38 research outputs found
FrictionalMonolith: A Monolithic Optimization-based Approach for Granular Flow with Contact-Aware Rigid-Body Coupling
We propose FrictionalMonolith, a monolithic pressure-friction-contact solver for more accurately, robustly, and efficiently simulating two-way interactions of rigid bodies with continuum granular materials or inviscid liquids. By carefully formulating the components of such systems within a single unified minimization problem, our solver can simultaneously handle unilateral incompressibility and implicit integration of friction for the interior of the continuum, frictional contact resolution among the rigid bodies, and mutual force exchanges between the continuum and rigid bodies. Our monolithic approach eliminates various problematic artifacts in existing weakly coupled approaches, including loss of volume in the continuum material, artificial drift and slip of the continuum at solid boundaries, interpenetrations of rigid bodies, and simulation instabilities. To efficiently handle this challenging monolithic minimization problem, we present a customized solver for the resulting quadratically constrained quadratic program that combines elements of staggered projections, augmented Lagrangian methods, inexact projected Newton, and active-set methods. We demonstrate the critical importance of a unified treatment and the effectiveness of our proposed solver in a range of practical scenarios.Natural Sciences and Engineering Research Council of Canada, Grant RGPIN-2021-02524
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Structure Preserving and Scalable Simulation of Colliding Systems
Predictive computational tools to study granular materials are important in fields ranging from the geosciences and civil engineering to computer graphics. The simulation of granular materials, however, presents many challenges. The behavior of a granular medium is fundamentally multi-scale, with pair-wise interactions between discrete granules able to influence the continuum-scale evolution of a bulk material. Computational techniques for studying granular materials must therefore contend with this multi-scale nature.
This research first addresses both the question of how to accurately model interactions between grains and the question of how to achieve multi-scale simulations of granular materials. We propose a novel rigid body contact model and a time integration technique that, for the first time, are able to simultaneously capture five key features of rigid body impact. We further validate this new model and time integration method by reproducing computationally challenging phenomena from granular physics.
We next propose a technique to couple discrete and continuum models of granular materials to one another. This hybrid model reveals a family of possible discretizations suitable for simulation. We derive an explicit integration technique from this framework that is able to capture phenomena previously reserved for discrete treatments, including frictional jamming, while treating bulk regions of the material with a continuum model. To effectively handle the large plastic deformations inherent in the evolution of a granular medium, we further propose a method to dynamically update which regions are treated with a discrete model and which regions are treated with a continuum model. We demonstrate that hybrid simulations of a dynamically evolving granular material are possible and practical, and lay the foundation for further algorithmic development in this space.
Finally, as the the tools used in computational science and engineering become progressively more complex, the ability to effectively train students in the field becomes increasingly important. We address the question of how to train students from a computer science background in numerical computation techniques by proposing a new system to automatically vet and identify problems in numerical simulations. This system has been deployed at the undergraduate and graduate level in a course on physical simulation at Columbia University, and has increased both student retention and student satisfaction with the course
Realtime Simulation of Stiff Threads for microsurgery training simulation
This thesis introduces the physical simulation of surgical thread for usage in a microsurgical training simulator for the education of medical students. To allow interactive simulation the thread must be real time capable. Importantly, in the simulation, the thread must behave in a way that it looks like a real thread to the user. The user can then "dive into" the simulation, because for the user, the simulation of the thread appears real. We refer to this "diving into" the simulation as "immersion".
The physical model of the thread is a mass-spring model based on the Kirchhoff theory for elastic rods. One challenge is the stiffness constraint of the thread. A
real world thread does not change it's length signiffcantly even under high stress. In a mass-spring model this property can be obtained by using high spring constants.
But if an explicit integration method is applied the so called "overshooting" effect presents a problem. It causes the system to diverge when the spring constants are
too high. In this thesis the problem is addressed by applying an implicit integration method. A key property of implicit integration methods is that it is unconditionally
stable and thereby allows a large time step in the numerical integration. But it also requires that a linear system of size equal to the number of degrees of freedom in
the system is solved. If the number of degrees of freedom is high this conflicts with the real-time requirement of the simulation. In this work it is shown that for the
case of the thread the matrix in the linear system is banded and can therefore be solved in linear time. Another advantage of the implicit integration is that forces
are propagated along the complete thread within one time step.
For the simulation of microsurgical sutures knots have to be modeled. A knot causes numerous contacts of the thread with itself. The contact forces are modeled and calculated using a physical model. Because all forces propagate along the whole thread within one time step all contacts interact with each other. A force applied at one contact affects all other contacts. Because of this all contact forces have to be solved for simultaneously. The interaction of the contacts due to the implicit integration are calculated resulting in a linear system which describes the relation between the contact forces and the relative movement of the thread at the contacts. Physically correct contact forces have to be found with this linear system. Similar to the simulation of rigid bodies, a linear complementary problem or a nonlinear complementary problem results depending
on the model that is used for the contact forces. In case of rigid body simulation the "projected Gauss-Seidel" is a proven method for solving the problem. In this thesis
the nonlinear conjugate gradient (NNCG) method from Silcowitz-Hansen et al. is applied. This method was originally developed for rigid body simulations.
The thread has been integrated into the microsurgical training simulator "MicroSim". Which is to say, interactions between the thread and tissue and forceps
have been modeled and incorporated into "MicroSim". These interactions have to be compatible with the implicit integration of the thread. In a joint work with Sismanidis and Schuppe a training module for MicroSim has been developed. This training module allows for training of a microsurgical anastomosis of blood vessels