Parallel Decomposition-based Contact Response

Fehmi Cirak

California Institute of Technology

Requirements to a contact library for the Virtual Test Facility Non-smooth geometries Modular software architecture for use with shell and solid solvers No problem dependent parameters Parallelization overhead in terms of implementation and

performance should be minimum

Some of the existing contact algorithms Explicit Methods

Penalty methods Include problem dependent parameters

Do not work for non-smooth geometries Explicit-implicit methods

Very hard to parallelize and/or not efficient

Motivation

Discrete Variational Mechanics Discrete action integral

with collision at time

Equilibrium and collision equations

Geometrically admissible configurations

Constraint on the variations

Inadmissible Configurations in 3DVertex-face

collisionEdge-edge collision

Constraint function g is defined as the

tetrahedron volume

Equilibrium equations

Collision equations Jumps in the momentum

Jumps in the kinetic energy

Collision events during explicit time-stepping of the equilibrium equations

Equilibrium and Collision Equations

Impact time tc Impact time approximation as used in

this work

Momentum Decompositions Prior to solving the collision equations the momenta

during the contact are decomposed into components

Normal component

Fix component does not lead to any relative motion

Solving the Collision Equations Non-frictional case

Closed form expressions for the momentum after the collision can be computed using the collision equations and momentum decompositions

Frictional case Friction is modeled as an impulse in the slide direction

Normal impulse same as in non-frictional case

Coulomb model for friction

Update nodal positions and velocities using standard time stepping schemes, such as Newmark

Search and remove inadmissible triangle-triangle intersections

Remove face-node penetrations by projecting the penetrating node to the closest point on the triangles surface

Remove edge-edge penetrations by projecting the penetrating edge to the closest point on the triangle edge

Transfer momenta between colliding vertices and triangles using momentum decompositions

Decompose the momenta prior to contact by computing , , , , and

Compute the normal impulse and the slide impulse Update momentum immediately after impact

DCR Algorithm (with Matt West)

Spheres Impact Without Friction

With Friction ( = 0.5)

Time step 500 Time step 2000

Time step 4000Time step 500 Time step 2000

Time step 4000

Spheres Impact without Friction

Radius 1.0 Neo-hookean material Thickness 0.05 Young’s modulus 21000

Poisson’s ratio 0.3Time step size 5.0e-6 Density 0.0785

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total kinetic internal

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total kinetic internal

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Spheres Impact with Friction (=0.5)

Length 1.0 Thickness 0.2

Time step size 5.0e-6

Neo-hookean material Young’s modulus

21000Poisson’s ratio 0.3Density

0.0785

Cubes Impact

Cubes Impact – Energies and Momenta

114.0

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total Energy kinetic Energy internal Energy

Data for non-smooth impact of five cubes

Parallel Contact Detection In large scale computations contact search takes up a

significant amount of time

There are basic differences in the communication patterns of contact search and element level computations

Contact search is an inherently global problem Finite element computations are local for explicit dynamics

For scalability different partitions for the solid and contact surface are necessary

ll

J L l

Contact partitioning with RCB algorithm

Solid partitioning with METIS

Parallel Contact Algorithm Solid solver provides the entire surface mesh and the

related vertex variables to all computational contact nodes

Surface mesh is partitioned with recursive coordinate bisection using Zoltan

An extended surface patch is assigned to each computational contact node

Each computational node performs on its assigned partition Serial search for collisions

Orthogonal range query with sparse buckets Local contact check for vertex-face and edge-edge penetrations

Apply the serial DCR algorithm

Collect all the modified vertex variables and return the surface mesh to the solid solver

Scalabililty - Two Disk Impact

Scalability runs performed on Frost by Sharon Brunett More tests for different examples in progress

0

0.25

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4 5 6 7 8

CPUs (log2)

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13632 elements54528 elements218112 elements

Integrated Simulation

5,2 M element solid mesh1,3 M cell fluid mesh4K timesteps on 512 Frost procs.

Time step 1700 Time step 2700

Time step 3700 Time step 4700