Implicit smoothed particle hydrodynamics model for simulating incompressible fluid-elastic coupling

Fluid simulation has been one of the most critical topics in computer graphics for its capacity to produce visually realistic effects. The intricacy of fluid simulation manifests most with interacting dynamic elements. The coupling for such scenarios has always been challenging to manage due to the numerical instability arising from the coupling boundary between different elements. Therefore, we propose an implicit smoothed particle hydrodynamics fluid-elastic coupling approach to reduce the instability issue for fluid-fluid, fluid-elastic, and elastic-elastic coupling circumstances. By deriving the relationship between the universal pressure field with the incompressible attribute of the fluid, we apply the number density scheme to solve the pressure Poisson equation for both fluid and elastic material to avoid the density error for multi-material coupling and conserve the non-penetration condition for elastic objects interacting with fluid particles. Experiments show that our method can effectively handle the multiphase fluids simulation with elastic objects under various physical properties

Sparse Surface Constraints for Combining Physics-based Elasticity Simulation and Correspondence-Free Object Reconstruction

We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable real-world data sources such as sparse observations without correspondences. We introduce a novel Lagrangian-Eulerian optimization formulation, including a cost function that penalizes differences to observations during an optimization run. This formulation matches correspondence-free, sparse observations from a single-view depth sequence with a finite element simulation of deformable bodies. In conjunction with an efficient hexahedral discretization and a stable, implicit formulation of collisions, our method can be used in demanding situation to recover a variety of material parameters, ranging from Young's modulus and Poisson ratio to gravity and stiffness damping, and even external boundaries. In a number of tests using synthetic datasets and real-world measurements, we analyse the robustness of our approach and the convergence behavior of the numerical optimization scheme

Locking-Proof Tetrahedra

The simulation of incompressible materials suffers from locking when using the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio gets close to 0.5 and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating incompressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure, and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young\u27s modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean, and we focus on adapting it to our method. For , we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking, which, in turn, affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis

CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce the dimensionality of discretized vector fields, our continuous reduced-order modeling (CROM) approach builds a smooth, low-dimensional manifold of the continuous vector fields themselves, not their discretization. We represent this reduced manifold using continuously differentiable neural fields, which may train on any and all available numerical solutions of the continuous system, even when they are obtained using diverse methods or discretizations. We validate our approach on an extensive range of PDEs with training data from voxel grids, meshes, and point clouds. Compared to prior discretization-dependent ROM methods, such as linear subspace proper orthogonal decomposition (POD) and nonlinear manifold neural-network-based autoencoders, CROM features higher accuracy, lower memory consumption, dynamically adaptive resolutions, and applicability to any discretization. For equal latent space dimension, CROM exhibits 79$\times$ and 49$\times$ better accuracy, and 39$\times$ and 132$\times$ smaller memory footprint, than POD and autoencoder methods, respectively. Experiments demonstrate 109$\times$ and 89$\times$ wall-clock speedups over unreduced models on CPUs and GPUs, respectively

A Geometric Nonlinear Solid-Shell Element Based on ANS, ANDES and EAS Concepts

In this work, first, a computational approach suitable for combined material and geometrically nonlinear analysis for 2D quadrilateral elements is explained. Its main advantage is reuse: once a finite element has been developed with good performance in linear analysis, extension to material and geometrically nonlinear problems is simplified. Extension to geometrically nonlinear problems is enabled by a corotational kinematic description, and that to material nonlinear problems by an optimization-based solution algorithm. The approach thus comprises three ingredients -- the development of high performance linear finite element using the Assumed natural deviatoric strain (ANDES) concept, a corotational kinematic description for quadrilateral element, and an optimization algorithm. The work illustrates the realization of the three ingredients on plane stress problems that exhibit elastoplastic material behavior. Numerical examples are presented to illustrate the effectiveness of the approach.Second, an eight-node solid-shell element based on ANS, ANDES and EAS concepts is presented. The mechanical response of the element is split into three parts: 1) In-plane response, which is also decomposed into membrane and bending, 2) Thickness response or normal strains in thickness direction; and 3) Transverse shear response. This separation gives the liberty of using any type of membrane quadrilateral formulation for the in-plane response. In the present work, ANDES membrane element is used for the in-plane response. ANS concept is implemented to account for the transverse shear and thickness strains, which has proven to circumvent the curvature thickness and transverse shear locking problems. EAS approach with one degree-of-freedom is applied on the thickness strain so as to alleviate the Poisson thickness locking. The formulation yields exact solution for both membrane and bending patch tests.Third, an eight-node solid-shell element based on ANS and EAS concepts is presented. Five enhanced degrees-of-freedom are used to improve the in-plane response of the element and one to alleviate the Poisson's thickness locking problem.Numerical results for some benchmarks show the robustness of both solid-shell formulations in geometrically linear problems.With the proposed linear element at hand, the corotational kinematic description is used to add geometric nonlinearity to this work. Problems with small strains are addressed in this work, however, EICR could be extended to large deformations. The Corotated frame is defined such that it is independent of whether the mid-surface is warped or not. Numerical results for geometric nonlinear solid-shell and the comparisons with other solid-shell and shell formulations are presented in the end

Novel Paradigms in Physics-Based Animation: Pointwise Divergence-Free Fluid Advection and Mixed-Dimensional Elastic Object Simulation

This thesis explores important but so far less studied aspects of physics-based animation: a simulation method for mixed-dimensional and/or non-manifold elastic objects, and a pointwise divergence-free velocity interpolation method applied to fluid simulation. Considering the popularity of single-type models e.g., hair, cloths, soft bodies, etc., in deformable body simulations, more complicated coupled models have gained less attention in graphics research, despite their relative ubiquity in daily life. This thesis presents a unified method to simulate such models: elastic bodies consisting of mixed-dimensional components represented with potentially non-manifold simplicial meshes. Building on well-known simplicial rod, shell, and solid models, this thesis categorizes and defines a comprehensive palette expressing all possible constraints and elastic energies for stiff and flexible connections between the 1D, 2D, and 3D components of a single conforming simplicial mesh. For fluid animation, this thesis proposes a novel methodology to enhance grid-based fluid animation with pointwise divergence-free velocity interpolation. Unlike previous methods which interpolate discrete velocity values directly for advection, this thesis proposes using intermediate steps involving vector potentials: first build a discrete vector potential field, interpolate these values to form a pointwise potential, and apply the continuous curl to recover a pointwise divergence-free flow field. Particles under these pointwise divergence-free flows exhibit significantly better particle distributions than divergent flows over time. To accelerate the use of vector potentials, this thesis proposes an efficient method that provides boundary-satisfying and smooth discrete potential fields on uniform and cut-cell grids. This thesis also introduces an improved ramping strategy for the “Curl-Noise” method of Bridson et al. (2007), which enforces exact no-normal-flow on the exterior domain boundaries and solid surfaces. The ramping method in the thesis effectively reduces the incidence of particles colliding with obstacles or creating erroneous gaps around the obstacles, while significantly alleviating the artifacts the original ramping strategy produces

Physically-based 6-DoF Nodes Deformable Models: Application to Connective Tissues Simulation and Soft-Robots Control

The medical simulation is an increasingly active research field. Yet, despite the promising advance observed over the past years, the complete virtual patient’s model is yet to come. There are still many avenues for improvements, especially concerning the mechanical modeling of boundary conditions on anatomical structures.So far, most of the work has been dedicated to organs simulation, which are generally simulated alone. This raises a real problem as the role of the surrounding organs in the boundary conditions is neglected. However, these interactions can be complex, involving contacts but also mechanical links provided by layers of soft tissues. The latter are known as connective tissues or fasciae. As a consequence, the mutual influences between the anatomical structures are generally simplified, weakening the realism of the simulations.This thesis aims at studying the importance of the connective tissues, and especially of a proper modeling of the boundary conditions. To this end, the role of the ligaments during laparoscopic liver surgery has been investigated. In order to enhance the simulations’ realism, a mechanical model dedicated to the connective tissues has been worked out. This has led to the development of a physically-based method relying on material points that can, not only translate, but also rotate themselves. The goal of this model is to enable the simulation of multiple organs linked by complex interactions.In addition, the work on the connective tissues model has been derived to be used in soft robotics. Indeed, the principle of relying on orientable material points has been used to developed a reduced model that can reproduce the behavior of more complex structures. The objective of this work is to provide the means to control – in real-time – a soft robot made of a deformable arm.La simulation médicale est un domaine de recherche de plus en plus actif. Cependant, malgré les avancées prometteuses observées ces dernières années, le modèle complet du patient virtuel reste un objectif ambitieux. Il existe encore de nombreuses opportunités de recherche, notamment concernant la modélisation mécanique des conditions aux limites des organes.Jusqu'à présent, la majorité des travaux était consacrée à la simulation d'organes, ces derniers étant généralement simulés seuls. Cette situation pose un réel problème car l'influence qu'ont les organes environnants sur les conditions aux limites est négligée. Ces interactions peuvent être complexes, impliquant des contacts mais aussi des liaisons mécaniques dues à des couches de tissus connus sous le nom de tissus conjonctifs ou fasciae. Pour cette raison, les influences mutuelles entre les structures anatomiques sont généralement simplifiées, diminuant le réalisme des simulations.Cette thèse visé à étudier l'importance des tissus conjonctifs, et plus particulièrement d'une bonne modélisation des conditions aux limites. Dans ce but, le rôle des ligaments lors d'une intervention chirurgicale sur la foie par laparoscopie a été étudié. Afin d'améliorer le réalisme des simulations, un modèle mécanique dédié aux tissus conjonctifs a été mis au point. Ainsi, une méthode basée sur la mécanique des milieux continus et un ensemble de nœuds à 6 degrés de liberté a été développée. L'objectif de ce modèle étant de permettre la simulation simultanée de plusieurs organes liés par des interaction complexes.En outre, les travaux sur les tissus conjonctifs ont donné lieu à la mise au point d'une méthode de modélisation utilisée dans le cadre des robots déformables. Cette méthode permet un contrôle précis, et temps-réel, d'un bras robotisé déformable. En effet, l'utilisation de nœuds orientables a permis de développer un modèle a nombre de degrés de liberté réduit, qui permet de reproduire le comportement de structures plus complexes

Management des Windrisikos bei weitgespannten Überdachungen

A number of modern structures characterized by a relevant impact and elegance often coupled with lightness and irregular shapes are dramatically exposed to the wind aerodynamic action, which becomes a key factor in their safety assessment. These structures are involved into a global and complex design process in which players like the environment and social sciences join engineering in order to guarantee an optimal result under several aspects, not the last the economical aspect. In this background, it is not possible trusting into unreliable deterministic considerations, where the over-engineering would assure the result. The attention is now shifted to overall frameworks of Performance-Based Design aimed to specific performance targets and their optimization. In particular, the criteria to ensure the achievement of the results are expressed in terms of risk of failure. This work of thesis presents a general framework for calculating all the possible structural damages and subsequently economic losses after a natural catastrophic event. The framework is adjusted and applied to the specific case study of the covering of the Stadium of Braga in Portugal, where the hazard of a windstorm, the loads that the latter enforces on the covering, the structural response, the resulting damages and other consequences are hierarchically calculated. Particular emphasis, and original contribution of the work, is paid on the evaluation of the dynamic response of the structure. Pressure fluctuations on buildings produced by storms have a complex temporal and spatial organization and their study, keeping under control the whole physical phenomena, is quite difficult. Accordingly, some suitable tools like the orthogonal decomposition are adopted in order to handle the huge amount of data. Moreover a consistent and operative procedure aimed at enhancing the assessment of the aerodynamic wind pressure on the covering is provided. This work addresses a fundamental topic for the risk assessment; the results achieved by the duly application of the framework can be successfully transferred to other actors involved in the management and the governmental processes devoted to natural hazards.Zahlreiche moderne Bauwerke zeichnen sich durch Eleganz, Helligkeit und unregelmäßige Formen aus und sind in extremer Weise aerodynamischen Kräften ausgesetzt, welche eine zentrale Rolle in Sicherheitsanalysen einnehmen. An der Planung derartiger Bauwerke sind viele Fachrichtungen, auch Umwelt- und Sozialwissenschaften, beteiligt, um einen optimalen Bauwerksentwurf zu gewährleisten, wobei nicht zuletzt ökonomische Aspekte von großer Bedeutung sind. Daher ist es oft nicht empfehlenswert, deterministische Verfahren einzusetzen, da diese zur Überdimensionierung von Bauelementen führen können. Stattdessen werden Bauwerke heutzutage zunehmend für verschiedene Gefährdungsstufen bemessen, um die Wirtschaftlichkeit der Baumaßnahme sicher zu stellen und das Versagensrisiko zu bewerten. In der vorliegenden Arbeit wird eine Methodik vorgestellt, mit der alle möglichen strukturellen Schäden eines Bauwerks rechnerisch erfassbar und die damit einhergehenden ökonomischen Schäden abschätzbar sind, die mit einer Naturkatastrophe einhergehen. Die Methodik wird auf die Überdachung des Stadions in Braga, Portugal, angewendet, wobei die Gefahr eines Sturms, die infolge des Sturms induzierten Lasten auf das Bauwerk, die strukturelle Antwort sowie die resultierenden Schäden und weitergehende Konsequenzen berechnet werden. Hierbei findet die Bewertung der dynamischen Antwort des Bauwerks besondere Beachtung, da Druckschwankungen infolge des Sturms komplexe zeitliche und räumliche Verteilungen aufweisen können. Daher werden Verfahren wie die orthogonale Zerlegung angewendet, um den Berechnungsaufwand zu verringern. Ferner wird eine konsistente operative Methode vorgestellt, die eine verbesserte Erfassung des aerodynamischen Winddrucks auf Überdachungen erlaubt. Die Arbeit adressiert eine fundamentale Fragestellung in der Risikobewertung. Die Ergebnisse, die aus der Anwendung der vorgestellten Methodik resultieren, können für alle im Risikomanagement von Naturkatastrophen involvierten Ingenieure und Institutionen von großer Bedeutung sein

Complexity Reduction in Image-Based Breast Cancer Care

The diversity of malignancies of the breast requires personalized diagnostic and therapeutic decision making in a complex situation. This thesis contributes in three clinical areas: (1) For clinical diagnostic image evaluation, computer-aided detection and diagnosis of mass and non-mass lesions in breast MRI is developed. 4D texture features characterize mass lesions. For non-mass lesions, a combined detection/characterisation method utilizes the bilateral symmetry of the breast s contrast agent uptake. (2) To improve clinical workflows, a breast MRI reading paradigm is proposed, exemplified by a breast MRI reading workstation prototype. Instead of mouse and keyboard, it is operated using multi-touch gestures. The concept is extended to mammography screening, introducing efficient navigation aids. (3) Contributions to finite element modeling of breast tissue deformations tackle two clinical problems: surgery planning and the prediction of the breast deformation in a MRI biopsy device

Fast Corotated FEM using Operator Splitting

In this paper we present a novel operator splitting approach for corotated FEM simulations. The deformation energy of the corotated linear material model consists of two additive terms. The first term models stretching in the individual spatial directions and the second term describes resistance to volume changes. By formulating the backward Euler time integration scheme as an optimization problem, we show that the first term is invariant to rotations. This allows us to use an operator splitting approach and to solve both terms individually with different numerical methods. The stretching part is solved accurately with an optimization integrator, which can be done very efficiently because the system matrix is constant over time such that its Cholesky factorization can be precomputed. The volume term is solved approximately by using the compliant constraints method and Gauss‐Seidel iterations. Further, we introduce the analytic polar decomposition which allows us to speed up the extraction of the rotational part of the deformation gradient and to recover inverted elements. Finally, this results in an extremely fast and robust simulation method with high visual quality that outperforms standard corotated FEMs by more than two orders of magnitude and even the fast but inaccurate PBD and shape matching methods by more than one order of magnitude without having their typical drawbacks. This enables a very efficient simulation of complex scenes containing more than a million elements