Doctor of Philosophy in Computing

dissertationPhysics-based animation has proven to be a powerful tool for creating compelling animations for film and games. Most techniques in graphics are based on methods developed for predictive simulation for engineering applications; however, the goals for graphics applications are dramatically different than the goals of engineering applications. As a result, most physics-based animation tools are difficult for artists to work with, providing little direct control over simulation results. In this thesis, we describe tools for physics-based animation designed with artist needs and expertise in mind. Most materials can be modeled as elastoplastic: they recover from small deformations, but large deformations permanently alter their rest shape. Unfortunately, large plastic deformations, common in graphical applications, cause simulation instabilities if not addressed. Most elastoplastic simulation techniques in graphics rely on a finite-element approach where objects are discretized into a tetrahedral mesh. Using these approaches, maintaining simulation stability during large plastic flows requires remeshing, a complex and computationally expensive process. We introduce a new point-based approach that does not rely on an explicit mesh and avoids the expense of remeshing. Our approach produces comparable results with much lower implementation complexity. Points are a ubiquitous primitive for many effects, so our approach also integrates well with existing artist pipelines. Next, we introduce a new technique for animating stylized images which we call Dynamic Sprites. Artists can use our tool to create digital assets that interact in a natural, but stylized, way in virtual environments. In order to support the types of nonphysical, exaggerated motions often desired by artists, our approach relies on a heavily modified deformable body simulator, equipped with a set of new intuitive controls and an example-based deformation model. Our approach allows artists to specify how the shape of the object should change as it moves and collides in interactive virtual environments. Finally, we introduce a new technique for animating destructive scenes. Our approach is built on the insight that the most important visual aspects of destruction are plastic deformation and fracture. Like with Dynamic Sprites, we use an example-based model of deformation for intuitive artist control. Our simulator treats objects as rigid when computing dynamics but allows them to deform plastically and fracture in between timesteps based on interactions with the other objects. We demonstrate that our approach can efficiently animate the types of destructive scenes common in film and games. These animation techniques are designed to exploit artist expertise to ease creation of complex animations. By using artist-friendly primitives and allowing artists to provide characteristic deformations as input, our techniques enable artists to create more compelling animations, more easily

Deformation embedding for point-based elastoplastic simulation

pre-printWe present a straightforward, easy-to-implement, point-based approach for animating elastoplastic materials. The core idea of our approach is the introduction of embedded space-the least-squares best fit of the material's rest state into three dimensions. Nearest neighbor queries in the embedded space efficiently update particle neighborhoods to account for plastic flow. These queries are simpler and more efficient than remeshing strategies employed in mesh-based finite element methods.We also introduce a new estimate for the volume of a particle, allowing particle masses to vary spatially and temporally with fixed density. Our approach can handle simultaneous extreme elastic and plastic deformations. We demonstrate our approach on a variety of examples that exhibit a wide range of material behaviors

Master of Science

thesisWe present a straightforward, easy-to-implement, point-based approach for animating elastoplastic materials. The core idea of our approach is the introduction of embedded space-the least-squares best fit of the material's rest state into three dimensions. Together with plastic offsets that map embedded space to rest space, the embedded space allows us to robustly estimate the deformation gradient, compute elastic forces, and account for plastic flow. We additionally introduce an estimate for the volume of a particle, opening the door for nonuniform sampling, and describe a technique to increase the robustness of point-based elastic simulation. Our approach can handle arbitrarily large elastic deformations and extreme plastic deformations. Because the approach is point-based, there is no need for complex remeshing-the corresponding operation is a simple neighborhood query in embedded space. We demonstrate our approach on a variety of examples that display a wide range of material behaviors

Continuous and discontinuous modelling of ductile fracture

In many metal forming processes (e.g. blanking, trimming, clipping, machining, cutting) fracture is triggered in order to induce material separation along with a desired product geometry. This type of fracture is preceded by a certain amount of plastic deformation and requires additional energy to be supplied in order for the crack to propagate. It is known as ductile fracture, as opposed to brittle fracture (as in ceramics, concrete, etc). Ductile fracture originates at a microscopic level, as the result of voids initiated at inclusions in the material matrix. These microscopic degradation processes lead to the degradation of the macroscopic mechanical properties, causing softening, strain localisation and finally the formation of macroscopic cracks. The initiation and propagation of cracks has traditionally been studied by fracture mechanics. Yet, the application of this theory to ductile fracture, where highly nonlinear degradation processes (material and geometrical) take place in the fracture process zone, raises many questions. To model these processes, continuum models can be used, either in the form of softening plasticity or continuum damage mechanics. Yet, continuous models can not be applied to model crack propagation, because displacements are no longer continuous across the crack. Hence, a proper model for ductile fracture requires a different approach, one that combines a continuous softening model with a strategy to represent cracks, i.e. displacement discontinuities. This has been the main goal of the present work. In a combined approach, the direction of crack propagation is automatically determined by the localisation pattern, and its rate strongly depends on the evolution of damage (or other internal variables responsible for the strain softening). This contrasts with fracture mechanics, where the material behaviour is not directly linked to the crack propagation criteria. Softening materials have to be supplied with an internal length, which acts as a localisation limiter, thereby ensuring the well-posedness of the governing partial differential equations and mesh independent results. For this purpose, a nonlocal gradient enhancement has been used in this work, which gives similar results to nonlocal models of an integral form. A number of numerical methods are available to model displacement discontinuities in a continuum. In the present context, we have used a remeshing strategy, since it has additional advantages when used with large strain localising material models: it prevents excessive element distortions and allows to optimise the element distriviii bution through mesh adaptivity. As a first step towards a continuum-discontinuum approach, an uncoupled damage model is used first, in which damage merely acts as a crack initiation-propagation indicator, without causing material softening. Since uncoupled models do not lead to material localisation, no regularisation is needed. Yet, uncoupled approaches can not capture the actual failure mechanisms and therefore, in general, can give reliable results only when the size of the fracture process zone is so small that its effect can be neglected. When the size of the fracture process zone is large enough, a truly combined model must be used, which is developed in the second part of this study. Due to softening, the transition from the continuous damage material to the discrete crack occurs gradually, with little stress redistribution, in contrast with the previous uncoupled approach. The gradient regularised softening behaviour is introduced in the yield behaviour of an elastoplastic material. The combined model has been applied satisfactorily to the prediction of ductile failure under shear loading conditions. Third, to be able to apply the model to more general loading conditions, the material description has been improved by introducing the influence of stress triaxiality in the damage evolution of a gradient regularised elastoplastic damage model. The model has been obtained using the continuum damage mechanics concept of effective stress. Results show how compressive (tensile) states of triaxiality may increase (decrease) the material ductility. Finally, the combined approach is applied to the modelling of actual metal forming processes, e.g. blanking, fine blanking, score forming. The gradient regularisation has been implemented in an operator-split manner, which can be very appealing for engineering purposes. To capture the large strain gradients in the localisation zones, a new mesh adaptivity criterion has been proposed. The results of the simulations are in good agreement with experimental data from literature

Efficient and accurate approach for powder compaction problems

In this paper, a new approach for powder cold compaction simulations is presented. A density-dependent plastic model within the framework of finite strain multiplicative hyperelastoplasticity is used to describe the highly nonlinear material behaviour; the Coulomb dry friction model is used to capture friction effects at die-powder contact; and an Arbitrary Lagrangian–Eulerian (ALE) formulation is used to avoid the (usual) excessive distortion of Lagrangian meshes caused by large mass fluxes. Several representative examples, involving structured and unstructured meshes are simulated. The results obtained agree with the experimental data and other numerical results reported in the literature. It is shown that, contrary to other Lagrangian and adaptive h-remeshing approaches recently reported for this type of problems, the present approach verifies the mass conservation principle with very low relative errors (less than 1% in all ALE examples and exactly in the pure Lagrangian examples). Moreover, thanks to the use of an ALE formulation and in contrast with other simulations, the presented density distributions do not present spurious oscillations

Key issues in computational geomechanics

As stated in the introduction, the three main topics covered in this report are actual research fields. Different analyses and new developments related with these fields have been presented in the previous chapters. In the following, after a brief summary of the contributions, some directions for future research are outlined. Detailed presentations of the conclusions of each contribution are included in the corresponding sections and subsections. The most relevant contributions of this report are the following: 1. With respect to the treatment of large boundary displacements: > Quasistatic and dynamic analyses of the vane test for soft materials using a fluid–based ALE formulation and different non-newtonian constitutive laws. > The development of a solid–based ALE formulation for finite strain hyperelastic–plastic models, with applications to isochoric and non-isochoric cases. 2. Referent to the solution of nonlinear systems of equations in solid mechanics: > The use of simple and robust numerical differentiation schemes for the computation of tangent operators, including examples with several non-trivial elastoplastic constitutive laws. > The development of consistent tangent operators for substepping time–integration rules, with the application to an adaptive time–integration scheme. 3. In the field of constitutive modelling of granular materials: > The efficient numerical modelling of different problems involving elastoplastic models, including work hardening–softening models for small–strain problems and density– dependent hyperelastic–plastic models in a large–strain context. > Robust and accurate simulations of several powder compaction processes, with detailed analysis of spatial density distributions and verification of the mass conservation principle

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

Real-time Error Control for Surgical Simulation

Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model. The problem is solved using finite elements within SOFA. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local $h$-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations.Comment: 12 pages, 16 figures, change of the title, submitted to IEEE TBM