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R. dell’Erba
14.5 Future Work and Conclusion
Flocking rule, used in robot swarm, can be used to describe the deformation of a
bidimensional continuum by a simple algorithm highly customizable and able to
adapt to take into account complex physical effects in a plausible way. The strain is
imposed on leader particles whose motion is assigned and the “follower” particles
move according to “position rules”. These displacements are determined, like in a bird
swarm, by the relative position of their neighbours. Therefore, the deformed configuration is calculated not by Newton’s law but only by the relative positions between
the particles of the system saving machine time for computing; edge effects are taken
into account by a frame, and fracture mechanism is described by a threshold effect.
Changes of some parameters, like lattice, interaction rules, fracture distance and
numbers of neighbours lead to different behaviours. In previous works, we showed
that the results of this tool have, in some cases, good similarity with the predictions
of standard FEM simulations, also in fracture cases. Essentially we have to compute
the action of a transformation operator between matrices and the job can be parallelized between the GPU cores of the powerful video card, saving the computational
cost needed to solve FEMs. Pseudo-energetic considerations have been introduced
to describe different deformation regimes, such as elastic and plastic, but only in a
preliminary form that still has to be cleared; the future aim is to find potential descriptive interactions depending on the relative distance between the particles, which are
able to reproduce the well-known physical behaviour. Differently from the PBD
methods used in computer graphics, we still do not ask for the knowledge of the
velocity and do not introduce any kind of forces to take into account mechanical
effects. The presented results are interesting but they still are at a preliminary stage.
We have collected some success showing plausible deformations in different conditions, but when we consider a beam under loading the need to connect constitutive
equations with the parameters of our tool emerges powerfully. Thus, the most important topic is to understand how material parameters are related with the choices
we make in our tool, to make a connection with the usual methods of continuum
mechanics. Actually, we have no criteria about how to direct our tools’ choices to
describe a particular material continuum. In the beam deformation, we have used
Young’s modulus and Poisson’s coefficient assigned but there is no relationship with
the parameters of our model. This is the reason of the discrepancy in the resulting
deformation. However, the tool has demonstrated enough flexibility to give chances
that, once connected with the constitutive parameters, we can describe many other
behaviours. Generalization in 3D would be easy but needs some optimization in the
code to keep the computation time in the order of seconds, by using a normal PC
Desktop. We are relaxing the hypothesis of Lagrangian neighbours to describe liquid
and gas; this forces us to add a calculation step. Indeed, it is necessary to compute the
neighbours, now defined as the particles inside a specified volume, at each time step.
Another interesting feature we are introducing is to add constraints on the particle’s
motion to describe structured object like pantograph. It can be described as a set of
beams with constrained point in the pivot; in the Hencky vision, it can be conceived
R. dell’Erba
14.5 Future Work and Conclusion
Flocking rule, used in robot swarm, can be used to describe the deformation of a
bidimensional continuum by a simple algorithm highly customizable and able to
adapt to take into account complex physical effects in a plausible way. The strain is
imposed on leader particles whose motion is assigned and the “follower” particles
move according to “position rules”. These displacements are determined, like in a bird
swarm, by the relative position of their neighbours. Therefore, the deformed configuration is calculated not by Newton’s law but only by the relative positions between
the particles of the system saving machine time for computing; edge effects are taken
into account by a frame, and fracture mechanism is described by a threshold effect.
Changes of some parameters, like lattice, interaction rules, fracture distance and
numbers of neighbours lead to different behaviours. In previous works, we showed
that the results of this tool have, in some cases, good similarity with the predictions
of standard FEM simulations, also in fracture cases. Essentially we have to compute
the action of a transformation operator between matrices and the job can be parallelized between the GPU cores of the powerful video card, saving the computational
cost needed to solve FEMs. Pseudo-energetic considerations have been introduced
to describe different deformation regimes, such as elastic and plastic, but only in a
preliminary form that still has to be cleared; the future aim is to find potential descriptive interactions depending on the relative distance between the particles, which are
able to reproduce the well-known physical behaviour. Differently from the PBD
methods used in computer graphics, we still do not ask for the knowledge of the
velocity and do not introduce any kind of forces to take into account mechanical
effects. The presented results are interesting but they still are at a preliminary stage.
We have collected some success showing plausible deformations in different conditions, but when we consider a beam under loading the need to connect constitutive
equations with the parameters of our tool emerges powerfully. Thus, the most important topic is to understand how material parameters are related with the choices
we make in our tool, to make a connection with the usual methods of continuum
mechanics. Actually, we have no criteria about how to direct our tools’ choices to
describe a particular material continuum. In the beam deformation, we have used
Young’s modulus and Poisson’s coefficient assigned but there is no relationship with
the parameters of our model. This is the reason of the discrepancy in the resulting
deformation. However, the tool has demonstrated enough flexibility to give chances
that, once connected with the constitutive parameters, we can describe many other
behaviours. Generalization in 3D would be easy but needs some optimization in the
code to keep the computation time in the order of seconds, by using a normal PC
Desktop. We are relaxing the hypothesis of Lagrangian neighbours to describe liquid
and gas; this forces us to add a calculation step. Indeed, it is necessary to compute the
neighbours, now defined as the particles inside a specified volume, at each time step.
Another interesting feature we are introducing is to add constraints on the particle’s
motion to describe structured object like pantograph. It can be described as a set of
beams with constrained point in the pivot; in the Hencky vision, it can be conceived