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We present a strongly coupled method for the robust simulation of linear magnetic rigid bodies. Our approach describes the magnetic effects as part of an incremental potential function. This potential is inserted into the reformulation of the equations of motion for rigid bodies as an optimization problem. For handling collision and friction, we lean on the Incremental Potential Contact (IPC) method. Furthermore, we provide a novel, hybrid explicit / implicit time integration scheme for the magnetic potential based on a distance criterion. This reduces the fill-in of the energy Hessian in cases where the change in magnetic potential energy is small, leading to a simulation speedup without compromising the stability of the system. The resulting system yields a strongly coupled method for the robust simulation of magnetic effects. We showcase the robustness in theory by analyzing the behavior of the magnetic attraction against the contact resolution. Furthermore, we display stability in practice by simulating exceedingly strong and arbitrarily shaped magnets. The results are free of artifacts like bouncing for time step sizes larger than with the equivalent weakly coupled approach. Finally, we showcase the utility of our method in different scenarios with complex joints and numerous magnets.

Continuum-based shell models are an established approach for the simulation of thin deformables in computer graphics. However, existing research in physically-based animation is mostly focused on shear-rigid Kirchhoff-Love shells. In this work we explore three-director Cosserat (micropolar) shells which introduce additional rotational degrees of freedom. This microrotation field models transverse shearing and in-plane drilling rotations. We propose an incremental potential formulation of the Cosserat shell dynamics which allows for strong coupling with frictional contact and other physical systems. We evaluate a corresponding finite element discretization for non-planar shells using second-order elements which alleviates shear-locking and permits simulation of curved geometries. Our formulation and the discretization, in particular of the rotational degrees of freedom, is designed to integrate well with typical simulation approaches in physically-based animation. While the discretization of the rotations requires some care, we demonstrate that they do not pose significant numerical challenges in Newton’s method. In our experiments we also show that the codimensional shell model is consistent with the respective three-dimensional model. We qualitatively compare our formulation with Kirchhoff-Love shells and demonstrate intriguing use cases for the additional modes of control over dynamic deformations offered by the Cosserat model such as directly prescribing rotations or angular velocities and influencing the shell’s curvature.

Cold metal transfer (CMT) is a variant of gas metal arc welding (GMAW) in which the molten metal of the wire is transferred to the weld pool mainly in the short-circuit phase. A special feature here is that the wire is retracted during this strongly controlled welding process. This allows precise and spatter-free formation of the weld seams with lower energy input. To simulate this process, a model based on the particle-based smoothed particle hydrodynamics (SPH) method is developed. This method provides a native solution for the mass and heat transfer. A simplified surrogate model was implemented as an arc heat source for welding simulation. This welding simulation model based on smoothed particle hydrodynamics method was augmented with surface effects, the Joule heating of the wire, and the effect of the electromagnetic forces. The model of metal transfer in the cold metal transfer process shows good qualitative agreement with real experiments.

The numerical simulation of surface tension is an active area of research in many different fields of application and has been attempted using a wide range of methods. Our contribution is the derivation and implementation of an implicit cohesion force based approach for the simulation of surface tension effects using the Smoothed Particle Hydrodynamics (SPH) method. We define a continuous formulation inspired by the properties of surface tension at the molecular scale which is spatially discretized using SPH. An adapted variant of the linearized backward Euler method is used for time discretization, which we also strongly couple with an implicit viscosity model. Finally, we extend our formulation with adhesion forces for interfaces with rigid objects.

Existing SPH approaches for surface tension in computer graphics are mostly based on explicit time integration, thereby lacking in stability for challenging settings. We compare our implicit surface tension method to these approaches and further evaluate our model on a wider variety of complex scenarios, showcasing its efficacy and versatility. Among others, these include but are not limited to simulations of a water crown, a dripping faucet and a droplet-toy.

Paper (ACM, Free of Charge)

We explore micropolar materials for the simulation of volumetric deformable solids. In graphics, micropolar models have only been used in the form of one-dimensional Cosserat rods, where a rotating frame is attached to each material point on the one-dimensional centerline. By carrying this idea over to volumetric solids, every material point is associated with a microrotation, an independent degree of freedom that can be coupled to the displacement through a material's strain energy density. The additional degrees of freedom give us more control over bending and torsion modes of a material. We propose a new orthotropic micropolar curvature energy that allows us to make materials stiff to bending in specific directions.

For the simulation of dynamic micropolar deformables we propose a novel incremental potential formulation with a consistent FEM discretization that is well suited for the use in physically-based animation. This allows us to easily couple micropolar deformables with dynamic collisions through a contact model inspired from the Incremental Potential Contact (IPC) approach. For the spatial discretization with FEM we discuss the challenges related to the rotational degrees of freedom and propose a scheme based on the interpolation of angular velocities followed by quaternion time integration at the quadrature points.

In our evaluation we validate the consistency and accuracy of our discretization approach and demonstrate several compelling use cases for micropolar materials. This includes explicit control over bending and torsion stiffness, deformation through prescription of a volumetric curvature field and robust interaction of micropolar deformables with dynamic collisions.

A well-known issue with the widely used Smoothed Particle Hydrodynamics (SPH) method is the neighborhood deficiency. Near the surface, the SPH interpolant fails to accurately capture the underlying fields due to a lack of neighboring particles. These errors may introduce ghost forces or other visual artifacts into the simulation.

In this work we investigate three different popular methods to correct the first-order spatial derivative SPH operators up to linear accuracy, namely the Kernel Gradient Correction (KGC), Moving Least Squares (MLS) and Reproducing Kernel Particle Method (RKPM). We provide a thorough, theoretical comparison in which we remark strong resemblance between the aforementioned methods. We support this by an analysis using synthetic test scenarios. Additionally, we apply the correction methods in simulations with boundary handling, viscosity, surface tension, vorticity and elastic solids to showcase the reduction or elimination of common numerical artifacts like ghost forces. Lastly, we show that incorporating the correction algorithms in a state-of-the-art SPH solver only incurs a negligible reduction in computational performance.

A common way to handle boundaries in SPH fluid simulations is to sample the surface of the boundary geometry using particles. These boundary particles are assigned the same properties as the fluid particles and are considered in the pressure force computation to avoid a penetration of the boundary. However, the pressure solver requires a pressure value for each particle. These are typically not computed for the boundary particles due to the computational overhead. Therefore, several strategies have been investigated in previous works to obtain boundary pressure values. A popular, simple technique is pressure mirroring, which mirrors the values from the fluid particles. This method is efficient, but may cause visual artifacts. More complex approaches like pressure extrapolation aim to avoid these artifacts at the cost of computation time.

We introduce a constraint-based derivation of Divergence-Free SPH (DFSPH) --- a common state-of-the-art pressure solver. This derivation gives us new insights on how to integrate boundary particles in the pressure solve without the need of explicitly computing boundary pressure values. This yields a more elegant formulation of the pressure solver that avoids the aforementioned problems.

In physically-based animation, producing detailed and realistic surface reconstructions for rendering is an important part of a simulation pipeline for particle-based fluids. In this paper we propose a post-processing approach to obtain smooth surfaces from "blobby" marching cubes triangulations without visual volume loss or shrinkage of drops and splashes. In contrast to other state-of-the-art methods that often require changes to the entire reconstruction pipeline our approach is easy to implement and less computationally expensive.

The main component is Laplacian mesh smoothing with our proposed feature weights that dampen the smoothing in regions of the mesh with splashes and isolated particles without reducing effectiveness in regions that are supposed to be flat. In addition, we suggest a specialized decimation procedure to avoid artifacts due to low-quality triangle configurations generated by marching cubes and a normal smoothing pass to further increase quality when visualizing the mesh with physically-based rendering. For improved computational efficiency of the method, we outline the option of integrating computation of our weights into an existing reconstruction pipeline as most involved quantities are already known during reconstruction. Finally, we evaluate our post-processing implementation on high-resolution smoothed particle hydrodynamics (SPH) simulations.

The properties of thermally sprayed coatings depend heavily on their microstructure. The microstructure is determined by the dynamics of the impact of the droplets on the substrate surface and the subsequent overlapping of the previously solidified and deformed droplets. Substrate preparation prior to spraying ensures strong adhesion of the coating. This includes roughening and preheating of the substrate surface. In the present study, the smoothed particle hydrodynamics (SPH) method is used to model the Al2O3 impact on a preheated substrate and a roughened substrate surface. A semi-implicit enthalpy–porosity method is applied to simulate the solidification process in the mushy zone. In addition, an implicit correction for SPH simulations is used to improve the performance and stability of the simulation. To investigate the dynamics of heat transfer in the contact between the surface and the droplet, the discretization of the substrate is also taken into account. The results show that the studied substrate surface conditions affect the splat morphology and the solidification process. Subsequently, the simulation of multiple droplets for coating formation is also performed and analyzed.

We present a new octree-based neighborhood search method for SPH simulation. A speedup of up to 1.9x is observed in comparison to state-of-the-art methods which rely on uniform grids. While our method focuses on maximizing performance in fixed-radius SPH simulations, we show that it can also be used in scenarios where the particle support radius is not constant thanks to the adaptive nature of the octree acceleration structure.

Neighborhood search methods typically consist of an acceleration structure that prunes the space of possible particle neighbor pairs, followed by direct distance comparisons between the remaining particle pairs. Previous works have focused on minimizing the number of comparisons. However, in an effort to minimize the actual computation time, we find that distance comparisons exhibit very high throughput on modern CPUs. By permitting more comparisons than strictly necessary, the time spent on preparing and searching the acceleration structure can be reduced, yielding a net positive speedup. The choice of an octree acceleration structure, instead of the uniform grid typically used in fixed-radius methods, ensures balanced computational tasks. This benefits both parallelism and provides consistently high computational intensity for the distance comparisons. We present a detailed account of high-level considerations that, together with low-level decisions, enable high throughput for performance-critical parts of the algorithm.

Finally, we demonstrate the high performance of our algorithm on a number of large-scale fixed-radius SPH benchmarks and show in experiments with a support radius ratio up to 3 that our method is also effective in multi-resolution SPH simulations.

While the application of the Smoothed Particle Hydrodynamics (SPH) method for the modeling of welding processes has become increasingly popular in recent years, little is yet known about the quantitative predictive capability of this method. We propose a novel SPH model for the simulation of the tungsten inert gas (TIG) spot welding process and conduct a thorough comparison between our SPH implementation and two Finite Element Method (FEM) based models. In order to be able to quantitatively compare the results of our SPH simulation method with grid based methods we additionally propose an improved particle to grid interpolation method based on linear least-squares with an optional hole-filling pass which accounts for missing particles. We show that SPH is able to yield excellent results, especially given the observed deviations between the investigated FEM methods and as such, we validate the accuracy of the method for an industrially relevant engineering application.

The properties of a thermally sprayed coating, such as its durability or thermal conductivity depend on its microstructure, which is in turn directly related to the particle impact process. To simulate this process we present a 3D Smoothed Particle Hydrodynamics (SPH) model, which represents the molten droplet as an incompressible fluid, while a semi-implicit Enthalpy-Porosity method is applied for modeling the phase change during solidification. In addition, we present an implicit correction for SPH simulations, based on well known approaches, from which we can observe improved performance and simulation stability. We apply our SPH method to the impact and solidification of Al₂O₃ droplets onto a substrate and perform a comprehensive quantitative comparison of our method with the commercial software Ansys Fluent using the Volume of Fluid (VOF) approach, while taking identical physical effects into consideration. The results are evaluated in depth and we discuss the applicability of either method for the simulation of thermal spray deposition. We also evaluate the droplet spread factor given varying initial droplet diameters and compare these results with an analytic expression from previous literature. We show that SPH is an excellent method for solving this free surface problem accurately and efficiently.

We develop a new operator splitting formulation for the simulation of corotated linearly elastic solids with Smoothed Particle Hydrodynamics (SPH). Based on the technique of Kugelstadt et al. [KKB2018] originally developed for the Finite Element Method (FEM), we split the elastic energy into two separate terms corresponding to stretching and volume conservation, and based on this principle, we design a splitting scheme compatible with SPH. The operator splitting scheme enables us to treat the two terms separately, and because the stretching forces lead to a stiffness matrix that is constant in time, we are able to prefactor the system matrix for the implicit integration step. Solid-solid contact and fluid-solid interaction is achieved through a unified pressure solve. We demonstrate more than an order of magnitude improvement in computation time compared to a state-of-the-art SPH simulator for elastic solids.

We further improve the stability and reliability of the simulation through several additional contributions. We introduce a new implicit penalty mechanism that suppresses zero-energy modes inherent in the SPH formulation for elastic solids, and present a new, physics-inspired sampling algorithm for generating high-quality particle distributions for the rest shape of an elastic solid. We finally also devise an efficient method for interpolating vertex positions of a high-resolution surface mesh based on the SPH particle positions for use in high-fidelity visualization.

Visually appealing and vivid simulations of deformable solids represent an important aspect of physically based computer animation. For the temporal discretization, it is customary in computer animation to use first-order accurate integration methods, such as Backward Euler, due to their simplicity and robustness. Although there is notable research on second-order methods, their use is not widespread. Many of these well-known methods have significant drawbacks such as severe numerical damping or scene-dependent time step restrictions to ensure stability. In this paper, we discuss the most relevant requirements on such methods in computer animation and motivate the interest beyond first-order accuracy. Keeping these requirements in mind, we investigate several promising methods from the families of diagonally implicit Runge-Kutta (DIRK) and Rosenbrock methods which currently do not appear to have considerable popularity in this field. We show that the usage of such methods improves the visual quality of physical animations. In addition, we demonstrate that they allow distinctly more control over damping at lower computational cost than classical methods. As part of our theoretical contribution, we review aspects of simulations that are often considered more intricate with higher-order methods, such as contact handling. To this end, we derive an implicit linearized contact model based on a predictor-corrector approach that leads to consistent behavior with higher-order integrators as predictors. Our contact model is well suited for the simulation of stiff, nonlinear materials with the integration methods presented in this paper and more common methods such as Backward Euler alike.