Support Size Adjustment Algorithm for Reproducing Kernel Particle Method with Semi-Lagrangian Formulation

As one of meshfree methods, reproducing kernel particle method (RKPM) is usually associated with semi-Lagrangian formulation for large deformation problem to avoid the failure of one-to-one mapping from current configuration to reference configuration. However, numerical crack may happen for large deformation problem working with semi-Lagrangian formulation, if we keep the support size of reproducing kernel shape function as constant. This paper proposed an algorithm to adjust the support size at every step and some numerical results are presented to demonstrate the improvement by the proposed algorithm. Meanwhile, this algorithm is very easy to implement for coding, which does not add much computational cost.

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Application of Reproducing Kernel Particle Method to Large Deformation Contact Analysis of Elastomers

Rubber Chemistry and Technology ◽

10.5254/1.3538479 ◽

1998 ◽

Vol 71 (2) ◽

pp. 191-213 ◽

Cited By ~ 24

Author(s):

Jiun-Shyan Chen ◽

Chunhui Pan ◽

Cheng-Tang Wu

Keyword(s):

Large Deformation ◽

Reproducing Kernel ◽

Variational Equation ◽

Galerkin Approximation ◽

Particle Method ◽

Contact Analysis ◽

Reproducing Kernel Particle Method ◽

Shape Functions ◽

Contact Conditions ◽

Reproducing Kernel Particle

Abstract A meshless formulation based on the Reproducing Kernel Particle Method (RKPM) is applied to the large deformation and contact analysis of elastomeric components. In this approach, a kernel estimate that ensures the completeness requirement of a linear field is introduced to construct the global Reproducing Kernel shape functions of the displacements. The Galerkin approximation of the variational equation is formulated using the Reproducing Kernel shape functions, and the discretization can be performed without the need of a structured mesh. In this paper, a RKPM formulation for rubber materials including frictional contact conditions is presented. The contact constraint equations and essential boundary conditions are formulated in the nodal coordinate using a direct transformation method. The global Reproducing Kernel shape functions expressed in a material description are used in the total Lagrangian formulation of hyperelasticity. By the use of the smooth Reproducing Kernel shape functions, the method is effective in dealing with large deformation and contact conditions in elastomeric applications.

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A semi-Lagrangian reproducing kernel particle method with particle-based shock algorithm for explosive welding simulation

Computational Mechanics ◽

10.1007/s00466-021-02008-2 ◽

2021 ◽

Author(s):

Jonghyuk Baek ◽

Jiun-Shyan Chen ◽

Guohua Zhou ◽

Kevin P. Arnett ◽

Michael C. Hillman ◽

...

Keyword(s):

Explosive Welding ◽

Reproducing Kernel ◽

Welding Process ◽

Volumetric Strain ◽

Particle Method ◽

Reproducing Kernel Particle Method ◽

Deformation Problem ◽

Wavy Interface ◽

Material Separation ◽

Reproducing Kernel Particle

AbstractThe explosive welding process is an extreme-deformation problem that involves shock waves, large plastic deformation, and fragmentation around the collision point, which are extremely challenging features to model for the traditional mesh-based methods. In this work, a particle-based Godunov shock algorithm under a semi-Lagrangian reproducing kernel particle method (SL-RKPM) is introduced into the volumetric strain energy to accurately embed the key shock physics in the absence of a mesh or grid, which is shown to also ensure the conservation of linear momentum. For kernel stability, a deformation-dependent anisotropic kernel support update algorithm is proposed, which is shown to capture excessive plastic flow and material separation. A quasi-conforming nodal integration is adopted to avoid the need of updating conforming cells which is tedious in extreme deformations. It is shown that the proposed formulation effectively captures shocks, jet formation, and smooth-to-wavy interface morphology transition with good agreement with experimental results.

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