Heuristic acceleration correction algorithm for use in SPH computations in impact mechanics

Shaw, Amit; Reid, S.R.

doi:10.1016/j.cma.2009.09.006

Cited by 44 publications

(18 citation statements)

References 26 publications

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“…It is relevant to mention the recent work by Shaw and Reid (2009) and Shaw et al (2011) on the effect of artificial viscosity in numerical computations. Therein a correction algorithm, coined the ''acceleration correction algorithm,'' was proposed through which the strength of the artificial viscosity may be optimized in space as well as time.…”

Section: Governing Equations and Discretizationmentioning

confidence: 98%

Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws

Zhou

2014

Rock Mech Rock Eng

306

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A novel meshless numerical method, called general particle dynamics (GPD), is proposed to simulate samples of rock-like brittle heterogeneous material containing four preexisting flaws under uniaxial compressive loads. Numerical simulations are conducted to investigate the initiation, growth, and coalescence of cracks using a GPD code. An elasto-brittle damage model based on an extension of the Hoek-Brown strength criterion is applied to reflect crack initiation, growth, and coalescence and the macrofailure of the rock-like material. The preexisting flaws are simulated by empty particles. The particle is killed when its stresses satisfy the Hoek-Brown strength criterion, and the growth path of cracks is captured through the sequence of such damaged particles. A statistical approach is applied to model the heterogeneity of the rocklike material. It is found from the numerical results that samples containing four preexisting flaws may produce five types of cracks at or near the tips of preexisting flaws including wing, coplanar or quasi-coplanar secondary, oblique secondary, out-of-plane tensile, and out-of-plane shear cracks. Four coalescence modes are observed from the numerical results: tensile (T), compression (C), shear (S), and mixed tension/shear (TS). A higher load is required to induce crack coalescence in the shear mode (S) than the tensile (T) or mixed (TS) mode. It is concluded from the numerical results that crack coalescence occurs following the weakest coalescence path among all possible paths between any two flaws. The numerical results are in good agreement with reported experimental observations.

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Section: Governing Equations and Discretizationmentioning

confidence: 98%

Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws

Zhou

2014

Rock Mech Rock Eng

306

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“…The artificial viscosity in the conventional SPH method was modified by Shaw and co-workers [37][38][39][40] to remove spurious high frequency oscillations in solutions. In this variant of SPH, the effect of the artificial viscosity term on the change in acceleration (with and without artificial viscosity) of the SPH particles was evaluated.…”

Section: Different Variants Of the Sph Methodsmentioning

confidence: 99%

Evaluation of Accuracy and Stability of the Classical SPH Method Under Uniaxial Compression

Das

Cleary

2014

J Sci Comput

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The accuracy and stability of the classical formulation of the smoothed particle hydrodynamics (SPH) method for modelling compression of elastic solids is studied to assess its suitability for predicting solid deformation. SPH has natural advantages for simulating problems involving compression of deformable solids arising from its ability to handle large deformation without re-meshing, complex free surface behaviour and tracking of multiple material interfaces. The 'classical SPH method', as originally proposed by Monaghan (in Ann Rev Astron 30: 543-574, 1992, Rep Prog Phys 68:1703-1759, 2005, has become broadly established as a robust method in different areas, especially involving fluid flows. However, limited attention has been paid to understanding of its numerical performance for elastic deformation problems. To address this, we evaluate the classical SPH method to explore its stability, accuracy and convergence and the effect of numerical parameters on elastic solutions using a generic uniaxial stress test. Short term transient and long term uniform state SPH solutions agree well with those from the finite element method (FEM). The SPH elastic deformation solution showed good convergence with increasing particle resolution. The tensile instability stabilisation method was found to have little impact on the solution, except for higher values of the correction factor which then produce small amplitude benign artificial banded stress patterns. The use of artificial viscosity is able to eliminate the instability and improve the accuracy of the solutions. Overall, the classical SPH method appears to be robust and suitable for accurate modelling of elastic solids under compression.

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“…However, when considering solids with complex equations of state an exact iterative solution is prohibitively expensive and an approximate non-iterative Riemann solver may be used instead, such as the two-shock solver of Dukowicz (1985) [3]. In the GSPH equations of Inutsuka (15), the P * ij and v * ij are replaced directly by the Riemann solutions in the star-region. This type of solution procedure corresponds to a spatially first-order Godunov method.…”

Section: Godunov Sph Reformulationmentioning

confidence: 99%

“…When using the artificial viscosity, without special treatments, care must be taken not to introduce excessive smoothing into smooth regions away from the shock. This may be achieved by a time-consuming trialand-error analysis [15] which may be very undesirable for the user. The special treatments mentioned rely on using higher-order terms [14,2] to detect shock-indicative flow convergence before it occurs or an estimation of the vorticity to minimize damping in regions of pure shear [1] so locally varying damping can be applied more optimally.…”

Section: Introductionmentioning

confidence: 99%

Godunov SPH with an operator-splitting procedure for materials with strength

Connolly¹,

Iannucci²

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. This paper presents a modification of the Godunov Smoothed Particle Hydrodynamics (GSPH) method of Parshikov et al. for isotropic materials with strength. The motivation behind this modification is that it facilitates a higher-order reconstruction of the left and right hand Riemann states, thus increasing the accuracy of the method. A consequence of this modification is that different smoothing kernel functions may be used within each timestep, which may be exploited to help alleviate the intrinsic instabilities of the SPH method. The paper begins with a description of the SPH method then reviews the different Godunov SPH formulations available. The modified GSPH procedure is then detailed and results are presented for one and two-dimensional test cases and compared with predictions made with the standard Artificial Viscosity SPH (AVSPH) formulation.

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Heuristic acceleration correction algorithm for use in SPH computations in impact mechanics

Cited by 44 publications

References 26 publications

Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws

Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws

Evaluation of Accuracy and Stability of the Classical SPH Method Under Uniaxial Compression

Godunov SPH with an operator-splitting procedure for materials with strength

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