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Add a set of csv results files for nodes

Sacha Duverger requested to merge add/nodes_csv into custom_cbgeo

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 than E_{tot}(t=0) (~ 10^2\phantom{.}J/m for W_{frict}, and ~ 10^6\phantom{.}J/m for E_{tot} )
Edited by Sacha Duverger

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