This paper is concerned with the physics-based simulation of light tracked vehicles operating on rough deformable terrain. The focus is on small autonomous vehicles, which weigh less than 100 lb and move on deformable and rough terrain that is feature rich and no longer representable using a continuum approach. A scenario of interest is, for instance, the simulation of a reconnaissance mission for a high mobility lightweight robot where objects such as a boulder or a ditch that could otherwise be considered small for a truck or tank, become major obstacles that can impede the mobility of the light autonomous vehicle and negatively impact the success of its mission. Analyzing and gauging the mobility and performance of these light vehicles is accomplished through a modeling and simulation capability called Chrono::Engine. Chrono::Engine relies on parallel execution on Graphics Processing Unit (GPU) cards.

We present several simulations carried out using Chrono::FSI and Chrono::Vehicle that highlight the two way coupling between the dynamics of a vehicle and the dynamics of a fluid that is free to move in a tank rigidly attached to the vehicle; i.e., a vehicle sloshing problem. The simulations are carried out in Chrono [1] using a monolithic solution; i.e., there is no co-simulation, the entire set of equations of motion are solved at the same time. The dynamics of the fluid phase is formulated using the mass and momentum balance equations, the latter known as the Navier-Stokes equations. The fluid herein is considered inviscid. The vehicle dynamics is formulated using a set of differential complementarity equations, which represent the combination of an index 3 set of differential algebraic equations with complementarity conditions that capture the Coulomb friction model [2]. The problem is discretized in space using a meshless approach – the Smoothed Particle Hydrodynamics (SPH) method [3, 4]. Incompressibility is enforced via kinematic constraint equations, which are stated in terms of the velocity of the SPH particles and enforce a constant fluid density constraint [5]. The set of equations is discretized in time using a symplectic half-implicit Euler scheme [6]. The overall discretized problem leads to a Cone Complementarity Problem that is solved using a Barzilai-Borwein type method [7].

This contribution highlights modeling and numerical solution techniques that enable the simulation of ground vehicles operating in off-road conditions. We briefly outline the equations of motion governing the time evolution of complex systems such as, for instance, large collections of granular material or full vehicles. Herein, we demonstrate how these equations of motion have been used in an open source multi-physics simulation software called Chrono to investigate the dynamics of wheeled and tracked vehicles operating on granular material. Next, we briefly discuss the fluid-solid interaction problem, which comes into play, for instance, when simulating fording operations in which a vehicle negotiates a body of water. The two salient attributes of the approach proposed are reliance on differential algebraic inequalities tomodel the dynamics of solid and fluid phases; and, leverage of parallel computing to handle systems with millions of degrees of freedom.

We provide an overview of a multi-physics dynamics engine called Chrono. Its forte is the handling of complex and large dynamic systems containing millions of rigid bodies that interact through frictional contact. Chrono has been recently augmented to support the modeling of fluid-solid interaction (FSI) problems and linear and nonlinear finite element analysis (FEA). We discuss Chrono’s software layout/design and outline some of the modeling and numerical solution techniques at the cornerstone of this dynamics engine. We briefly report on some validation studies that gauge the predictive attribute of the software solution. Chrono is released as open source under a permissive BSD3 license and available for download on GitHub.

Systems composed of rigid bodies interacting through frictional contact are manifest in several science and engineering problems. The number of contacts can be small, such as in robotics and geared machinery, or large, such as in terramechanics applications, additive manufacturing, farming, food industry, and pharmaceutical industry. Currently, there are two popular approaches for handling the frictional contact problem in dynamic systems. The penalty method calculates the frictional contact force based on the kinematics of the interaction, some representative parameters, and an empirical force law. Alternatively, the complementarily method, based on a differential variational inequality (DVI), enforces non penetration of rigid bodies via a complementarity condition. This contribution concentrates on the latter approach and investigates the impact of an anti-relaxation step that improves the accuracy of the frictional contact solution. We show that the proposed anti-relaxation step incurs a relatively modest cost to improve the quality of a numerical solution strategy which poses the calculation of the frictional contact forces as a cone-complementarity problem..

In the context of additive manufacturing, we illustrate how computational multi-body dynamics (CMBD) analysis can (a) increase printing throughput; and, (b) play a role in improving the quality of 3D printed parts. Throughput is increased by packing the printing volume with as many parts as possible. The problem becomes one of determining where each component that needs to be printed finds itself inside the printing volume. Finding the position and orientation of each part is accomplished through CMBD analysis, a point illustrated through an example in which an open-source dynamics engine called Chrono is used to simulate the filling of the active printing volume with a dress that is subsequently 3D printed. This approach, which is general in purpose, enables one to print in one pass multiple parts that are virtually; i.e., through simulation, dropped inside the printing volume to fully fill it up, thus improving efficiencies. In relation to (b), we use million-body dynamics simulations to gauge how various granular mixture parameters and rolling regimes combine to ultimately control the roughness of the surface being sintered.

This paper describes an open source parallel simulation framework capable of simulating large-scale granular and multi-body dynamics problems. This framework, called Chrono::Parallel, builds upon the modeling capabilities of Chrono::Engine, another open source simulation package, and leverages parallel data structures to enable scalable simulation of large problems. Chrono::Parallel is somewhat unique in that it was designed from the ground up to leverage parallel data structures and algorithms so that it scales across a wide range of computer architectures and yet has a rich modeling capability for simulating many different types of problems. The modeling capabilities of Chrono::Parallel will be demonstrated in the context of additive manufacturing and 3D printing by modeling the Selective Layer Sintering layering process and simulating large complex interlocking structures which require compression and folding to fit into a 3D printer's build volume.

Systems composed of rigid bodies interacting through frictional contact are manifest in several science and engineering problems. The number of contacts can be small, such as in robotics and geared machinery, or large, such as in terramechanics applications, additive manufacturing, farming, food industry, and pharmaceutical industry. Currently, there are two popular approaches for handling the frictional contact problem in dynamic systems. The penalty method calculates the frictional contact force based on the kinematics of the interaction, some representative parameters, and an empirical force law. Alternatively, the complementarity method, based on a differential variational inequality (DVI), enforces non-penetration of rigid bodies via a complementarity condition. This contribution concentrates on the latter approach and investigates the impact of an anti-relaxation step that improves the accuracy of the frictional contact solution. We show that the proposed anti-relaxation step incurs a relatively modest cost to improve the quality of a numerical solution strategy which poses the calculation of the frictional contact forces as a cone-complementarity problem.

We present a solution method that, compared to the traditional Gauss-Seidel approach, reduces the time required to simulate the dynamics of large systems of rigid bodies interacting through frictional contact by one to two orders of magnitude. Unlike Gauss-Seidel, it can be easily parallelized, which allows for the physics-based simulation of systems with millions of bodies. The proposed accelerated projected gradient descent (APGD) method relies on an approach by Nesterov in which a quadratic optimization problem with conic constraints is solved at each simulation time step to recover the normal and friction forces present in the system. The APGD method is validated against experimental data, compared in terms of speed of convergence and solution time with the Gauss-Seidel and Jacobi methods, and demonstrated in conjunction with snow modeling, bulldozer dynamics, and several benchmark tests that highlight the interplay between the friction and cohesion forces.

This paper describes a web-enabled tool capable of generating high quality videos and images from multibody dynamics simulation results. This tool, called Chrono::Render, uses the Blender modeling software as the front end with Pixars RenderMan used to create high quality images. Blender is a free and open source tool used to create and visualize 3D content and provides a robust plugin framework which Chrono::Render leverages. To produce the final image, the Blender front end passes data to a RenderMan compliant rendering engine. Along with Pixars PhotoRealistic RenderMan (PRMan), several open source options such as Aqsis, JrMan, or Pixie can be used. Preprocessing is performed on the client side, where the front end generates a work order for the RenderMan compliant rendering engine to process. This work order, which contains several scripts that define the visualization parameters, along with the pre-processed simulation data and other user-defined geometry assets is uploaded to a remote server hosted by the Simulation Based Engineering Lab. This server contains more than a thousand CPU cores used for high performance computing applications, which can be used to render many frames of an animation in parallel. Chrono::Render is free and open source software released under a BSD3 license.

1 Abstract This paper describes a modeling, simulation, and visualization framework aimed at enabling physicsbased analysis of ground vehicle mobility. This framework, called Chrono, has been built to leverage parallel computing both on distributed and shared memory architectures. Chrono is both modular and extensible. Modularity stems from the design decision to build vertical applications whose goal is to reduce the end-to-end time from vision-to-modelto-solution-to-visualization for a targeted application field. The extensibility is a consequence of the design of the foundation modules, which can be enhanced with new features that benefit all the vertical applications. Two factors motivated the development of Chrono. First, there is a manifest need of modeling approaches and simulation tools to support mobility analysis on deformable terrain. Second, the hardware available today has improved to a point where the amount of sheer computer power, the memory size, and the available software stack (productivity tools and programming languages) support computing on a scale that allows integrating highly accurate vehicle dynamics and physics-based terramechanics models. Although commercial software is available nowadays for simulating vehicle and tire models that operate on paved roads; deformable terrain models that complement the fidelity of present day vehicle and tire models have been lacking due to the complexity of soil behavior. This paper demonstrates Chrono’s ability to handle these difficult mobility situations through several simulations, including: (i) urban operations, (ii) muddy terrain operations, (iii) gravel slope operations, and (iv) river fording.

This paper presents a novel approach to the generation of particle flows. Usual methods for the initialization of granular material in multi-body simulations are based on the generation of particles in random positions, where the size of the particles follows a statistical distribution given by a single granulometric curve. Although this is sufficient in various applications, there are cases where other properties of the particles should be subject to randomization, for example friction coefficients. To this end we developed a novel systematic approach where particles can be sorted from a probability space that involves also other parameters such as density, aspect ratio, geometric properties, and so on. The method is fully parametric, in the sense that most properties of the generated particles can be assigned to statistical distributions, using a modular implementation in our simulation software. Probability distributions are introduced as C++ objects; we implemented a library of distributions of various types, either as probability density functions or cumulative distribution functions. The random variates are generated using the Smirnov theorem on inverse transform sampling. Shapes of the particles can belong to different classes, for instance convex hulls, spheres, beams, and so on; those classes are unlimited since they can be extended by means of object oriented programming, and each class introduces statistical distributions about its geometric parameters. Each shape generator can be assigned to a particle family; those families are sorted according to a discrete statistical distribution. Particle families can be organized in hierarchical trees of sub-families, hence obtaining a high level of configuration of the system. The way that particle families, generators and statistical distributions are assembled can be defined by an optional configuration file that leverages the JSON serialization format; we refer to this information as the DNA of the granular flow. This opens the road to parametric studies where such granular flow DNA Figure 1: Multidisperse granular flow from a single shape class. Figure 2: Multidisperse granular flow from multiple shape classes. is automatically changed during multiple simulation runs, for instance in optimization or in sensitivity analysis. Figure 1 shows an example of a random generation of particles in a multidisperse granular flow from a single particle class, namely convex hulls that represent fragments in a shredding process. Here shape parameters follow statistical distributions about size, aspect ratio and amount of detail, to name a few. As shown in Figure 2, multiple families with particles of different classes can be mixed in a stochastic way, according to a provided discrete statistical distribution. We tested this framework within our multibody simulation software whose formulation, based on Differential Variational Inclusions (DVI), can target problems with a massive number of particles with frictional contacts [1]. To this end we performed benchmarks with hundreds of thousands of particles on a parallel computing architecture [2]; in order to improve the efficiency of the collision detection algorithm we designed an innovative optimization strategy where the probability space is discretized by pre-sampling it with a limited number of particle that we call particle prototypes, so that all following particles are just clones of these prototypes. This saves memory because geometric details of clones can be referenced by sharing a single data structure. This approach to the generation of multidisperse granular flow originated from our researches on separation processes used in recycling plants of electronic waste [3], where particles have stochastic properties of geometry, density, electric charge and material type; then we extended this concept to other applications that benefit from this parametric framework, for instance in simulations of earth-moving machines interacting with granular soil.

This paper addresses three questions related to the use of parallel computing in multibody dynamics (MBD) simulation. The “why parallel computing?” question is answered based on the argument that in the upcoming decade parallel computing represents the main source of speed improvement in MBD simulation. The answer to “when is it relevant?” is built around the observation that MBD software users are increasingly interested in multi-physics problems that cross disciplinary boundaries and lead to large sets of equations. The “how?” question is addressed by providing an overview of the state of the art in parallel computing. Emphasis is placed on parallelization approaches and support tools specific to MBD simulation. Three MBD applications are presented where parallel computing has been used to increase problem size and/or reduce time to solution. The paper concludes with a summary of best practices relevant when mapping MBD solutions onto parallel computing hardware.

Motivated by the desire to investigate vehicle fording scenarios, we analyze four frameworks for the simulation of the fluid-solid interaction problem. While all of these approaches rely on a general multibody dynamics simulation framework that supports impact, contact, and constraint, they differ in (i) the fluid representation; (ii) the simulation methodology; and (iii) the fluid-solid interfacing mechanism. The first approach relies on an explicit-implicit, Lagrangian-Lagrangian (LL), solution to the coupled Navier-Stokes and Newton-Euler equations of motion. The fluid momentum and continuity equations, dv dt =− 1 ρ ∇p+ μ ρ ∇2v+ f (1)

1 Accelerating Multi-Body Simulation and Visualization with GPU Computing 3 Hammad Mazhar, Toby Heyn, Daniel Melanz, Arman Pazouki, Aaron Bartholomew, Dan Negrut, Paramsothy Jayakumar and Alessandro Tasora 1.

This paper describes a modeling, simulation, and visualization framework aimed at enabling physics-based analysis of ground vehicle mobility. This framework, called Chrono, has been built to leverage parallel computing both on distributed and shared memory architectures. Chrono is both modular and extensible. Modularity stems from the design decision to build vertical applications whose goal is to reduce the end-to-end time from vision-to-model-to-solution-to visualization for a targeted application field. The extensibility is a consequence of the design of the foundation modules, which can be enhanced with new features that benefit all the vertical applications. Two factors motivated the development of Chrono. First, there is a manifest need of modeling approaches and simulation tools to support mobility analysis on deformable terrain. Second, the hardware available today has improved to a point where the amount of sheer computer power, the memory size, and the available software stack (productivity tools and programming languages) support computing on a scale that allows integrating highly accurate vehicle dynamics and physics-based terramechanics models. Although commercial software is available nowadays for simulating vehicle and tire models that operate on paved roads; deformable terrain models that complement the fidelity of present day vehicle and tire models have been lacking due to the complexity of soil behavior. This paper demonstrates Chrono's ability to handle these difficult mobility situations through several simulations, including: (i) urban operations, (ii) muddy terrain operations, (iii) gravel slope operations, and (iv) river fording.

Using particle based methods to simulate the behavior of compliant material is a complex task. When investigating the behavior of compliant terrain with hundreds of thousands of bodies in contact, millions of unknowns need to be determined. The size of problems solvable using traditional methods such as Jacobi or Gauss Seidel are severely limited due to the poor rate of convergence. This rate of convergence is typical when the equations of motion are posed as a differential variational inequality (DVI) problem that captures contact events between rigid bodies. The methods used for this framework rely on iterative krylov subspace methods such as Conjugate Gradient and Minimum Residual, which show good convergence for large problems. However, this class of iterative algorithms is not generally suitable for solving DVI problems for dynamics simulation. This document will show that these methods, while not specifically designed to solve rigid body dynamics problems, are very capable of doing so and converge very quicky.

This paper presents an effort to use physics based simulation techniques to model the Selective Laser Sintering (SLS) layering process. SLS is an additive manufacturing process to form complex parts, that involves melting thin layers of extremely fine powder, composed of particles with an average diameter of 58 microns. In the numerical model, each powder particle is modeled as a discrete object with 632,000 objects used for the final SLS layering simulation. We first performed an experiment to measure of the angle of repose for the polyamide 12 (PA 650) powder used in the SLS process. This measurement was used to determine the correct friction parameters and calibrate the numerical model. Once the angle of repose was validated initial simulations for the SLS layering process were performed in order to measure the changes in the surface profile of the powder. Future work will study the effect that different powders and roller speeds have on the surface roughness of a newly deposited powder layer along with determining the changes to density and porosity in the final part.