r-Factor Strategies for the Augmented Lagrangian Approach in Multi-Body Contact Mechanics

Foerg, M.; Geier, Thomas; Neumann, Lutz; Ulbrich, H.

doi:10.1007/1-4020-5370-3_316

Cited by 22 publications

(5 citation statements)

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“…By iteratively updating

\smash{{p_{i}}}

and

\smash{{\vec{\lambda }_{r}}}

using Equation (24), one generates a sequence of iterates that converges locally if the spectral radius of the Jacobian of the right‐hand side of Equation (24) is smaller than one [Erl17]. This requirement can be met by setting

{{\alpha }^{P}}

and

{{\alpha }^{F}}

sufficiently small [FGNU06, PB14]. While there exist approaches that employ backtracking strategies to find safe values for

{{\alpha }^{P}}

and

{{\alpha }^{F}}

[Erl17], we found that using values that correspond to a modified Jacobi update similar to Tonge et al.…”

Section: Methodsmentioning

confidence: 99%

Monolithic Friction and Contact Handling for Rigid Bodies and Fluids Using SPH

Probst

Teschner

2023

Computer Graphics Forum

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We propose a novel monolithic pure SPH formulation to simulate fluids strongly coupled with rigid bodies. This includes fluid incompressibility, fluid-rigid interface handling and rigid-rigid contact handling with a viable implicit particle-based dry friction formulation. The resulting global system is solved using a new accelerated solver implementation that outperforms existing fluid and coupled rigid-fluid simulation approaches. We compare results of our simulation method to analytical solutions, show performance evaluations of our solver and present a variety of new and challenging simulation scenarios.

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“…By iteratively updating

\smash{{p_{i}}}

and

\smash{{\vec{\lambda }_{r}}}

{{\alpha }^{P}}

and

{{\alpha }^{F}}

sufficiently small [FGNU06, PB14]. While there exist approaches that employ backtracking strategies to find safe values for

{{\alpha }^{P}}

and

{{\alpha }^{F}}

[Erl17], we found that using values that correspond to a modified Jacobi update similar to Tonge et al.…”

Section: Methodsmentioning

confidence: 99%

Monolithic Friction and Contact Handling for Rigid Bodies and Fluids Using SPH

Probst

Teschner

2023

Computer Graphics Forum

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“…Let us study a rigid rocking rod impacting two supports, see Fig. 7, which has already been studied by several authors [52][53][54]. In this example, the contact occurs between the support points and the face represented by the rod, meaning that the contact surface does not remain still.…”

Section: A Rocking Rod Impacting Two Supportsmentioning

confidence: 99%

A nonsmooth frictional contact formulation for multibody system dynamics

Galvez

Cavalieri

Cosimo

et al. 2020

Numerical Meth Engineering

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We present a new node-to-face frictional contact element for the simulation of the nonsmooth dynamics of systems composed of rigid and flexible bodies connected by kinematic joints. The equations of motion are integrated using a nonsmooth generalized-α time integration scheme and the frictional contact problem is formulated using a mixed approach, based on an augmented Lagrangian technique and a Coulomb friction law. The numerical results are independent of any user-defined penalty parameter for the normal or tangential component of the forces and, the bilateral and the unilateral constraints are exactly fulfilled both at position and velocity levels. Finally, the robustness and the performance of the proposed algorithm are demonstrated by solving several numerical examples of nonsmooth mechanical systems involving frictional contact.

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“…where r is a parameter that plays a vital role on the rate of convergence, strategies on how to tune r can be found here [29] BPMD Database A convention is required in order to store simulation data in a standard way that will be useful when reconstructing various problems for comparisons of solvers.…”

Section: Solversmentioning

confidence: 99%

A Framework for Problem Standardization and Algorithm Comparison in Multibody System

Williams

Trinkle

et al. 2014

Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

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The underlying dynamic model of multibody systems takes the form of a differential Complementarity Problem (dCP), which is nonsmooth and thus challenging to integrate. The dCP is typically solved by discretizing it in time, thus converting the simulation problem into the problem of solving a sequence of complementarity problems (CPs). Because the CPs are difficult to solve, many modelling options that affect the dCPs and CPs have been tested, and some reformulation and relaxation options affecting the properties of the CPs and solvers have been studied in the hopes to find the “best” simulation method. One challenge within the existing literature is that there is no standard set of benchmark simulations. In this paper, we propose a framework of Benchmark Problems for Multibody Dynamics (BPMD) to support the fair testing of various simulation algorithms. We designed and constructed a BPMD database and collected an initial set of solution algorithms for testing. The data stored for each simulation problem is sufficient to construct the CPs corresponding to several different simulation design decisions. Once the CPs are constructed from the data, there are several solver options including the PATH solver, nonsmooth Newton methods, fixed-point iteration methods for nonlinear problems, and Lemke’s algorithm for linear problems. Additionally, a user-friendly interface is provided to add customized models and solvers. As an example benchmark comparison, we use data from physical planar grasping experiments. Using the input from a physical experiment to drive the simulation, uncertain model parameters such as friction coefficients are determined. This is repeated for different simulation methods and the parameter estimation error serves as a measure of the suitability of each method to predict the observed physical behavior.

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r-Factor Strategies for the Augmented Lagrangian Approach in Multi-Body Contact Mechanics

Cited by 22 publications

References 0 publications

Monolithic Friction and Contact Handling for Rigid Bodies and Fluids Using SPH

Monolithic Friction and Contact Handling for Rigid Bodies and Fluids Using SPH

A nonsmooth frictional contact formulation for multibody system dynamics

A Framework for Problem Standardization and Algorithm Comparison in Multibody System

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