Abstract
Peridynamic equation of motion is usually solved numerically by using meshless approaches. Family search process is one of the most time-consuming parts of a peridynamic analysis. Especially for problems which require continuous update of family members inside the horizon of a material point, the time spent to search for family members becomes crucial. Hence, efficient algorithms are required to reduce the computational time. In this study, various family member search algorithms suitable for peridynamic simulations are presented including brute-force search, region partitioning, and tree data structures. By considering problem cases for different number of material points, computational time between different algorithms is compared and the most efficient algorithm is determined.
Highlights
The peridynamic (PD) theory was first introduced by Silling in the year of 2000 [1]
It is basically the re-formulation of classical continuum mechanics (CCM) equations using integro-differential equations, in which derivatives only come into picture with time derivatives of displacements
In CCM, the traction vectors are expressed in the form of stress tensor, σ ij and its equation of motion can be expressed as ρ(x)u (x, t) = σ ij,j + b(x, t) with i & j = 1, 2, 3 (1)
Summary
The peridynamic (PD) theory was first introduced by Silling in the year of 2000 [1]. It is basically the re-formulation of classical continuum mechanics (CCM) equations using integro-differential equations, in which derivatives only come into picture with time derivatives of displacements. Commonly used mesh-free methods in peridynamics experience serious issues with accuracy and convergence due to rough approximation of the contribution of family nodes close to the horizon boundary [12] This means that when creating efficient and accurate PD codes, one needs to take into account family search or surface corrections, and accurate computation of volumes near the boundary of the horizon. As explained in Le and Bobaru [13], there are several surface effect correction methods such as volume method, force density method, energy method, force normalization method, and fictitious nodes method Most of these methods do not influence the family search process as they do not add any additional spatial data into the peridynamic model and mainly modify either the bond stiffness or the force state for bonds near the boundaries of the surface. The main aim of this study is to compare various family member search algorithms available in the literature and propose the most convenient form for peridynamic analysis depending on the type of the problem
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