Smoothed particle hydrodynamics in a generalized coordinate system with a finite‐deformation constitutive model

Abstract

SUMMARYThis study proposes smoothed particle hydrodynamics (SPH) in a generalized coordinate system. The present approach allocates particles inhomogeneously in the Cartesian coordinate system and arranges them via mapping in a generalized coordinate system in which the particles are aligned at a uniform spacing. This characteristic enables us to employ fine division only in the direction required, for example, in the through‐thickness direction for a thin‐plate problem and thus to reduce computation cost. This study provides the formulation of SPH in a generalized coordinate system with a finite‐deformation constitutive model and then verifies it by analyzing quasi‐static and dynamic problems of solids. High‐velocity impact test was also performed with an aluminum target and a steel sphere, and the predicted crater shape agreed well with the experiment. Furthermore, the numerical study demonstrated that the present approach successfully reduced the computation cost with marginal degradation of accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

Generalized smoothed particle hydrodynamics with overset methods in total Lagrangian formulations

“…Nevertheless, the transformation above are purely derived from the definitions of covariant and contravariant basis instead of relying on only the Chain-rule transformation, which focuses merely on components and ignores the existence of basis, and thus, the present formulation revisits and provides a rigorous derivation in terms of vector and tensor analyses. Such a tensor-analysis-based coordinate transformation has been adopted as the generalized coordinate SPH for solid dynamics in Yashiro and Okabe [28] without curved coordinates.…”

“…This study provides a straightforward extension of the tensor-analysis-based generalized SPH by Yashiro and Okabe [28] to the curved coordinates in solid dynamics. Furthermore, the proposed tensor-analysis-based generalized SPH is augmented by an overset methodology to introduce a local coordinate and deal with singularities.…”

“…Yashiro and Okabe [28] proposed SPH in generalized coordinate systems, i.e., generalized SPH (GSPH). In the GSPH, particles are nonuniformly, typically in the boundary-conforming way, distributed in the physical space, wherein the governing equation is formulated in the generalized space so that the particles are uniformly distributed in the generalized space and solvable using a standard SPH with coordinate transformation matrix.…”

“…This study aims at extending the original GSPH to more complex geometries including curved boundaries, wherein the tensor-analysis-based coordinate transformation [28] are reformulated based on the TLSPH in the solid mechanics. Furthermore, to overcome a drawback in the coordinate singularity as above and provide a more flexible refinement configuration, we propose the GSPH augmented by an overset method.…”

Application of particle simulation methods to composite materials: a review

“…Yashiro and Okabe [82] proposed the other approach to reduce calculation cost by solving SPH equations in a generalized coordinate system. This method achieved non-uniform initial particle arrangement; more specifically, particles were first allocated with a fine spacing in a direction required, and the particles were rearranged in a generalized coordinate system with a constant spacing in three directions.…”