Degree of freedom | Functional of the deformation function | Geometric meaning |
---|---|---|
\(u_{1,0,0}\) | \( \mathrm{Re} \left( {{{\mathrm{\mathrm{Log}}}}{\mathinner { \frac{\partial {^{}}\mathbf {x}_\xi }{\partial {{{\mathbf {x}}_0}_\xi ^{}}} }} ({0, 0})}\right) \) | Strain |
\(u_{1,1,0}\) | \(\mathrm{Im} \left( {{{\mathrm{\mathrm{Log}}}}{\mathinner { \frac{\partial {^{}}\mathbf {x}_\xi }{\partial {{{\mathbf {x}}_0}_\xi ^{}}} }} ({0, 0})}\right) \) | Rotation |
\(u_{1,0,1}\) | \({\dot{\varepsilon }^\mathrm {mat}}({0, 0}) - {\dot{\varepsilon }_0^\mathrm {mat}}({0, 0})\) | Material derivative of strain |
\(u_{1,1,1}\) | \({\kappa ^\mathrm {mat}}({0, 0}) - {\kappa _0^\mathrm {mat}} ({0, 0})\) | Material curvature |