Chapter 18
A Plausible Description of Continuum
Material Behavior Derived by Swarm
Robot Flocking Rules
Ramiro dell’Erba
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.
Keywords Continuum mechanics · Swarm robotics · Flocking rules
R. dell’Erba (B)
ENEA Technical Unit Technologies for Energy and Industry—Robotics Laboratory, Rome, Italy
e-mail: ramiro.dellerba@enea.it
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_18
329
A Plausible Description of Continuum
Material Behavior Derived by Swarm
Robot Flocking Rules
Ramiro dell’Erba
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.
Keywords Continuum mechanics · Swarm robotics · Flocking rules
R. dell’Erba (B)
ENEA Technical Unit Technologies for Energy and Industry—Robotics Laboratory, Rome, Italy
e-mail: ramiro.dellerba@enea.it
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_18
329