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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. . 2015.Using Nesterov's method to accelerate multibody dynamics with friction and contact.

The paper presents theoretical and implementation aspects related to a numerical integrator used for the simulation of large mechanical systems with flexible bodies and contact/impact. The proposed algorithm is based on the Hilber-Hughes-Taylor (HHT) implicit method and is tailored to answer the challenges posed by the numerical solution of index 3 differential-algebraic equations that govern the time evolution of a multibody system. One of the salient attributes of the algorithm is the good conditioning of the Jacobian matrix associated with the implicit integrator. Error estimation, integration step-size control, and nonlinear system stopping criteria are discussed in detail. Simulations using the proposed algorithm of an engine model, a model with contacts, and a model with flexible bodies indicate a 2 to 3 speedup factor when compared against benchmark MSC.ADAMS runs. The proposed HHT-based algorithm has been released in the 2005 version of the MSC.ADAMS/Solver.

In the context of simulating the frictional contact dynamics of large systems of rigid bodies, this paper reviews a novel method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss-Seidel and Gauss-Jacobi methods with over-relaxation for symmetric convex linear complementarity problems. Convergent under fairly standard assumptions, the method is implemented in a parallel framework by using a single instruction multiple data computation paradigm promoted by the Compute Unified Device Architecture library for graphical processing unit programming. The framework supports the simulation of problems with more than one million bodies in contact. Simulation thus becomes a viable tool for investigating the dynamics of complex systems such as ground vehicles running on sand, powder composites, and granular material flow.

The objective of this study was to assess the use of an advanced collision detection algorithm to simulate cartilage contact pressure patterns within dynamic musculoskeletal simulations of movement. We created a knee model that included articular cartilage contact for the tibiofemoral and patellofemoral joints. Knee mechanics were then predicted within the context of a dynamic gait simulation. At each time step of a simulation, ray-casting was used in conjunction with hierarchical oriented bounding boxes (OBB) to rapidly identify regions of overlap between articulating cartilage surfaces. Local cartilage contact pressure was then computed using an elastic foundation model. Collision detection implemented in parallel on a GPU provided up to a 10× speed increase when using high resolution mesh densities that had >10 triangles/mm2. However, pressure magnitudes converged at considerably lower mesh densities (2.6 triangles/mm2) where CPU and GPU implementations of collision detection exhibited equivalent performance. Simulated tibiofemoral contact locations were comparable to prior experimental measurements, while pressure magnitudes were similar to those predicted by finite element models. We conclude the use of ray-casting with hierarchical OBB for collision detection is a viable method for simulating joint contact mechanics in human movement.