On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics

Abstract

Smoothed particle hydrodynamics (SPH), as one of the earliest meshfree methods, has broad prospects in modeling a wide range of problems in engineering and science, including extremely large deformation problems such as explosion and high velocity impact. This paper aims to provide a comprehensive overview on the recent advances of SPH method in the fields of fluid, solid, and biomechanics. First, the theory of SPH is described, and improved algorithms of SPH with high accuracy are summarized, such as the finite particle method (FPM). Techniques used in SPH method for simulating fluid, solid and biomechanics problems are discussed. The δ -SPH method and Godunov SPH (GSPH) based on the Riemann model are described for handling instability issues in fluid dynamics. Next, the interface contact algorithm for fluid-structure interaction is also discussed. The common algorithms for improving the tensile instability and the framework of total Lagrangian SPH are examined for challenging tasks in solid mechanics. In terms of biomechanics, the governing equations and the coupling forces based on SPH method are exemplified. Then, various typical engineering applications and recent advances are elaborated. The application of fluid mainly depicts the interaction between fluid and rigid body as well as elastomer, while some complicated fluid-structure interaction ocean engineering problems are also presented. In the aspect of solid dynamics, galaxy, geotechnical mechanics, explosion and impact, and additive manufacturing are summarized. Furthermore, the recent advancements of SPH method in biomechanics, such as hemodynamically and gut health, are discussed in general. In addition, to overcome the limitations of computational efficiency and computational scale, the multiscale adaptive resolution, the parallel algorithm and the automated mesh generation are addressed. The development of SPH software in China and abroad is also summarized. Finally, the challenging task of SPH method in the future is summarized. In future research work, the establishment of multi-scale coupled SPH model and deep learning technology in solid and biodynamics will be the focus of expanding the engineering applications of SPH methods.

Damage evolution law and failure mechanism of rock impacted by high-pressure water jet under in-situ stress condition

“…The particle obeys the conservation theorem of mass, momentum, and energy, and is solved in combination with the constitutive equation of material, so as to obtain the motion law of matter. It has been widely used to solve extreme deformation and failure types such as explosion simulation, 36 , 37 high-speed collision, 38 , 39 penetration calculation, 23 , 39 , 40 and brittle fracture. 24 , 41 …”

“…The particle obeys the conservation theorem of mass, momentum, and energy, and is solved in combination with the constitutive equation of material, so as to obtain the motion law of matter. It has been widely used to solve extreme deformation and failure types such as explosion simulation, 36,37 high-speed collision, 38,39 penetration calculation, 23,39,40 and brittle fracture. 24,41 Unlike the finite element method, a kernel approximation is used in SPH based on randomly distributed interpolation points, and the points are neighbors to calculate spatial derivatives.…”

Numerical simulation and experimental study on seafloor sampling of an anchor-type mud collector based on SPH-FEM coupling method

“…SPH is a lattice-free particle method based on Lagrangian descriptions, originally developed for fluid mechanics problems. 27,28 The basic idea of the method is to describe a continuous fluid (or solid) using interacting mass points, each carrying different physical quantities (mass, velocity, etc. ), by solving the kinetic equations for the set of mass points and tracking the trajectory of each mass point, which leads to the construction of the SPH equations.…”

Contact framework for total Lagrangian smoothed particle hydrodynamics using an adaptive hybrid kernel scheme

“…Other reviews on the development and application of SPH for fluid, solid, biomechanics, and fluid-structure interaction can be found in literature. [12][13][14][15] Classical SPH using the updated Lagrangian formulation, in which the Eulerian kernel is used, provides a promising alternative to solve the difficulty of the mesh-based method, especially problems that involve large deformations, deformable boundaries, and moving interfaces. 16,17 Other problems, including plastic behaviour and ductile fracture, can be solved using the classical SPH method.…”

“…Recent applications of SPH, particularly in explosive‐metal systems, demonstrate the natural fit of the method to such problems, and further advancements are expected to enhance the results significantly. Other reviews on the development and application of SPH for fluid, solid, biomechanics, and fluid‐structure interaction can be found in literature 12–15 …”