Algorithm 2 GMM algorithm.

Material DATA: E, $\nu$, $\rho$

Initial data on material points: $m_p$, ${\mathbf{x}}_p^n$, ${\displaystyle \Delta t,{\mathbf{F}}_p^n=\sum _I\frac{\partial N_I}{\partial {\mathbf{x}}_I^0}·{\mathbf{x}}_I^n}$${\displaystyle \Delta {\mathbf{F}}_p=\sum _I\frac{\partial N_I}{\partial {\mathbf{x}}_I^n}·{\mathbf{x}}_I^{n+1}}$

Initial data on nodes: ${\mathbf{u}}_I^n,{\mathbf{v}}_I^n,{\mathbf{a}}_I^n$

OUTPUT of calculations: ${\mathbf{u}}_I^{n+1}{\mathit{\sigma }}_p^{n+1}$

INITIALIZATION PHASE for every material point with position ${\mathbf{x}}_p^n$ gather the cloud of nodes with position ${\mathbf{x}}_I^n$ such that $\left|{\mathbf{x}}_p-{\mathbf{x}}_I\right|<R$ compute the shape functions $N_I\left({\mathbf{x}}_p^n\right)$ for all nodes I in the cloud Newmark method: PREDICTOR for the prediction of displacement, unlike Equation (42), ${}^{it+1}{\mathbf{u}}_I^{n+1}={\mathbf{u}}_I^n$, while for the prediction of nodal velocity and nodal acceleration, see Equations (43) and (44) UL-FEM PHASE (identical to MPM) CONVECTIVE PHASE Update position of the material points by means of an interpolation of nodal solution (a) for p = 1:$N_p$ ${\mathbf{x}}_p^{n+1}={\mathbf{x}}_p^n+\sum N_I\Delta {\mathbf{u}}_I^{n+1}$ Save state of stress ${\mathit{\sigma }}_p^{n+1}$, state of strain ${\mathit{ϵ}}_p^{n+1}$ and total deformation gradient ${\mathbf{F}}_p^{n+1}$ on material points (the latter by ${\mathbf{F}}_p^{n+1}=\Delta {\mathbf{F}}_p·{\mathbf{F}}_p^n$)