The investigation of a method to generate conformal lattice structures for additive manufacturing

Additive manufacturing (AM) allows a geometric complexity in products not seen in conventional manufacturing. This geometric freedom facilitates the design and fabrication of conformal hierarchical structures. Entire parts or regions of a part can be populated with lattice structure, designed to exhibit properties that differ from the solid material used in fabrication. Current computer aided design (CAD) software used to design products is not suitable for the generation of lattice structure models. Although conceptually simple, the memory requirements to store a virtual CAD model of a lattice structure are prohibitively high. Conventional CAD software defines geometry through boundary representation (B-rep); shapes are described by the connectivity of faces, edges and vertices. While useful for representing accurate models of complex shape, the sheer quantity of individual surfaces required to represent each of the relatively simple individual struts that comprise a lattice structure ensure that memory limitations are soon reached. Additionally, the conventional data flow from CAD to manufactured part is arduous, involving several conversions between file formats. As well as a lengthy process, each conversion risks the generation of geometric errors that must be fixed before manufacture. A method was developed to specifically generate large arrays of lattice structures, based on a general voxel modelling method identified in the literature review. The method is much less sensitive to geometric complexity than conventional methods and thus facilitates the design of considerably more complex structures. The ability to grade structure designs across regions of a part (termed functional grading ) was also investigated, as well as a method to retain connectivity between boundary struts of a conformal structure. In addition, the method streamlines the data flow from design to manufacture: earlier steps of the data conversion process are bypassed entirely. The effect of the modelling method on surface roughness of parts produced was investigated, as voxel models define boundaries with discrete, stepped blocks. It was concluded that the effect of this stepping on surface roughness was minimal. This thesis concludes with suggestions for further work to improve the efficiency, capability and usability of the conformal structure method developed in this work

Mandoline: robust cut-cell generation for arbitrary triangle meshes

Although geometry arising "in the wild" most often comes in the form of a surface representation, a plethora of geometrical and physical applications require the construction of volumetric embeddings either of the geometry itself or the domain surrounding it. Cartesian cut-cell-based mesh generation provides an attractive solution in which volumetric elements are constructed from the intersection of the input surface geometry with a uniform or adaptive hexahedral grid. This choice, especially common in computational fluid dynamics, has the potential to efficiently generate accurate, surface-conforming cells; unfortunately, current solutions are often slow, fragile, or cannot handle many common topological situations. We therefore propose a novel, robust cut-cell construction technique for triangle surface meshes that explicitly computes the precise geometry of the intersection cells, even on meshes that are open or non-manifold. Its fundamental geometric primitive is the intersection of an arbitrary segment with an axis-aligned plane. Beginning from the set of intersection points between triangle mesh edges and grid planes, our bottom-up approach robustly determines cut-edges, cut-faces, and finally cut-cells, in a manner designed to guarantee topological correctness. We demonstrate its effectiveness and speed on a wide range of input meshes and grid resolutions, and make the code available as open source.This work is graciously supported by NSERC Discovery Grants (RGPIN-04360-2014 & RGPIN-2017-05524), NSERC Accelerator Grant (RGPAS-2017-507909), Connaught Fund (503114), and the Canada Research Chairs Program

Animating physical phenomena with embedded surface meshes

Accurate computational representations of highly deformable surfaces are indispensable in the fields of computer animation, medical simulation, computer vision, digital modeling, and computational physics. The focus of this dissertation is on the animation of physics-based phenomena with highly detailed deformable surfaces represented by triangle meshes. We first present results from an algorithm that generates continuum mechanics animations with intricate surface features. This method combines a finite element method with a tetrahedral mesh generator and a high resolution surface mesh, and it is orders of magnitude more efficient than previous approaches. Next, we present an efficient solution for the challenging problem of computing topological changes in detailed dynamic surface meshes. We then introduce a new physics-inspired surface tracking algorithm that is capable of preserving arbitrarily thin features and reproducing realistic fine-scale topological changes like Rayleigh-Plateau instabilities. This physics-inspired surface tracking technique also opens the door for a unique coupling between surficial finite element methods and volumetric finite difference methods, in order to simulate liquid surface tension phenomena more efficiently than any previous method. Due to its dramatic increase in computational resolution and efficiency, this method yielded the first computer simulations of a fully developed crown splash with droplet pinch off.Ph.D.Committee Chair: Turk, Greg; Committee Member: Essa, Irfan; Committee Member: Liu, Karen; Committee Member: Mucha, Peter J.; Committee Member: Rossignac, Jare

Accelerating and simulating detected physical interations

The aim of this doctoral thesis is to present a body of work aimed at improving performance and developing new methods for animating physical interactions using simulation in virtual environments. To this end we develop a number of novel parallel collision detection and fracture simulation algorithms. Methods for traversing and constructing bounding volume hierarchies (BVH) on graphics processing units (GPU) have had a wide success. In particular, they have been adopted widely in simulators, libraries and benchmarks as they allow applications to reach new heights in terms of performance. Even with such a development however, a thorough adoption of techniques has not occurred in commercial and practical applications. Due to this, parallel collision detection on GPUs remains a relatively niche problem and a wide number of applications could benefit from a significant boost in proclaimed performance gains. In fracture simulations, explicit surface tracking methods have a good track record of success. In particular they have been adopted thoroughly in 3D modelling and animation software like Houdini [124] as they allow accurate simulation of intricate fracture patterns with complex interactions, which are generated using physical laws. Even so, existing methods can pose restrictions on the geometries of simulated objects. Further, they often have tight dependencies on implicit surfaces (e.g. level sets) for representing cracks and performing cutting to produce rigid-body fragments. Due to these restrictions, catering to various geometries can be a challenge and the memory cost of using implicit surfaces can be detrimental and without guarantee on the preservation of sharp features. We present our work in four main chapters. We first tackle the problem in the accelerating collision detection on the GPU via BVH traversal - one of the most demanding components during collision detection. Secondly, we show the construction of a new representation of the BVH called the ostensibly implicit tree - a layout of nodes in memory which is encoded using the bitwise representation of the number of enclosed objects in the tree (e.g. polygons). Thirdly, we shift paradigm to the task of simulating breaking objects after collision: we show how traditional finite elements can be extended as a way to prevent frequent re-meshing during fracture evolution problems. Finally, we show how the fracture surface–represented as an explicit (e.g. triangulated) surface mesh–is used to generate rigid body fragments using a novel approach to mesh cutting

Efficient integration of software components for scientific simulations

Abstract unavailable please refer to PD

The Constitutive Relation Inference Toolkit: A Semi-Automated Framework for Inverse Problems in Materials Science

Constitutive relations (CRs) are mathematical models that describe how materials respond to changes in their environment, such as stresses and temperature changes. Accurate knowledge of a material's constitutive relation is critical for simulations of that material to be useful in engineering, biology, geology, and other scientific applications. However, determining a CR from experimental data is not always straightforward, requiring the scientist to solve an inverse problem to infer the CR that best describes that data. In this thesis, we introduce the Constitutive Relation Inference Toolkit (CRIKit), a software library that integrates parallel partial differential equation (PDE) solvers from FEniCS and machine learning (ML) packages like TensorFlow, JAX, and PyMC3 in order to make the process of setting up and solving such inverse problems significantly easier. Furthermore, we describe the theory of invariant tensor functions developed by Zheng Quanshi and its practical implementation in CRIKit, which automatically generates invariants of tensor functions describing any physically possible symmetry. We also use CRIKit to compare the pointwise squared (L2) distance and (sliced) quadratic Wasserstein (W2) distance on a nonlinear Stokes flow problem to determine which should be recommended as a default general-purpose loss function for inference with CRIKit, and find that the quadratic Wasserstein distance is likely the better choice.</p