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.

We report on an open-source, publicly available C++ software module called Chrono::GPU, which uses the Discrete Element Method (DEM) to simulate large granular systems on Graphics Processing Unit (GPU) cards. The solver supports the integration of granular material with geometries defined by triangle meshes, as well as co-simulation with the multi-physics simulation engine Chrono. Chrono::GPU adopts a smooth contact formulation and implements various common contact force models, such as the Hertzian model for normal force and the Mindlin friction force model, which takes into account the history of tangential displacement, rolling frictional torques, and cohesion. We report on the code structure and highlight its use of mixed data types for reducing the memory footprint and increasing simulation speed. We discuss several validation tests (wave propagation, rotating drum, direct shear test, crater test) that compare the simulation results against experimental data or results reported in the literature. In another benchmark test, we demonstrate linear scaling with a problem size up to the GPU memory capacity; specifically, for systems with 130 million DEM elements. The simulation infrastructure is demonstrated in conjunction with simulations of the NASA Curiosity rover, which is currently active on Mars.

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We outline a phenomenological model to assess friction at the interface between two bodies in mutual contact. Although the approach is general, the application inspiring the approach is the Discrete Element Method. The kinematics of the friction process is expressed in terms of the relative 3D motion of the contact point on the two surfaces in mutual contact. The model produces expressions for three friction loads: slide force, roll torque, and spin torque. The cornerstone of the methodology is the process of tracking the evolution/path of the contact point on the surface of the two bodies in mutual contact. The salient attribute of the model lies with its ability to simultaneously compute, in a 3D setup, the slide, roll, and spin friction loads for smooth bodies of arbitrary geometry while accounting for both static and kinematic friction coefficients.