In this chapter, we are considering a material continuum, discretized as two-dimensional lattice of particles, undergone a prefixed strain of some its parts, and we calculate its time evolution without using Newton’s laws but using position-based dynamics rules. This means that the new position of a particle is determined by the spatial position of its neighbors without defining forces. The aim of the model is to reproduce the behavior of deformable bodies with standard or generalized (Cauchy or second gradient) deformation energy density. The tool that we have realized gives a plausible simulation of continuum deformation also in fracture case. It can be useful to describe final and sometime intermediate configuration of a continuum material under assigned strain of some of its points; the advantages are in saving computational time, with respect to solving classical differential equation. It is very flexible to be adapted for complex geometry samples. The numerical results suggest that the system can effectively reproduce the behavior of first and second gradient continua. We checked coherence with the principle of Saint Venant, and it is able to manage complex effects like lateral contraction, anisotropy or elastoplasticity. Its origin lies in our experience in evolution and control of robotic swarm; for a swarm robotics, just as for an animal swarm in Nature, one of the aims is to reach and maintain a desired geometric configuration. One of the possibilities to achieve this result is to see what its neighbors are doing. This approach generates a rules system governing the movement of the single robot just by reference to neighbor’s motion that we have used to describe the continuum deformation. Many aspects have to be still investigated, like the relationships describing the interaction rules between particles and constitutive equations and some results, like beam under shear stress, do not sound very good.

A Plausible Description of Continuum Material Behavior Derived by Swarm Robot Flocking Rules

dell'Erba R.
2021

Abstract

In this chapter, we are considering a material continuum, discretized as two-dimensional lattice of particles, undergone a prefixed strain of some its parts, and we calculate its time evolution without using Newton’s laws but using position-based dynamics rules. This means that the new position of a particle is determined by the spatial position of its neighbors without defining forces. The aim of the model is to reproduce the behavior of deformable bodies with standard or generalized (Cauchy or second gradient) deformation energy density. The tool that we have realized gives a plausible simulation of continuum deformation also in fracture case. It can be useful to describe final and sometime intermediate configuration of a continuum material under assigned strain of some of its points; the advantages are in saving computational time, with respect to solving classical differential equation. It is very flexible to be adapted for complex geometry samples. The numerical results suggest that the system can effectively reproduce the behavior of first and second gradient continua. We checked coherence with the principle of Saint Venant, and it is able to manage complex effects like lateral contraction, anisotropy or elastoplasticity. Its origin lies in our experience in evolution and control of robotic swarm; for a swarm robotics, just as for an animal swarm in Nature, one of the aims is to reach and maintain a desired geometric configuration. One of the possibilities to achieve this result is to see what its neighbors are doing. This approach generates a rules system governing the movement of the single robot just by reference to neighbor’s motion that we have used to describe the continuum deformation. Many aspects have to be still investigated, like the relationships describing the interaction rules between particles and constitutive equations and some results, like beam under shear stress, do not sound very good.
978-3-030-53754-8
978-3-030-53755-5
Continuum mechanics
Flocking rules
Swarm robotics
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12079/56009
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