Sintering - msolids/musen GitHub Wiki

During modeling of sintering process rotation of particles is not considered.

Velocities

$\bar{v}_{rel} = \bar{v}_2 - \bar{v}_1$

$\bar{v}_{rel,n}=\bar{r}_n\cdot(\bar{r}_n\cdot\bar{v}_{rel})$

$\bar{v}_{rel,t}=\bar{v}_{rel}-\bar{v}_{rel,n}$

Additional parameters

$\xi_n=r_1+r_2-|O_2-O_1|$

$R^* = \frac{r_1 \cdot r_2}{r_1 + r_2}$

$a_s=(4 \cdot R^* \cdot \xi_n )^{0.5}$

Normal force

$F_n=1.125 \cdot \pi \cdot 2 \cdot R^* \cdot \gamma - v_{rel,n} \cdot \pi \cdot \frac{a_s^4}{8 \cdot D}$

Tangential force

$F_t = v_{rel,t} \cdot (-0.01) \cdot \pi \cdot a_s^2 \cdot \frac{(2\cdot R^*)^2}{8D}$

Summarized forces and moments acting on particle (wall)

$\bar F_{tot} = \bar F_n + \bar F_t$

$\bar F_{1} = \bar F_n + \bar F_t$

$\bar F_{2} = -\bar F_n - \bar F_t$

Literatur Bessler R., da Silva M.R., do Rosario J.J., Dosta M., Heinrich S., Janssen R. (2015). Sintering Simulation of Periodic Macro Porous Alumina, Journal of Americ. Ceramic Society 98, 3496-3502.

Parhami F., McMeeking R. (1998). A network model for initial stage sintering, Mech. Mat. 2, 111–124.

Martin C., Bordia R. (2009). The effect of a substrate on the sintering of constrained films, Acta Mater. 2, 549–558.

Symbol	Description
$\bar F_n,\, \bar F_t$	Force in normal and tangential directions [N]
$O_1,\,O_2$	Centers of contact partners [m]
$R^*$	Equivalent radius [m]
$r_1,\,r_2$	Particle radii [m]
$\bar r_c$	Contact vector [m]
$\bar r_n$	Normalized contact vector [-]
$\bar v_{rel}$	Relative velocity [m/s]
$\bar v_1,\, \bar v_2$	Velocities of contact partners [m/s]
$\Delta\bar\xi_t$	Increment of tangential displacement in the current step [m]
$\gamma$	Surface energy []
$\xi_n$	Normal overlap [m]