Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

A new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centred at the particles in three dimensions, lines centred at the particles in two dimensions. The model is applied to several 2D problems and compared to experimental data. Copyright © 2004 John Wiley & Sons, Ltd.

Cracking particles: A simplified meshfree method for arbitrary evolving cracks

https://orbilu.uni.lu/bitstream/10993/13726/1/phu-meshless.pdf

Review: Meshless methods: A review and computer implementation aspects

A three dimensional large deformation meshfree method for arbitrary evolving cracks

Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics ~SPH! is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been an active research area in recent years, are reviewed. Third, some applications of molecular dynamics ~MD! in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics. This review article includes 397 references. @DOI: 10.1115/1.1431547#

Meshfree and particle methods and their applications

A uni ed stability analysis of meshless methods with Eulerian and Lagrangian kernels is presented. Three types of instabilities were identi ed in one dimension: an instability due to rank de ciency, a tensile instability and a material instability which is also found in continua. The stability of particle methods with Eulerian and Lagrangian kernels is markedly di erent: Lagrangian kernels do not exhibit the tensile instability. In both kernels, the instability due to rank de ciency can be suppressed by stress points. In two dimensions the stabilizing e ect of stress points is dependent on their locations. It was found that the best approach to stable particle discretizations is to use Lagrangian kernels with stress points. The stability of the least-squares stabilization was also studied. Copyright ? 2000 John Wiley & Sons, Ltd.

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A unified stability analysis of meshless particle methods

A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis

A Coupled Meshfree/Finite Element Method for Automotive Crashworthiness Simulations

Composite triangles consisting of four three-node triangles originally proposed by Camacho and Ortiz are studied. It is shown that the original element does not satisfy the Babuska–Brezzi condition nor pass the patch test. Remedies for these shortcomings are described. It is shown that the resulting elements are very robust for large deformation problems. In addition, composite triangular elements generated from four-node quadrilaterals are briefly examined; their accuracy is found to be not as good as the composite triangles.

Triangular composite finite elements

A novel meshfree approach for the elastic analysis of composite solids is proposed. This approach introduces a new meshfree discretization technique that can be applied to the composite solids with overlapping sub-domains. Since each sub-domain is discretized individually by the finite element model, substantial user interaction for generating the conforming mesh is avoided. A meshfree convex approximation is employed taking advantage of the naturally conforming property to approximate the overlapping sub-domains and to enforce the global Dirichlet boundary condition. In addition, a Kronecker-delta property is imposed on the approximation of interfacial nodes leading to a point-wise continuity in displacements across the interface. As a result, a non-conforming meshfree Galerkin method for the elasticity interface problem is devised and is shown to satisfy an optimal error estimate in the energy norm. This method is applicable to both macro and microscopic analyses of composite solids such as particle and fiber-reinforced composites. Three numerical benchmarks in two-dimensional case are provided to demonstrate effectiveness and accuracy of the proposed method.

Yong Guo

Papers

A unified stability analysis of meshless particle methods

A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis

A Coupled Meshfree/Finite Element Method for Automotive Crashworthiness Simulations

Triangular composite finite elements

Numerical modeling of composite solids using an immersed meshfree Galerkin method