Open AccessJournal Article10.1002/NME.1689

CBS‐based stabilization in explicit solid dynamics

- 04 Jun 2006

- International Journal for Numerical Meth...

- Vol. 66, Iss: 10, pp 1547-1568

TL;DR: The characteristic-based split (CBS) stabilization procedure developed originally in fluid mechanics has been adapted successfully to solid mechanics problems and has been implemented within a finite element program using an explicit time integration scheme.

Abstract: The characteristic-based split (CBS) stabilization procedure developed originally in fluid mechanics has been adapted successfully to solid mechanics problems. The CBS algorithm has been implemented within a finite element program using an explicit time integration scheme. Volumetric locking of linear triangular and tetrahedral elements has been successfully eliminated. The performance of the numerical algorithm is illustrated with numerical results. Comparisons with an alternative stabilization technique based on the finite calculus method also are given. Copyright © 2006 John Wiley & Sons, Ltd.

AI Agents for this Paper

Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps

Most frequently asked questions

1. What are the contributions mentioned in the paper "Cbs-based stabilization in explicit solid dynamics" ?

In this paper, the authors present a characterization of the characteristic-based split ( CBS ) stabilization procedure in the case of linear triangles and tetrahedra.

Figure 8. 3D solution using the FIC formulation ( = 0.01) with tetrahedral elements: (a) deformed mesh; (b) pressure distribution; and (c) effective plastic strain distribution.

Figure 7. 3D using the CBS formulation with tetrahedral elements: (a) deformed mesh; (b) pressure distribution; and (c) effective plastic strain distribution.

Figure 5. 2D solution using the CBS algorithm ( t = 0.15 tcr) with triangular elements: (a) deformed mesh; (b) pressure distribution; and (c) effective plastic strain distribution.

Figure 6. 2D solution using the FIC formulation ( = 0.01) with triangular elements: (a) deformed mesh; (b) pressure distribution; and (c) effective plastic strain distribution.

Figure 11. Sidepressing of a cylinder: (a) initial tetrahedral mesh; and (b) initial hexahedral mesh.

Figure 14. Sidepressing of a cylinder, CBS algorithm, tetrahedra, coarse mesh (4090 elements): (a) effective plastic strain; and (b) pressure distribution.

Citations

Proceedings Article•10.1145/1275808.1276394

Volume conserving finite element simulations of deformable models

Geoffrey Irving, +2 more

- 29 Jul 2007

TL;DR: This work proposes a numerical method for modeling highly deformable nonlinear incompressible solids that conserves the volume locally near each node in a finite element mesh that enforces incompressibility per node (in a one-ring), and demonstrates that it is free from locking.

...read moreread less

126

Journal Article•10.1002/NME.5138

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach

Guglielmo Scovazzi, +3 more

- 08 Jun 2016

- International Journal for Numerical Meth...

113

•Journal Article•10.1016/J.CMA.2016.07.015

Implicit finite incompressible elastodynamics with linear finite elements: A stabilized method in rate form

Simone Rossi, +2 more

- 01 Nov 2016

- Computer Methods in Applied Mechanics an...

TL;DR: In this article, a generalized framework for stabilization and implicit time integration of nearly and fully incompressible nonlinear elastodynamics models is proposed, which can comprehensively be applied to the class of all isotropic hyperelastic models.

...read moreread less

Journal Article•10.1016/J.ENGANABOUND.2015.04.019

An edge-based/node-based selective smoothed finite element method using tetrahedrons for cardiovascular tissues

Chen Jiang, +5 more

- 01 Oct 2015

- Engineering Analysis With Boundary Eleme...

TL;DR: Three-dimensional selective smoothed finite element method with edge-based and node-based strain smoothing techniques for nonlinear anisotropic large deformation analyses of nearly incompressible cardiovascular tissues and outperforms the standard FEM and other S-FEMs.

...read moreread less

•Journal Article•10.1007/S11831-018-09313-9

Numerical Methods for the Modelling of Chip Formation

J. M. Rodríguez, +2 more

- 01 Apr 2020

- Archives of Computational Methods in Eng...

TL;DR: A review on the numerical modeling methods and techniques used for the simulation of machining processes covering mesh-less methods, particle-based methods and different possibilities of Eulerian and Lagrangian approaches is presented.

...read moreread less

...

Expand

References

Journal Article•10.1016/0045-7825(82)90071-8

Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations

A. N. Brooks, +1 more

- 01 Sep 1990

- Computer Methods in Applied Mechanics an...

TL;DR: In this article, a new finite element formulation for convection dominated flows is developed, based on the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes.

...read moreread less

5.6K

Journal Article•10.1006/JCPH.1997.5716

A Numerical Method for Solving Incompressible Viscous Flow Problems

Alexandre J. Chorin

- 01 Aug 1997

- Journal of Computational Physics

TL;DR: In this article, a numerical method for solving incompressible viscous flow problems is introduced, which uses the velocities and the pressure as variables and is equally applicable to problems in two and three space dimensions.

...read moreread less

2.9K

•Journal Article•10.1051/M2AN/197408R201291

On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers

Franco Brezzi

- 01 Jan 1974

TL;DR: In this paper, the authors describe a fitting for hose end fittings that is suitable for use in conjunction with a cross-linked polyethylene hose or pipe, where a body incorporating a nipple adapted for insertion in a pipe end and a clamping ring normally retained on the body and adapted for clamping action about the outer surface of said pipe end is described.

...read moreread less

2.7K

Journal Article•10.1007/BF01436561

The finite element method with Lagrangian multipliers

Ivo Babuška

- 01 Jun 1973

- Numerische Mathematik

TL;DR: In this article, the Dirichlet problem for second order differential equations is chosen as a model problem to show how the finite element method may be implemented to avoid difficulty in fulfilling essential (stable) boundary conditions.

...read moreread less

1.7K

Journal Article•10.1016/0045-7825(89)90111-4

A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations

Thomas J. R. Hughes, +2 more

- 01 May 1989

- Computer Methods in Applied Mechanics an...

TL;DR: Galerkin/least-squares finite element methods for advective-diffusive equations are presented in this paper, and a convergence analysis and error estimates are presented.

...read moreread less

1.5K

...

Expand

CBS‐based stabilization in explicit solid dynamics

Chat with Paper

AI Agents for this Paper

Most frequently asked questions

1. What are the contributions mentioned in the paper "Cbs-based stabilization in explicit solid dynamics" ?

Figures

Citations

Volume conserving finite element simulations of deformable models

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach

Implicit finite incompressible elastodynamics with linear finite elements: A stabilized method in rate form

An edge-based/node-based selective smoothed finite element method using tetrahedrons for cardiovascular tissues

Numerical Methods for the Modelling of Chip Formation

References

Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations

A Numerical Method for Solving Incompressible Viscous Flow Problems

On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers

The finite element method with Lagrangian multipliers

A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations

Related Papers (5)

A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications

F‐bar‐based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking

Mixed linear/linear simplicial elements for incompressible elasticity and plasticity

Triangular composite finite elements

An assessment of the average nodal volume formulation for the analysis of nearly incompressible solids under finite strains