Semi-Lagrangian reproducing kernel particle method for fragment-impact problems

Guan, Pai-Chen; Chi, Sheng‐Wei; Chen, J. S.; Slawson, Thomas R.; Roth, Michael

doi:10.1016/j.ijimpeng.2011.08.001

Cited by 109 publications

(83 citation statements)

References 22 publications

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“…The tractions in Equation (35) are determined through Equations (27) and (31)- (34). The solution of Equation (35) is difficult to obtain because of the restriction in Equation (37).…”

Section: A Friction-like Plasticity Modelmentioning

confidence: 99%

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A level set enhanced natural kernel contact algorithm for impact and penetration modeling

Wei

Lee

Chen

et al. 2014

Numerical Meth Engineering

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SUMMARYA natural kernel contact (NKC) algorithm under the framework of the semi-Lagrangian reproducing kernel particle method (semi-Lagrangian RKPM) is proposed to model multi-body contact with specific consideration for impact and penetration modeling. The NKC algorithm utilizes the interaction of the semiLagrangian kernel functions associated with contacting bodies to serve as the non-penetration condition. The effects of friction are represented by introducing a layer of the friction-like elasto-plasticity material between contacting bodies. This approach allows the frictional contact conditions and the associated kinematics to be naturally embedded in the semi-Lagrangian RKPM inter-particle force calculation. The equivalence in the Karush-Kuhn-Tucker conditions between the proposed NKC algorithm and the conventional contact kinematic constraints as well as the associated state variable relationships are identified. A level set method is further introduced in the NKC algorithm to represent the contact surfaces without pre-defined potential contact surfaces. The stability analysis performed in this work shows that temporal stability in the semiLagrangian RKPM with NKC algorithms is related to the velocity gradient between contacting bodies. The proposed methods have been verified by several benchmark problems and applied to the simulation of impact and penetration processes.

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“…The tractions in Equation (35) are determined through Equations (27) and (31)- (34). The solution of Equation (35) is difficult to obtain because of the restriction in Equation (37).…”

Section: A Friction-like Plasticity Modelmentioning

confidence: 99%

“…Therefore, in the present work, we adopt the stabilized non-conforming nodal integration (SNNI) [27,37] as a simplification of the SCNI scheme. Figure 2(b) shows a typical scheme for SNNI where the smoothing zone¨L associated with node L is non-conforming.…”

mentioning

confidence: 99%

A level set enhanced natural kernel contact algorithm for impact and penetration modeling

Wei

Lee

Chen

et al. 2014

Numerical Meth Engineering

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“…The RK approximation with linear basis is introduced with several integration methods considered: DNI, Gauss integration (GI) with increasing order m (denoted herein as m × m G I ), the first order variationally consistent method SCNI [9], and stabilized non-conforming nodal integration (SNNI) [8,14], shown in Fig. 1.…”

Section: Reproducing Kernel (Rk) Approximationmentioning

confidence: 99%

“…More recently, similar assumed strain constructions have been proposed for second order variationally consistency in [13]. Simplifications of SCNI for extremely large deformation problems have been proposed such as stabilized nonconforming nodal integration (SNNI) [8,14]. Here the smoothing zones are simply cells constructed around the nodes with the conforming condition relaxed, as shown in Fig.…”

Section: Variationally Consistent Integrationmentioning

confidence: 99%

Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems

Hillman¹,

Chen²,

Wei

2014

Comp. Part. Mech.

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Galerkin meshfree methods can suffer from instability and suboptimal convergence if the issue of quadrature is not properly addressed. The instability due to quadrature is further magnified in high strain rate events when nodal integration is used. In this paper, several stable and convergent nodal integration methods are presented and applied to transient and large deformation impact problems, and an eigenvalue analysis of the methods is also provided. Optimal convergence is attained using variationally consistent integration, and stability is achieved by employing strain smoothing and strain energy stabilization. The proposed integration methods show superior performance over standard nodal integration in the wave propagation and Taylor bar impact problems tested.

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“…So the RKPM can work well over the whole domain. It has wide application in many engineering fields, such as, rolling plane strain problem [13], bucking analysis of thin plates [14], large deformation nonlinear elastic problems [15][16][17][18], metal forming problem [19][20][21][22], elastic-plastic problems [23,24], convection-diffusion problem [25][26][27], heat conduction problems [28][29][30], and fragment-impact problem [31,32]. But up to now, to the best of our knowledge, there is still lack of literature on the application of RKPM for radiative heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Reproducing Kernel Particle Method for Radiative Heat Transfer in 1D Participating Media

Zhang

Dong

2015

Mathematical Problems in Engineering

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The reproducing kernel particle method (RKPM), which is a Lagrangian meshless method, is employed for the calculation of radiative heat transfer in participating media. In the present method, for each discrete particle (i.e., spatial node) within a local support domain, the approximate formulas of the radiative intensity and its derivatives are constructed by the reproducing kernel interpolation function, and the residual function is obtained when these parameters are substituted into the radiative transfer equation. Then the least-squares point collocation technique (LSPCT) is introduced by minimizing the summation of residual function. Five test cases are considered and quantified to verify the meshless method, including isotropic scattering medium, first-order forward scattering medium, pure absorbing medium, absorbing scattering medium, and absorbing, scattering emitting medium. The results are in good agreement with the benchmark methods, showing the reproducing kernel particle method is an efficient, accurate, and stable method for the calculation of radiative transfer in participating media.

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Semi-Lagrangian reproducing kernel particle method for fragment-impact problems

Cited by 109 publications

References 22 publications

A level set enhanced natural kernel contact algorithm for impact and penetration modeling

A level set enhanced natural kernel contact algorithm for impact and penetration modeling

Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems

Reproducing Kernel Particle Method for Radiative Heat Transfer in 1D Participating Media

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