Claude Lacoursière

Constraint Fluids

We present a fluid simulation method based on Smoothed Particle Hydrodynamics (SPH) in which incompressibility and boundary conditions are enforced using holonomic kinematic constraints on the density. This formulation enables systematic multiphysics integration in which interactions are modeled via similar constraints between the fluid pseudoparticles and impenetrable surfaces of other bodies. These conditions embody Archimedes principle for solids and thus buoyancy results as a direct consequence. We use a variational time stepping scheme suitable for general constrained multibody systems we call SPOOK. Each step requires the solution of only one Mixed Linear Complementarity Problem (MLCP) with very few inequalities, corresponding to solid boundary conditions. We solve this MLCP with a fast iterative method. Overall stability is vastly improved in comparison to the unconstrained version of SPH, and this allows much larger time steps, and an increase in overall performance by two orders of magnitude. Proof of concept is given for computer graphics applications and interactive simulations.

Rigid Body Cable for Virtual Environments

The present paper addresses the real-time simulation of cables for virtual environments. A faithful physical model based on constrained rigid bodies is introduced and discretized. The performance and stability of the numerical method are analyzed in detail and found to meet the requirements of interactive heavy hoisting simulations. The physical model is well behaved in the limit of infinite stiffness, as well as in the elastic regime, and the tuning parameters correspond directly to conventional material constants. The integration scheme mixes the well-known Stormer-Verlet method for the dynamics equations with the linearly implicit Euler method for the constraint equations and enables physical constraint relaxation and stabilization terms. The technique is shown to have superior numerical stability properties in comparison with either chain-link systems or spring and damper models. Experimental results are presented to show that the method results in stable real-time simulations. Stability persists for moderately large fixed integration step of Deltat = 1/60 s, with hoisting loads of up to 105 times heavier than the elements of the cable. Further numerical experiments validating the physical model are also presented.

Massless Cable for Real-time Simulation

A technique for real‐time simulation of hoisting cable systems based on a multibody nonideal constraint is presented. The hoisting cable constraint is derived from the cable internal energies for stretching and twisting. Each hoisting cable introduces two constraint equations, one for stretching and one for torsion, which include all the rigid bodies attached by the same cable. The computation produces the global tension and torsion in the cable as well as the resulting forces and torques on each attached body. The complexity of the computation grows linearly with the number of bodies attached to a given cable and is weakly coupled to the rest of the simulation. The nonideal constraint formulation allows stable simulations of cables over wide ranges of linear and torsional stiffness, including the rigid limit. This contrasts with lumped element formulations including the cable internal degrees of freedom in which computational complexity grows at least linearly with the number of cable elements – usually proportional to cable length – and where numerical stability is sensitive to the mass ratio between the load and the lumped elements.

Rigid multibody simulation of a helix-like structure: the dynamics of bacterial adhesion pili

We present a coarse-grained rigid multibody model of a subunit assembled helix-like polymer, e.g., adhesion pili expressed by bacteria, that is capable of describing the polymer’s force-extension response. With building blocks representing individual subunits, the model appropriately describes the complex behavior of pili expressed by the gram-negative uropathogenic Escherichia coli bacteria under the action of an external force. Numerical simulations show that the dynamics of the model, which include the effects of both unwinding and rewinding, are in good quantitative agreement with the characteristic force-extension response as observed experimentally for type 1 and P pili. By tuning the model, it is also possible to reproduce the force-extension response in the presence of anti-shaft antibodies, which dramatically changes the mechanical properties. Thus, the model and results in this work give enhanced understanding of how a pilus unwinds under the action of external forces and provide a new perspective of the complex bacterial adhesion processes.

A parallel block iterative method for interactive contacting rigid multibody simulations on multicore PCs

A hybrid, asynchronous, block parallel method to approximately solve complementarity problems (CPs) in real-time on multicore CPUs is described. These problems arise from interactive real-time simulations of systems of constrained, contacting rigid bodies, which are useful in virtual operator training systems for instance. A graph analysis phase identifies components which are weakly coupled using simple heuristics. Each component is then solved in parallel using either a block principal pivot or a projected block Gauss-Seidel method running in separate threads. Couplings which generate forces between the subsystems are handled iteratively using a Gauss-Seidel process which communicates updates between the interacting subsystems asynchronously. Preliminary results show that this approach delivers good performance while keeping overhead small.

Variational Time Stepping for Nonsmooth Analytical System Dynamics

The discrete time variational principle is applied to the Lagrangian formulation of multidomain nonsmooth dynamics to produce a stable time stepping scheme. Examples from electronics are used to demonstrate how to construct pseudo-potentials of nonsmooth devices such as transistors.