Fiber-Reinforced Composite Materials#
Mathematical Model:
\[\begin{split}
\begin{align*}
&\text{Matrix Phase:} \quad \nabla \cdot (\mathbf{C}_{\text{matrix}} : \boldsymbol{\varepsilon}_{\text{matrix}}) = 0 \\
&\text{Fiber Phase:} \quad \nabla \cdot (\mathbf{C}_{\text{fiber}} : \boldsymbol{\varepsilon}_{\text{fiber}}) = 0
\end{align*}
\end{split}\]
Weak Formulation:
\[\begin{split}
\begin{align*}
&\text{Matrix Phase:} \quad \int_{\Omega_{\text{matrix}}} \nabla \cdot (\mathbf{C}_{\text{matrix}} : \boldsymbol{\varepsilon}_{\text{matrix}}) \cdot \boldsymbol{\phi}_{\text{matrix}} \,d\Omega_{\text{matrix}} = 0 \\
&\text{Fiber Phase:} \quad \int_{\Omega_{\text{fiber}}} \nabla \cdot (\mathbf{C}_{\text{fiber}} : \boldsymbol{\varepsilon}_{\text{fiber}}) \cdot \boldsymbol{\phi}_{\text{fiber}} \,d\Omega_{\text{fiber}} = 0
\end{align*}
\end{split}\]