A contact domain method for large deformation frictional contact problems. Part 2: Numerical aspects

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

doi:10.1016/j.cma.2009.03.009

Cited by 61 publications

(49 citation statements)

References 19 publications

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“…Regarding the case with friction, the curves shown in Fig. 12 exhibit the characteristic form found in previously published results [10,13]. Nevertheless, there are important quantitative differences.…”

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confidence: 59%

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An unconstrained integral approximation of large sliding frictional contact between deformable solids

Poulios¹,

Renard²

2015

Computers & Structures

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A new integral approximation of frictional contact problems under large deformations is presented. Impenetrability, friction and the relevant complementarity conditions are expressed through a non-smooth equation, considered in the continuous setting. A weak formulation of this non-smooth complementarity equation is discretized through a standard Galerkin procedure, is linearized consistently and incorporated in a generalized Newton solution process. The resulting integral handling of contact and friction complementarity conditions, previously implemented for small deformations only, is extended in the present paper to large deformations. In total, the proposed method is relatively simple to implement, while its robustness is illustrated through numerical examples.

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confidence: 59%

“…An indenter with a circular arc shaped bottom edge is pressed against a rectangular block and is forced to slide along the block length. This example can also be found, for instance, in [10] and [13]. Fig.…”

Section: Shallow Ironingmentioning

confidence: 95%

An unconstrained integral approximation of large sliding frictional contact between deformable solids

Poulios¹,

Renard²

2015

Computers & Structures

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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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“…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 2: Numerical aspects

Cited by 61 publications

References 19 publications

An unconstrained integral approximation of large sliding frictional contact between deformable solids

An unconstrained integral approximation of large sliding frictional contact between deformable solids

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

PFEM-based modeling of industrial granular flows

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