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. [2018] 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.

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.

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.

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 Al$$_2$$ 2 O$$_3$$ 3 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 the previous literature. We show that SPH is an excellent method for solving this free surface problem accurately and efficiently.

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.