Add a set of csv results files for nodes
This MR adds the possibility to write CSV files which contains information about all nodes in the simulation (currently: id, mass, coord_x, coord_y, coord_z, friction_energy). For now, the nodes CSV files are always written, but an upcoming commit will make this feature optional though the use of a flag in the analysis inputs.
Also, this MR adds the computation of the dissipated frictional energy, computed incrementally for each node:
W_{frict}(t + \Delta t) = W_{frict}(t) + P_{frict}(t)\Delta t
P_{frict} = \vec{F}_{frict} \cdot{} \vec{V}_{node}
Regarding the computation of \vec{F}_{frict}
, because CB-Geo MPM computes the resulting acceleration rather than the force, I simply computed it as the product of the nodal acceleration and mass:
\vec{F}_{frict} = m_{node} \vec{a}_{frict}
With these equations, I obtain what I expect during a granular columns collapse:
- a negative, always decreasing
W_{frict}
, - only bottom nodes located next to moving material points have
P_{frict}\neq 0
- the
\sum_{all\phantom{.}nodes}|W_{frict}(t\rightarrow\infty)|
energy is much smaller thanE_{tot}(t=0)
(~10^2\phantom{.}J/m
forW_{frict}
, and ~10^6\phantom{.}J/m
forE_{tot}
)