18 A Plausible Description of Continuum …
371
18.6 Conclusion
In this work, we have discussed about a tool, presented in previous works, able
to describe strain deformation of a continuum medium taking in account complex
physical effects in a plausible way. Flocking rule, used in robot swarm, can be used
to describe deformation of bidimensional continuum medium by a simple algorithm
highly customizable and able to adapt to take in account complex physical effects in
a plausible way. The tool is based on position-based dynamics. Differently from the
PBD methods used in computer graphics, we still do not ask for the knowledge of
the velocity and do not introduce some kind of forces to take in account mechanical
effects. The strain is imposed on some particles (leaders) whose motion is assigned
and the other particles (followers) move according to some rules governing particle
position. The motion of the followers is determined, like in a bird swarm, by the
position of their neighbors. So far the deformed configuration is calculated not by
Newton’s law but only by the relative positions between the particles of the system,
the characteristics of the lattice and by rules describing the how a particle would
like to place with respect to its neighbors. Changes of some parameters like, lattice,
interaction rules, fracture distance, numbers of neighbors (i.e., to introduce first and
second gradient theory) lead to different behavior. One of the principal advantages
is in the saving machine time for computing. Computational costs are low because
we do not solve differential equations but only algebraically equation systems.
Being based on a linear operation, the computational cost of the algorithm
increases linearly with the number of the elements; on the contrary, usually, cost
usually associated with FEMs has over-exponential growth.
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 computational cost need to solve FEMs.
The tool we propose could be considered as just a graphic representation of a
plausible behavior because, actually, we imitate a known behavior adjusting the
algorithm parameters.
Anyway, the proposed algorithm is intrinsically accounting for geometrically
nonlinear deformations, which is a crucial theme in modern structural mechanics.
This is not a new kind of physics, just a graphic representation of a plausible
behavior; keep in mind that, up to now, you do not start from the constitutive equations
of the materials leading to the rules governing points displacement. Actually, we just
imitate a known behavior adjusting the algorithm parameters. Anyway the results
are also interesting even if still in a preliminary form.
The presented results are interesting, but they still are at a preliminary stage.
Edge effects are taken in account by a frame, and fracture mechanism is described
by a threshold effect. We have showed as changing some parameters like, lattice,
interaction rules, fracture distance, numbers of neighbors much different behavior
can be described.
In a preceding work, we verified the results of this tool that are in accordance with
results obtained by FEM, also in the fracture case; the results showed good similarity
371
18.6 Conclusion
In this work, we have discussed about a tool, presented in previous works, able
to describe strain deformation of a continuum medium taking in account complex
physical effects in a plausible way. Flocking rule, used in robot swarm, can be used
to describe deformation of bidimensional continuum medium by a simple algorithm
highly customizable and able to adapt to take in account complex physical effects in
a plausible way. The tool is based on position-based dynamics. Differently from the
PBD methods used in computer graphics, we still do not ask for the knowledge of
the velocity and do not introduce some kind of forces to take in account mechanical
effects. The strain is imposed on some particles (leaders) whose motion is assigned
and the other particles (followers) move according to some rules governing particle
position. The motion of the followers is determined, like in a bird swarm, by the
position of their neighbors. So far the deformed configuration is calculated not by
Newton’s law but only by the relative positions between the particles of the system,
the characteristics of the lattice and by rules describing the how a particle would
like to place with respect to its neighbors. Changes of some parameters like, lattice,
interaction rules, fracture distance, numbers of neighbors (i.e., to introduce first and
second gradient theory) lead to different behavior. One of the principal advantages
is in the saving machine time for computing. Computational costs are low because
we do not solve differential equations but only algebraically equation systems.
Being based on a linear operation, the computational cost of the algorithm
increases linearly with the number of the elements; on the contrary, usually, cost
usually associated with FEMs has over-exponential growth.
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 computational cost need to solve FEMs.
The tool we propose could be considered as just a graphic representation of a
plausible behavior because, actually, we imitate a known behavior adjusting the
algorithm parameters.
Anyway, the proposed algorithm is intrinsically accounting for geometrically
nonlinear deformations, which is a crucial theme in modern structural mechanics.
This is not a new kind of physics, just a graphic representation of a plausible
behavior; keep in mind that, up to now, you do not start from the constitutive equations
of the materials leading to the rules governing points displacement. Actually, we just
imitate a known behavior adjusting the algorithm parameters. Anyway the results
are also interesting even if still in a preliminary form.
The presented results are interesting, but they still are at a preliminary stage.
Edge effects are taken in account by a frame, and fracture mechanism is described
by a threshold effect. We have showed as changing some parameters like, lattice,
interaction rules, fracture distance, numbers of neighbors much different behavior
can be described.
In a preceding work, we verified the results of this tool that are in accordance with
results obtained by FEM, also in the fracture case; the results showed good similarity