Residual Stress Simulation in Selective Laser Melting (SLM)#
Mathematical Model:
\[\begin{split}
\begin{align*}
&\text{Mechanical Deformation:} \quad \nabla \cdot \boldsymbol{\sigma} = \mathbf{0} \\
&\text{Thermal Simulation:} \quad \rho c \frac{\partial T}{\partial t} - \nabla \cdot (k \nabla T) = Q
\end{align*}
\end{split}\]
Weak Formulation:
\[
\begin{align*}
&\int_{\Omega} \left(\nabla \cdot \boldsymbol{\sigma} \cdot \boldsymbol{\varepsilon} + \nabla \cdot (k \nabla T) \phi - Q \phi\right) \,d\Omega = 0
\end{align*}
\]