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Abstract. The last decade witnessed a manifest shift in the microprocessor industry towards chip designs that promote parallel computing. Until recently the privilege of a select group of large research centers, Teraflop computing is becoming a commodity owing to inexpensive GPU cards and multi to many-core x86 processors. This paradigm shift towards large scale parallel computing has been leveraged in Chrono, a freely available C++ multi-physics simulation package. Chrono is made up of a collection of loosely coupled components that facilitate different aspects of multi-physics modeling, simulation, and visualization. This contribution provides an overview of Chrono::Engine, Chrono::Flex, Chrono::Fluid, and Chrono::Render, which are modules that can capitalize on the processing power of hundreds of parallel processors. Problems that can be tackled in Chrono include but are not limited to granular material dynamics, tangled large flexible structures with self contact, particulate flows, and tracked vehicle mobility. The paper presents an overview of each of these modules and illustrates through several examples the potential of this multi-physics library.

We investigate two classes of solvers used to determine the time evolution of large systems of rigid bodies that mutually interact through contact with friction. The contact is modeled through a complementarity condition; the friction is posed as a variational problem. The system dynamics is described by a set of differential algebraic equations coupled with differential variational inequalities (DVI). Upon discretization in time, the complementarity conditions enforced at the velocity level are relaxed to obtain a cone complementarity problem (CCP). The solution of the CCP, which becomes the simulation bottleneck, is found by minimizing an equivalent quadratic optimization problem with conic constraints. Herein, we investigate two classes of solvers for this constrained optimization problem. The projected Gauss-Jacobi (PGJ), projected Gauss-Seidel (PGS), and accelerated projected gradient descent (APGD) methods are exponents of the first class of solvers. They are first order, using only costfunction value and gradient information. The second class of solvers is represented by a symmetric cone interior point (SCIP) method and a primal-dual interior point (PDIP) method. These second order methods rely on a Newton step to identify the descent direction and a line search to compute the step size. All five methods draw on parallel computing on Graphics Processing Unit (GPU) cards; the Newton step employs a sparse parallel GPU solver. Two types of numerical experiments, filling and drafting, are carried out to evaluate the performance of the five solution strategies in terms of convergence rate, accuracy, and computational cost. For consistency, all numerical experiments were performed in the same open source code modified to host the five methods of interest.

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The observation motivating this contribution was a perceived lack of expeditious deformable terrain models that can match in mobility analysis studies the level of fidelity delivered by today's vehicle models. Typically, the deformable terrain-tire interaction has been modeled using Finite Element Method (FEM), which continues to require prohibitively long analysis times owing to the complexity of soil behavior. Recent attempts to model deformable terrain have resorted to the use of the Discrete Element Method (DEM) to capture the soil's complex interaction with a wheeled vehicle. We assess herein a DEM approach that employs a complementarity condition to enforce non-penetration between colliding rigid bodies that make up the deformable terrain. To this end, we consider three standard terramechanics experiments: direct shear, pressure-sinkage, and single-wheel tests. We report on the validation of the complementarity form of contact dynamics with friction, assess the potential of the DEM-based exploration of fundamental phenomena in terramechanics, and identify numerical solution challenges associated with solving large-scale, quadratic optimization problems with conic constraints. 1. DEM for Terramechanics: Modeling and Numerical Solution Strategies Adopted This contribution is motivated by an ongoing effort to identify predictive modeling approaches that can characterize dynamics of off-road vehicles. The salient feature of off-road maneuvers is the presence of deformable terrain. Owing to the complex soil behavior, deformable terrain continues to pose significant hurdles that limit the spectrum of scenarios that can be analyzed through computer modeling. The task undertaken is timely, given that it is difficult and expensive to evaluate a vehicle's performance during a majority of off-road maneuvers using physical experiments. Indeed, the range of scenarios that can be considered for physical testing is limited due to time and cost constraints. It is thus desirable to employ computer modeling in a virtual prototyping exercise that, when drawing on physics-based, predictive models, can improve designs, compress the release cycle, and reduce costs.