Stability of DPD and SPH

Randles, P. W.; Petschek, A. G.; Libersky, Larry D.; Dyka, C. T.

doi:10.1007/978-3-642-56103-0_24

Cited by 7 publications

(13 citation statements)

References 22 publications

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“…The results obtained by Randles et al [24] differ from ours in that they conclude that a particle method is stable when it is linear complete. The difference in conclusions may arise from their assumption of a linear isotropic material response; we have considered a material that possesses an unstable domain.…”

Section: Resultscontrasting

confidence: 54%

“…• Stress point quadrature, in which additional quadrature points are added at the centers of the Delaunay triangulation of the particles. The idea was proposed by Dyka et al [10,11] and it has been applied and modified by Randles et al [24]. Note that Randles et al only integrate on the stress points, whereas in the method we analyze the set of quadrature points includes both the particles and the stress points.…”

Section: Particle Methodsmentioning

confidence: 98%

“…Substituting (49) and (50) into (48) using the perturbation of displacement given in (24), the dispersion equations for nodal integration with an Eulerian kernel are…”

Section: Eulerian Kernelmentioning

confidence: 99%

“…The Lagrangian kernel, however, reproduces the onset of material instability exactly in 1D. Randles et al [24] investigated the stability of dual particle dynamics and smooth particle dynamics. They found that linear completeness led to stability; their conclusions differ from ours as discussed in section 9.…”

Section: Introductionmentioning

confidence: 96%

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Material stability analysis of particle methods

Xiao

Belytschko

2005

Adv Comput Math

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Material instabilities are precursors to phenomena such as shear bands and fracture. Therefore, numerical methods that are intended for failure simulation need to reproduce the onset of material instabilities with reasonable fidelity. Here the effectiveness of particle discretizations in reproducing of the onset of material instabilities is analyzed in two dimensions. For this purpose, a simplified hyperelastic law and a Blatz-Ko material are used. It is shown that the Eulerian kernels used in smooth particle hydrodynamics severely distort the domain of material stability, so that material instabilities can occur in stress states that should be stable. In particular, for the uniaxial case, material instabilities occur at much lower stresses, which is often called the tensile instability. On the other hand, for Lagrangian kernels, the domain of material stability is reproduced very well. We also show that particle methods without stress points exhibit instabilities due to rank deficiency of the discrete equations.

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Section: Resultscontrasting

confidence: 54%

Section: Particle Methodsmentioning

confidence: 98%

“…Substituting (49) and (50) into (48) using the perturbation of displacement given in (24), the dispersion equations for nodal integration with an Eulerian kernel are…”

Section: Eulerian Kernelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 2 more Smart Citations

Material stability analysis of particle methods

Xiao

Belytschko

2005

Adv Comput Math

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“…[28][29][30]. Other stabilization techniques are currently under investigation and will be discussed in a forthcoming publication [31].…”

Section: Numerical Examplesmentioning

confidence: 99%

Continuous blending of SPH with finite elements

Fernández‐Méndez

Bonet²,

Huerta

2005

Computers & Structures

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This paper proposes a methodology for the continuous blending of the finite element method and Smooth Particle Hydrodynamics. The coupled approximation with finite elements and particles, and the discretization of the boundary value problem with a coupled integration, are described. An integration correction is also proposed to stabilize the solution. Some numerical examples demonstrate the applicability of the method.

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Dynamic failure simulation of quasi‐brittle material in dual particle dynamics

Sanchez

Randles

2012

Numerical Meth Engineering

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The feasibility of simulating dynamic fracture in quasi-brittle material using a dual particle computational method with a smeared-crack representation of material failure is explored. The computational approach utilized is dual particle dynamics, which incorporates a moving least squares interpolation of field variables between two sets of particles that discretize the spatial domain, and a Lagrangian description of the moving least squares weight function. Material failure is represented by an inelastic continuum strain contribution obtained from smearing the effect of a cohesive failure model over a discrete volume of material. A threedimensional simulation of the initiation and development of a dynamic mode I failure is performed for the case of approximate plane wave propagation. Post failure wave interaction with the resulting global failure surface replicates the behavior of a stress-free boundary condition. The computational material failure approach is applied to problems of spalling in split Hopkinson pressure bar tests. Experimental failure trends are reproduced successfully.The use of zero thickness interface elements placed along inter-element boundaries is a widely used approach for simulation of material failure [2,3]. In this failure representation, the discrete constitutive model (traction versus displacement discontinuity) is applied across the interface element to model localization and fracture. The downside of using interface elements is that the macro-crack trajectory is restricted to follow the element boundaries. Consequently, the results are always mesh dependent. A summary of interface elements is provided by Rots [4].Computational failure methods based on automatic mesh generation have also been utilized [5,6]. Like the interface element method, cracks are confined to element boundaries, but the mesh structure changes throughout the computation to accommodate the changing crack path. The discontinuity is the result of the changing mesh structure, and remeshing only needs to be performed locally near the crack tip. The drawback of this approach is the complicated implementation of the automated meshing procedure and the potentially high computational cost of remeshing many times throughout the course of the simulation.The smeared-crack representation of material failure utilizes a classical continuum description of the problem. In this method, also known as a crack band model [7], the fracture process zone is idealized as a band of finite width, as opposed to a discrete surface. The effect of localization within the band is represented by an inelastic strain contribution. Consequently, the effect of failure is "smeared" across the width of the band. The smeared-crack approach has been utilized to model failure of concrete structures [8,9]. A thorough overview of smeared-crack models is provided by Rots [4,10,11]. Implementation of smeared-crack failure representation is straightforward and can be done with minimal changes to existing codes. Limitations of the method in FEM are mesh orien...

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Stability of DPD and SPH

Cited by 7 publications

References 22 publications

Material stability analysis of particle methods

Material stability analysis of particle methods

Continuous blending of SPH with finite elements

Dynamic failure simulation of quasi‐brittle material in dual particle dynamics

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