A contact domain method for large deformation frictional contact problems. Part 1: Theoretical basis

Oliver, J.; Hartmann, Stefan; Cante, Juan; Weyler, R.; Hernández, J.A.

doi:10.1016/j.cma.2009.03.006

Cited by 74 publications

(96 citation statements)

References 33 publications

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“…Moreover, the use of Lagrange multipliers delivers a non-positive system and additional degrees of freedom are introduced. There are many studies that deal with these issues and propose solutions on how to choose L h [14][15][16]; further alternative formulations such as Nitsche's method or stabilized Lagrange multipliers, respectively, have also been advocated [17][18][19][20][21][22][23][24][25]. For our purpose of benchmark testing, the classic Lagrange multiplier approach works nicely as we can control L h a-priori.…”

Section: Extended Finite Element Methods (X-fem)mentioning

confidence: 99%

A high-order immersed boundary discontinuous-Galerkin method for Poisson's equation with discontinuous coefficients and singular sources

Brandstetter

Govindjee

2014

Int. J. Numer. Meth. Engng

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SUMMARYWe adopt a numerical method to solve Poisson's equation on a fixed grid with embedded boundary conditions, where we put a special focus on the accurate representation of the normal gradient on the boundary. The lack of accuracy in the gradient evaluation on the boundary is a common issue with low-order embedded boundary methods. Whereas a direct evaluation of the gradient is preferable, one typically uses postprocessing techniques to improve the quality of the gradient. Here, we adopt a new method based on the discontinuous-Galerkin (DG) finite element method, inspired by the recent work of [A.J. Lew and G.C. Buscaglia. A discontinuous-Galerkin-based immersed boundary method. International Journal for Numerical Methods in Engineering, 76:427-454, 2008]. The method has been enhanced in two aspects: firstly, we approximate the boundary shape locally by higher-order geometric primitives. Secondly, we employ higherorder shape functions within intersected elements. These are derived for the various geometric features of the boundary based on analytical solutions of the underlying partial differential equation. The development includes three basic geometric features in two dimensions for the solution of Poisson's equation: a straight boundary, a circular boundary, and a boundary with a discontinuity. We demonstrate the performance of the method via analytical benchmark examples with a smooth circular boundary as well as in the presence of a singularity due to a re-entrant corner. Results are compared to a low-order extended finite element method as well as the DG method of [1]. We report improved accuracy of the gradient on the boundary by one order of magnitude, as well as improved convergence rates in the presence of a singular source. In principle, the method can be extended to three dimensions, more complicated boundary shapes, and other partial differential equations.

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Section: Extended Finite Element Methods (X-fem)mentioning

confidence: 99%

A high-order immersed boundary discontinuous-Galerkin method for Poisson's equation with discontinuous coefficients and singular sources

Brandstetter

Govindjee

2014

Int. J. Numer. Meth. Engng

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“…In this method, the enforcement of contact constraints is applied in a weak sense throughout the contact interface. The calculation of contact can also be done by other ways such as contact domain methods [27,17] and intermediate mortar surface method [25]. A theoretical and algorithmic background for the contact between two deformable bodies undergoing large deformations is detailed in, e.g., [23,37].…”

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confidence: 99%

An unbiased Nitsche’s formulation of large deformation frictional contact and self-contact

Mlika

Renard

Chouly

2017

Computer Methods in Applied Mechanics and Engineering

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In this paper we propose an extension of Nitsche's method for frictional contact in large elastic deformations. In fact we develop an unbiased strategy in which no asymmetry is considered between contact surfaces, conversely to the master-slave strategy. This enables to take into account within the same formalism contact of two elastic bodies as well as self-contact. We provide a numerical study of the performance and robustness of the method.Keywords: large deformation contact, frictional contact and self-contact, Nitsche's method, unbiased formulation. IntroductionFrictional contact problems involve difficulties from both theoretical and numerical viewpoints, especially in large deformations, where complex geometrical and mechanical quantities depend on an a priori unknown mapping between contact surfaces. Contact problems are inherently non-linear, even non-smooth, and involve variational inequalities and constrained minimization. In the literature, many attempts have been developed to deal with such problems using the finite element method. In most cases, the difficulty caused by the nondifferentiability of contact and friction laws is resolved with either a method of regularization, such as penalization or augmented Lagrangian [21,34], or a mixed method [20,3].Moreover, the spatial discretization of the problem produces difficulties at level of the calculation of mechanical contact. Evaluating the quantities involved in the equations of mechanical contact is difficult when the two boundaries are discretized. The most commonly used method is the node-to-surface (NTS) approach under a master-slave configuration [24,30]. The use of the NTS method involves a loss of accuracy in the calculation of displacements and stresses in the contact area. This results from the amplification of spatial discretization errors caused by the node-wise contact constraint enforcement. A way to overcome this problem is the use of the mortar method which has been successfully applied to solve contact problems with finite deformations [15,31,28]. In this method, the enforcement of contact constraints is applied in a weak sense throughout the contact interface. The calculation of contact can also be done by other ways such as contact domain methods [27,17] and intermediate mortar surface method [25]. A theoretical and algorithmic background for the contact between two deformable bodies undergoing large deformations is detailed in, e.g., [23,37].In this paper we introduce a Nitsche's method for the large deformation contact problem. Nitsche's method was originally proposed in [26] to take into account a Dirichlet condition weakly. It was adapted to bilateral contact in [18,38] and to unilateral contact in [8,9]. This method aims at treating the interface conditions in a weak sense, thanks to a consistent penalty term. So it differs from standard penalization techniques which are nonconsistent. Conversely to mixed method and augmented Lagrangian method, the proposed approach is primal; this allows us to eliminate an outer augme...

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“…Granular-tool friction-contact conditions are imposed using the so-called Contact Domain Method described in Oliver [31], Hartmann [32] in which interacting portions of contacting bodies are identified via an interface mesh. The interface mesh, having zero thickness, has the same dimension as the contacting bodies, and provides a complete, continuous and non-overlapping, pairing of the contact surfaces.…”

Section: Numerical Implementationmentioning

confidence: 99%

PFEM-based modeling of industrial granular flows

et al. 2014

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The potential of numerical methods for the solution and optimization of industrial granular flows problems is widely accepted by the industries of this field, the challenge being to promote effectively their industrial practice. In this paper, we attempt to make an exploratory step in this regard by using a numerical model based on continuous mechanics and on the so-called Particle Finite Element Method (PFEM). This goal is achieved by focusing two specific industrial applications in mining industry and pellet manufacturing: silo discharge and calculation of power draw in tumbling mills. Both examples are representative of variations on the granular material mechanical response -varying from a stagnant configuration to a flow condition. The silo discharge is validated using the experimental data, collected on a full-scale flat bottomed cylindrical silo. The simulation is conducted with the aim of characterizing and understanding the correlation between flow patterns and pressures for concentric discharges. In the second example, the potential of PFEM as a numerical tool to track the positions of the particles inside the drum is analyzed. Pressures and wall pressures distribution are also studied. The power draw is also computed and validated against experiments in which the power is plotted in terms of the rotational speed of the drum.

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A contact domain method for large deformation frictional contact problems. Part 1: Theoretical basis

Cited by 74 publications

References 33 publications

A high-order immersed boundary discontinuous-Galerkin method for Poisson's equation with discontinuous coefficients and singular sources

A high-order immersed boundary discontinuous-Galerkin method for Poisson's equation with discontinuous coefficients and singular sources

An unbiased Nitsche’s formulation of large deformation frictional contact and self-contact

PFEM-based modeling of industrial granular flows

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