion framework. Model personalization relies only on a forward model for the growth process and on image likelihood. We take advantage of an adaptive sparse grid approximation for efficient inference via Markov Chain Monte Carlo sampling. The approach can be used for integrating information from different multi-modal imaging protocols and can easily be adapted to other tumor growth models.German Academy of Sciences Leopoldina (Fellowship Programme LPDS 2009-10)Academy of Finland (133611)National Institutes of Health (U.S.) (NIBIB NAMIC U54-EB005149)National Institutes of Health (U.S.) (NCRR NAC P41- RR13218)National Institutes of Health (U.S.) (NINDS R01-NS051826)National Institutes of Health (U.S.) (NIH R01-NS052585)National Institutes of Health (U.S.) (NIH R01-EB006758)National Institutes of Health (U.S.) (NIH R01-EB009051)National Institutes of Health (U.S.) (NIH P41-RR014075)National Science Foundation (U.S.) (CAREER Award 0642971

Scale selection in nonlinear fracture mechanics of heterogeneous materials

A new adaptive multiscale method for the non-linear fracture simulation of heterogeneous materials is proposed. The two major sources of errors in the finite element simulation are discretization and modelling errors. In the failure problems, the discretization error increases due to the strain localization which is also a source for the error in the homogenization of the underlying microstructure. In this paper, the discretization error is controlled by an adaptive mesh refinement procedure following the Zienkiewicz–Zhu technique, and the modelling error, which is the resultant of homogenization of microstructure, is controlled by replacing the macroscopic model with the underlying heterogeneous microstructure. The scale adaptation criterion which is based on an error indicator for homogenization is employed for our non-linear fracture problem. The control of both discretization and homogenization errors is the main feature of the proposed multiscale method

Data-driven finite elements for geometry and material design

Crafting the behavior of a deformable object is difficult---whether it is a biomechanically accurate character model or a new multimaterial 3D printable design. Getting it right requires constant iteration, performed either manually or driven by an automated system. Unfortunately, Previous algorithms for accelerating three-dimensional finite element analysis of elastic objects suffer from expensive precomputation stages that rely on a priori knowledge of the object's geometry and material composition. In this paper we introduce Data-Driven Finite Elements as a solution to this problem. Given a material palette, our method constructs a metamaterial library which is reusable for subsequent simulations, regardless of object geometry and/or material composition. At runtime, we perform fast coarsening of a simulation mesh using a simple table lookup to select the appropriate metamaterial model for the coarsened elements. When the object's material distribution or geometry changes, we do not need to update the metamaterial library---we simply need to update the metamaterial assignments to the coarsened elements. An important advantage of our approach is that it is applicable to non-linear material models. This is important for designing objects that undergo finite deformation (such as those produced by multimaterial 3D printing). Our method yields speed gains of up to two orders of magnitude while maintaining good accuracy. We demonstrate the effectiveness of the method on both virtual and 3D printed examples in order to show its utility as a tool for deformable object design.National Science Foundation (U.S.) (Grant CCF-1138967)United States. Defense Advanced Research Projects Agency (N66001-12-1-4242

Doctor of Philosophy

dissertationPhysical simulation has become an essential tool in computer animation. As the use of visual effects increases, the need for simulating real-world materials increases. In this dissertation, we consider three problems in physics-based animation: large-scale splashing liquids, elastoplastic material simulation, and dimensionality reduction techniques for fluid simulation. Fluid simulation has been one of the greatest successes of physics-based animation, generating hundreds of research papers and a great many special effects over the last fifteen years. However, the animation of large-scale, splashing liquids remains challenging. We show that a novel combination of unilateral incompressibility, mass-full FLIP, and blurred boundaries is extremely well-suited to the animation of large-scale, violent, splashing liquids. Materials that incorporate both plastic and elastic deformations, also referred to as elastioplastic materials, are frequently encountered in everyday life. Methods for animating such common real-world materials are useful for effects practitioners and have been successfully employed in films. We describe a point-based method for animating elastoplastic materials. Our primary contribution is a simple method for computing the deformation gradient for each particle in the simulation. Given the deformation gradient, we can apply arbitrary constitutive models and compute the resulting elastic forces. Our method has two primary advantages: we do not store or compare to an initial rest configuration and we work directly with the deformation gradient. The first advantage avoids poor numerical conditioning and the second naturally leads to a multiplicative model of deformation appropriate for finite deformations. One of the most significant drawbacks of physics-based animation is that ever-higher fidelity leads to an explosion in the number of degrees of freedom

IST Austria Thesis

This thesis describes a brittle fracture simulation method for visual effects applications. Building upon a symmetric Galerkin boundary element method, we first compute stress intensity factors following the theory of linear elastic fracture mechanics. We then use these stress intensities to simulate the motion of a propagating crack front at a significantly higher resolution than the overall deformation of the breaking object. Allowing for spatial variations of the material's toughness during crack propagation produces visually realistic, highly-detailed fracture surfaces. Furthermore, we introduce approximations for stress intensities and crack opening displacements, resulting in both practical speed-up and theoretically superior runtime complexity compared to previous methods. While we choose a quasi-static approach to fracture mechanics, ignoring dynamic deformations, we also couple our fracture simulation framework to a standard rigid-body dynamics solver, enabling visual effects artists to simulate both large scale motion, as well as fracturing due to collision forces in a combined system. As fractures inside of an object grow, their geometry must be represented both in the coarse boundary element mesh, as well as at the desired fine output resolution. Using a boundary element method, we avoid complicated volumetric meshing operations. Instead we describe a simple set of surface meshing operations that allow us to progressively add cracks to the mesh of an object and still re-use all previously computed entries of the linear boundary element system matrix. On the high resolution level, we opt for an implicit surface representation. We then describe how to capture fracture surfaces during crack propagation, as well as separate the individual fragments resulting from the fracture process, based on this implicit representation. We show results obtained with our method, either solving the full boundary element system in every time step, or alternatively using our fast approximations. These results demonstrate that both of these methods perform well in basic test cases and produce realistic fracture surfaces. Furthermore we show that our fast approximations substantially out-perform the standard approach in more demanding scenarios. Finally, these two methods naturally combine, using the full solution while the problem size is manageably small and switching to the fast approximations later on. The resulting hybrid method gives the user a direct way to choose between speed and accuracy of the simulation

Unravelling the Mechanics of Knitted Fabrics Through Hierarchical Geometric Representation

Knitting interloops one-dimensional yarns into three-dimensional fabrics that exhibit behaviours beyond their constitutive materials. How extensibility and anisotropy emerge from the hierarchical organization of yarns into knitted fabrics has long been unresolved. We sought to unravel the mechanical roles of tensile mechanics, assembly and dynamics arising from the yarn level on fabric nonlinearity by developing a yarn-based dynamical model. This physically validated model captures the fundamental mechanical response of knitted fabrics, analogous to flexible metamaterials and biological fiber networks due to geometric nonlinearity within such hierarchical systems. We identify the dictating factors of the mechanics of knitted fabrics, highlighting the previously overlooked but critical effect of pre-tension. Fabric anisotropy originates from observed yarn--yarn rearrangements during alignment dynamics and is topology-dependent. This yarn-based model also provides design flexibility of knitted fabrics to embed functionalities by allowing variation in both geometric configuration and material property. Our hierarchical approach to build up a knitted fabrics computationally modernizes an ancient craft and represents a first step towards mechanical programmability of knitted fabrics in wide engineering applications