```liujun said:     (by the date of Wed, 4 Oct 2006 10:51:53 +0800)

> I am a teacher of an University of China, Now I am developing a code to
> simulate fracture process of concrete under blast. I used a model named
> "Lattice Solid Model", which is constructed in the frame of DEM. i.e.

> (1)Discretize the concrete structure using Qhull library,
>    Delaunay or Voronoi lattice;
> (2)create beams between tetrahedra or polyhedra in contact;
> (3)calculating deformation of each beam by the relative dispalcement
>    of two tetrahedra or polyhedra at the end of beam;
> (4) verifying each beam exists or not by a law described by deformation.
> (5) visulizing the result using OpenGL.

> My questions as follows:

> (1)what's difference between your lattice-beam model and my method above mentioned?

1) Discretize the structure by positioning nodes at specified regular
intervals (triangular or orthogonal mesh) inside the structure. Displace
each node by some random number in specified range (zero range gives
regular mesh, non-zero generates meshes with desired amount of non
regularity).

2) Connect nodes to create beams obeying following parameters:
- maximum/minimum beam length,
- minimum angle between two beams.

3) Calculate new position of each beam nodes using only infomation about the:
- beam rotation and movement in previous time step
- beam length vs. original beam length
- angle between the beam and each of its neighbours vs. original angle

4) verifying that each beam exists or not, depending on its current length

> (2)what's difference between Discrete Element Method with Moment Law
> (in your web Screen shot section) and lattice-beam model?

lattice beam model is quasi-static. No mass, and no time is used in the
formulas. The simulation elements are beams, the interactions are
angular springs between the beams.

In MDEM the elements are spheres, and interactions are (spring) forces
at contact between two spheres.

> (3)Is your contact detection method based on Deep-Swift?

In lattice beam model, there is no contact detection. In quasi-static
simulations I cannot have an impact, only fracture propagation, so
contact detection is unnecessary.

In DEM contact detection is Sweep and Prune collider. It uses three
std::vector (one for each dimension x,y,z) where start and end
coordinates for each box bounding volume are stored. If a certain
bounding volume crosses another one in all three vectors (by comparing
their start and end coordinates), then they are in potential contact.
This method is very fast, because the vectors can be sorted on each
interation at very small cost: only swapping of few vector elementes is
needed, because the spheres are not moving that much during one time
step. This method is slow if the simulation elements displace by large
distances between single time step.

> (4)Can you briefly introduce the theory Lattice-beam model?

All explanations you have above. As you can see it will not be useful
for impact simulation, only quasi-static fracture propagation in brittle
materials. This model is explicit (no global matrix is built), and the
formulas are quite fast. A simulation with 200 000 lattice elements
takes only 15 hours to complete on one processor of AMD 4600+.
More processors can reduce time even more (we are working on that).

Possibly later I will extend it to detect collisions, but still - this
is not a dynamic simulation, so still not good for impacts.

If you want to see the formulas I use to calculate lattice beam, just
let me know, and I can send you them.

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Janek Kozicki                                                         |
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