# Time Integration

- $N$
- Number of nodes for considered elements

The scale factor should be reduced to 0.7 and 0.5 for multi-physics laws.

Explicit time integration based on Newmark method is conditionally stable. The Courant condition
also takes into account the flow of material through the elements gives the
stability condition as:(1)
(2)

$$\text{\Delta}t\le \text{\hspace{0.17em}}{S}_{f}*\frac{\text{\Delta}l}{c+v-w}$$

$$v-w=\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^{3}{\displaystyle \sum _{l=1}^{N}{\left({v}_{i}^{l}-{w}_{i}^{l}\right)}^{2}}}}$$

Where,

- $N$
- Number of nodes for considered elements

The scale factor should be reduced to 0.7 and 0.5 for multi-physics laws.