Frictional Contact on Smooth Elastic Solids

2021 ◽  
Vol 40 (2) ◽  
pp. 1-17
Author(s):  
Egor Larionov ◽  
Ye Fan ◽  
Dinesh K. Pai
Keyword(s):  
Frictional Contact ◽  
Linear Optimization ◽  
Parallel Transport ◽  
Inequality Constraints ◽  
Rigid Bodies ◽  
Implicit Surface ◽  
Elastic Solids ◽  
Time Step ◽  
Frictional Contacts ◽  
Simulation Problem

Frictional contact between deformable elastic objects remains a difficult simulation problem in computer graphics. Traditionally, contact has been resolved using sophisticated collision detection schemes and methods that build on the assumption that contact happens between polygons. While polygonal surfaces are an efficient representation for solids, they lack some intrinsic properties that are important for contact resolution. Generally, polygonal surfaces are not equipped with an intrinsic inside and outside partitioning or a smooth distance field close to the surface. Here we propose a new method for resolving frictional contacts against deforming implicit surface representations that addresses these problems. We augment a moving least squares (MLS) implicit surface formulation with a local kernel for resolving contacts, and develop a simple parallel transport approximation to enable transfer of frictional impulses. Our variational formulation of dynamics and elasticity enables us to naturally include contact constraints, which are resolved as one Newton-Raphson solve with linear inequality constraints. We extend this formulation by forwarding friction impulses from one time step to the next, used as external forces in the elasticity solve. This maintains the decoupling of friction from elasticity thus allowing for different solvers to be used in each step. In addition, we develop a variation of staggered projections, that relies solely on a non-linear optimization without constraints and does not require a discretization of the friction cone. Our results compare favorably to a popular industrial elasticity solver (used for visual effects), as well as recent academic work in frictional contact, both of which rely on polygons for contact resolution. We present examples of coupling between rigid bodies, cloth and elastic solids.

Formulation of Multibody Dynamics as Complementarity Problems

2003 ◽  
Author(s):  
J. C. Trinkle
Keyword(s):  
Discrete Time ◽  
Complementarity Problem ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Integration Scheme ◽  
Time Step ◽  
Stick Slip ◽  
Frictional Contacts ◽  
Time Formulation

Multibody systems with rigid bodies and unilateral contacts are difficult to simulate due to discontinuities associated with gaining and losing contacts and stick-slip transitions. Methods for simulating such systems fall into two categories: penalty methods and complementarity methods. The former calculate penetration depths of virtual rigid bodies at every time step and compute restoring forces to repair penetrations, while the latter assume that the bodies are truly rigid and compute contact forces that prevent penetration from occurring at all. In this paper, we are concerned with complementarity methods. We present an instantaneous formulation of the equations of motion of multi-rigid-body systems with frictional contacts as a complementarity problem. The unknowns in this formulation are accelerations and forces at the contacts. Since it is known that this model does not always admit a finite solution, it is problematic to use it directly in an integration scheme. This fact motivates the discrete-time formulation presented second. Although the discrete-time formulation also takes the form of a complementarity problem, it does not suffer from non-existence, and thus it is suitable for simulation. Numerical results are compared to the exact solution for a sphere initially sliding, then rolling, on a horizontal plane.

A Convex Complementarity Approach for Simulating Large Granular Flows

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Alessandro Tasora ◽  
Mihai Anitescu
Keyword(s):  
Granular Flow ◽  
Complementarity Problems ◽  
Particle Interaction ◽  
Granular Flows ◽  
Rigid Bodies ◽  
Integration Time ◽  
Frictional Contacts ◽  
Physical Experiments ◽  
Dense Granular Flow ◽  
Number Of Particles

Aiming at the simulation of dense granular flows, we propose and test a numerical method based on successive convex complementarity problems. This approach originates from a multibody description of the granular flow: all the particles are simulated as rigid bodies with arbitrary shapes and frictional contacts. Unlike the discrete element method (DEM), the proposed approach does not require small integration time steps typical of stiff particle interaction; this fact, together with the development of optimized algorithms that can run also on parallel computing architectures, allows an efficient application of the proposed methodology to granular flows with a large number of particles. We present an application to the analysis of the refueling flow in pebble-bed nuclear reactors. Extensive validation of our method against both DEM and physical experiments results indicates that essential collective characteristics of dense granular flow are accurately predicted.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

Semismooth Newton method for frictional contact between pseudo-rigid bodies

2008 ◽  
Vol 197 (33-40) ◽  
pp. 2763-2777 ◽  
Author(s):  
Tomasz Koziara ◽  
Nenad Bićanić
Keyword(s):  
Newton Method ◽  
Frictional Contact ◽  
Rigid Bodies ◽  
Semismooth Newton Method ◽  
Semismooth Newton

Direct Simulation of Lateral Migration of Buoyant Particles in Channel Flow Using GPU Computing

2012 ◽  
Author(s):  
Arman Pazouki ◽  
Dan Negrut
Keyword(s):  
Fluid Flow ◽  
Time Evolution ◽  
Rigid Bodies ◽  
3D Simulation ◽  
Spherical Particles ◽  
Current Work ◽  
Processing Unit ◽  
Lateral Migration ◽  
Sph Method ◽  
Frictional Contacts

The current work promotes the implementation of the Smoothed Particle Hydrodynamics (SPH) method for the Fluid-Solid Interaction (FSI) problems on three levels: 1- an algorithm is described to simulate FSI problems, 2- a parallel GPU implementation is described to efficiently alleviate the performance problem of the SPH method, and 3- validations against other numerical methods and experimental results are presented to demonstrate the accuracy of SPH and SPH-based FSI simulations. While the numerical solution of the fluid dynamics is performed via SPH method, the general Newton-Euler equations of motion are solved for the time evolution of the rigid bodies. Moreover, the frictional contacts in the solid phase are resolved by the Discrete Element Method (DEM), which draws on a viscoelastic model for the mutual interactions. SPH is a Lagrangian method and allows an efficient and straightforward coupling of the fluid and solid phases, where any interface, including boundaries, can be decomposed by SPH particles. Therefore, with a single SPH algorithm, fluid flow and interfacial interactions, namely force and motion, are considered. Furthermore, without any extra effort, the contact resolution of rigid bodies with complex geometries benefits from the spherical decomposition of solid surfaces. Although SPH provides 2nd order accuracy in the discretization of mass and momentum equations, the pressure field may still exhibit large oscillations. One of the most straightforward and computationally inexpensive solutions to this problem is the density re-initialization technique. Additionally, to prevent particle interpenetration and improve the incompressibility of the flow field, the XSPH correction is adopted herein. Despite being relatively straightforward to implement for the analysis of both internal and free surface flows, a naïve SPH simulation does not exhibit the efficiency required for the 3D simulation of real-life fluid flow problems. To address this issue, the software implementation of the proposed framework relies on parallel implementation of the spatial subdivision method on the Graphics Processing Unit (GPU), which allows for an efficient 3D simulation of the fluid flow. Similarly, the time evolution and contact resolution of rigid bodies are implemented using independent GPU-based kernels, which results in an embarrassingly parallel algorithm. Three problems are considered in the current work to show the accuracy of SPH and FSI algorithms. In the first problem, the simulation of the transient Poiseuille flow exhibits an exact match with the analytical solution in series form. The lateral migration of the neutrally buoyant circular cylinder, referred to as tubular pinch effect, is successfully captured in the second problem. In the third problem, the migration of spherical particles in pipe flow was simulated. Two tests were performed to demonstrate whether the Magnus effect or the curvature of the velocity profile cause the particle migration. At the end, the original experiment of the Segre and Silberberg (Segre and Silberberg, Nature 189 (1961) 209–210), which is composed of 3D fluid flow and several rigid particles, is simulated.

On the Importance of Displacement History in Soft-Body Contact Models

2015 ◽  
Vol 11 (4) ◽  
Author(s):  
Jonathan Fleischmann ◽  
Radu Serban ◽  
Dan Negrut ◽  
Paramsothy Jayakumar
Keyword(s):  
Frictional Contact ◽  
Local Deformation ◽  
Friction Model ◽  
Direct Shear ◽  
Nonpenetration Condition ◽  
Time Step ◽  
Tangential Contact ◽  
Direct Shear Tests ◽  
Contact Models ◽  
Contact Displacement

Two approaches are commonly used for handling frictional contact within the framework of the discrete element method (DEM). One relies on the complementarity method (CM) to enforce a nonpenetration condition and the Coulomb dry-friction model at the interface between two bodies in mutual contact. The second approach, called the penalty method (PM), invokes an elasticity argument to produce a frictional contact force that factors in the local deformation and relative motion of the bodies in contact. We give a brief presentation of a DEM-PM contact model that includes multi-time-step tangential contact displacement history. We show that its implementation in an open-source simulation capability called Chrono is capable of accurately reproducing results from physical tests typical of the field of geomechanics, i.e., direct shear tests on a monodisperse material. Keeping track of the tangential contact displacement history emerges as a key element of the model. We show that identical simulations using contact models that include either no tangential contact displacement history or only single-time-step tangential contact displacement history are unable to accurately model the direct shear test.

scholarly journals Stiffness of frictional contact of dissimilar elastic solids

2018 ◽  
Vol 112 ◽  
pp. 318-333 ◽  
Author(s):  
Jin Haeng Lee ◽  
Yanfei Gao ◽  
Allan F. Bower ◽  
Haitao Xu ◽  
George M. Pharr
Keyword(s):  
Frictional Contact ◽  
Elastic Solids

On fuzzy solution of a linear optimization problem with max-aggregation function relation inequality constraints

2017 ◽  
Vol 269 (1-2) ◽  
pp. 521-533
Author(s):  
Radko Mesiar ◽  
Fateme Kouchakinejad ◽  
Alexandra Šipošová
Keyword(s):  
Optimization Problem ◽  
Linear Optimization ◽  
Inequality Constraints ◽  
Aggregation Function ◽  
Linear Optimization Problem ◽  
Fuzzy Solution ◽  
Function Relation
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