Static elastic equilibrium
= Static elastic equilibrium
{title2=$\sigma_{ij,j}+f_i=0$}
A symmetric <stress tensor> is in <static elastic equilibrium> when its divergence balances the prescribed <body force>. Its boundary <traction> is $t_i=\sigma_{ij}n_j$. With zero <body force>, <integration by parts> gives $\int_\Omega\sigma:\operatorname{sym}\nabla v=\int_{\partial\Omega}t\cdot v$. This is the weak <principle of virtual work> for a static elastic body.