Position-based dynamic of a particle system: a configurable algorithm to describe complex behaviour of continuum material starting from swarm robotics

Abstract

In a previous work we considered a two-dimensional lattice of particles and calculated its time evolution by using an interaction law based on the spatial position of the particles themselves. The model reproduced the behaviour of deformable bodies both according to the standard Cauchy model and second gradient theory; this success led us to use this method in more complex cases. This work is intended as the natural evolution of the previous one in which we shall consider both energy aspects, coherence with the principle of Saint Venant and we start to manage a more general tool that can be adapted to different physical phenomena, supporting complex effects like lateral contraction, anisotropy or elastoplasticity.

Rules governing swarm robot in continuum mechanics

“…This means that the displacements, at each time step, involve a larger and larger shell of points until they affect all points in the lattice. In second gradient [31], we also considered the neighbours of the first neighbours.…”

“…In this section, we briefly take up some results obtained using this tool in the previous work [29,31,[56][57][58][59], where many different strains of the leaders were considered, with different choices, including the behaviour of some ASTM samples and compliance with the Saint-Venant principle. In this paper, we want to focus our attention on some simple simulation to outline what we need to improve and what we need to understand better.…”

“…The system we propose [29,30] shows very different behaviours by changing its internal parameters. A complete description of the algorithm can be found in dell'Erba [29,31], now we just resume some basic concepts. The continuous two-dimensional body is discretized into a finite number of particles that occupy, in their initial configuration, the nodes of a lattice chosen from the five flat Bravais lattices or, sometimes, even the honeycomb lattice useful in some isotropic condition; the lattice is the first choice we have to make.…”

“…Actually, is only a graphic utility for a better understanding of the deformation. Extended use of them can be found in dell'Erba [31]. Anyway, the idea comes out form the consideration that the centroid of a set of points (equation ( 1)) is a point that minimizes the sum of squared distances between them.…”

Bio-Inspired Design of a Porous Resorbable Scaffold for Bone Reconstruction: A Preliminary Study

“…Alternatively, one can implement an ad hoc numerical formulation that guarantees an inherent high continuity for the unknown fields, namely the isogeometric analysis (see, e.g., [ 84 , 85 , 86 , 87 , 88 , 89 , 90 ]). A novel numerical algorithm has recently been developed based on a particle system that has shown a beneficial capability to model second gradient materials and multi-crack evolution [ 91 , 92 ].…”