18 A Plausible Description of Continuum …
359
Fig. 18.33 Oblique lattice tensile test. Red points are leaders, blue point followers and yellow the
frame. First gradient case. Note the asymmetry of the leaders with respect of the frame
Generally, a larger number of time steps are required for relaxation, owing to the
larger number of points employed to describe the specimen; this does not mean a
longer relaxation time, because unit time is arbitrary, only that the influence of the
displacement propagates at one shell (first gradient case) each time step so we need
many steps to involve the whole sample. Once again the second gradient case seems
to be stiffer with respect of the first gradient.
It should be noted that, in our pictures, the sample does not reach a symmetric
final configuration as we can expect because of the long time required.
If we consider the simple tensile tests (see Figs. 18.35 and 18.36), little quantitative
differences in point distribution can be observed during the classical elongation of the
specimen in different cases. We can observe differences in the internal distribution
on the points and in the convexity of the propagation front of the deformation (see
Fig. 18.41), i.e., see the convexity of the points between the two figures. We are
working on this and on higher gradient computations.
On the contrary if we use a rectangular shape sample, it does (the points are
equally spaced) as can be seen in Fig. 18.37. There is no physical reason for this, our
opinion is that this effect is linked to the particular equilibrium condition generate by
the geometry. It can be outlined as final configuration is more similar to a symmetric
one, in second gradient case, owing to the larger number of points involved in the
computation.
In the two cases, we are considering Poisson’s effect (Figs. 18.38 and 18.39); it
is possible to see lateral contraction. It seems the points cluster to create islands, but
this effect must be investigated better. In case of second gradient interaction, this
359
Fig. 18.33 Oblique lattice tensile test. Red points are leaders, blue point followers and yellow the
frame. First gradient case. Note the asymmetry of the leaders with respect of the frame
Generally, a larger number of time steps are required for relaxation, owing to the
larger number of points employed to describe the specimen; this does not mean a
longer relaxation time, because unit time is arbitrary, only that the influence of the
displacement propagates at one shell (first gradient case) each time step so we need
many steps to involve the whole sample. Once again the second gradient case seems
to be stiffer with respect of the first gradient.
It should be noted that, in our pictures, the sample does not reach a symmetric
final configuration as we can expect because of the long time required.
If we consider the simple tensile tests (see Figs. 18.35 and 18.36), little quantitative
differences in point distribution can be observed during the classical elongation of the
specimen in different cases. We can observe differences in the internal distribution
on the points and in the convexity of the propagation front of the deformation (see
Fig. 18.41), i.e., see the convexity of the points between the two figures. We are
working on this and on higher gradient computations.
On the contrary if we use a rectangular shape sample, it does (the points are
equally spaced) as can be seen in Fig. 18.37. There is no physical reason for this, our
opinion is that this effect is linked to the particular equilibrium condition generate by
the geometry. It can be outlined as final configuration is more similar to a symmetric
one, in second gradient case, owing to the larger number of points involved in the
computation.
In the two cases, we are considering Poisson’s effect (Figs. 18.38 and 18.39); it
is possible to see lateral contraction. It seems the points cluster to create islands, but
this effect must be investigated better. In case of second gradient interaction, this