Adaptive multigrid for finite element computations in plasticity

Ekevid, Torbjörn; Kettil, Per; Wiberg, Nils‐Erik

doi:10.1016/j.compstruc.2004.04.013

Cited by 6 publications

(6 citation statements)

References 12 publications

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“…The discrete non-linear system of Equations (15), (16) and (17) is rewritten using only one kinematic unknown (either U,U orÜ). In the proposed multigrid strategy, we choose the displacement U to update the system of equations.…”

Section: Non-linear Iterative Solver For the Relaxation Stepsmentioning

confidence: 99%

Multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems

Biotteau¹,

Gravouil²,

Lubrecht³

et al. 2010

Numerical Meth Engineering

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International audienceThis paper presents an adaptive refinement strategy based on a hierarchical element subdivision dedicated to modeling elastoplastic materials in transient dynamics. At each time step, the refinement is automatic and starts with the calculation of the solution on a coarse mesh. Then, an error indicator is used to control the accuracy of the solution and a finer localized mesh is created where the user prescribed accuracy is not reached. A new calculation is performed on this new mesh using the non linear ``Full Approximation Scheme'' (FAS) multigrid strategy. Applying the error indicator and the refinement strategy recursively, the optimal mesh is obtained. This mesh verifies the error indicator on the whole structure. The multigrid strategy is used for two purposes. First, it optimizes the computational cost of the solution on the finest localized mesh. Second, it ensures information transfer amongst the different hierarchical meshes. A standard time integration scheme is used and the mesh is reassessed at each time step

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Section: Non-linear Iterative Solver For the Relaxation Stepsmentioning

confidence: 99%

Multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems

Biotteau¹,

Gravouil²,

Lubrecht³

et al. 2010

Numerical Meth Engineering

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“…This fact is explained mostly by the following: (i) the code is still sequential (ii) the code utilizes a linear solver which is not numerically scalable (Farhat et al, 2000). To remove these disadvantages, we plan to extend our code in the following mainstream directions of linear solver technology: (i) Direct parallel multifrontal solvers (Gupta et al, 1997;Amestoy et al, 2000) (ii) Multigrid methods with adaptation for plasticity (Adams, 2000;Ekevid et al, 2004) (iii) Dual-primal domain decomposition methods (Farhat et al, 2000) At the same time, we are planning to parallelize the entire finite element routines using the MPI package.…”

Section: What Is Next?mentioning

confidence: 99%

SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology

Popov

Sobolev

2008

Physics of the Earth and Planetary Interiors

187

159

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We describe a new technique for three-dimensional lithospheric-scale modeling of solid state deformation including strain localization processes. The new code, SLIM3D, includes a coupled thermo-mechanical treatment of deformation processes and allows for an elasto-visco-plastic rheology with diffusion, dislocation and Peierls creep mechanisms and Mohr-Coulomb plasticity. The code incorporates an Arbitrary Lagrangian Eulerian formulation with free surface and Winkler boundary conditions. SLIM3D is developed and implemented using the C++ objectoriented programming language. We describe aspects of physical models as well as details of the numerical implementation, including the Newton-Raphson solver, the stress update procedure, and the tangent operator. The applicability of the code to lithospheric-scale modeling is demonstrated by a number of benchmark problems that include: (i) the bending of an elastic plate, (ii) the sinking of a rigid cylinder into a viscous fluid, (iii) the initiation of shear bands in the brittle crust, (iv) triaxial compression test, and (v) lithospheric transpressional deformation. Finally, we discuss possible directions of further development.

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“…(13), which verifies the system of Eqs. (7)(8)(9), the initial conditions (5) and the constitutive law (12).…”

Section: Reference Problemmentioning

confidence: 90%

“…Indeed, for a quasi-static loading, the geometrical shape induces plastic deformations in the vicinity of the circular holes in the plate. The error in energy is then concentrated in this region and the grid refinement occurs around the holes (see [13] for numerical examples). Figure 13 represents the isovalues of the Von-Mises stress field calculated using the meshes of Fig.…”

Section: Behavior Of the Mesh Refinementmentioning

confidence: 99%

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Three dimensional automatic refinement method for transient small strain elastoplastic finite element computations

et al. 2011

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Adaptive multigrid for finite element computations in plasticity

Cited by 6 publications

References 12 publications

Multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems

Multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems

SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology

Three dimensional automatic refinement method for transient small strain elastoplastic finite element computations

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