Singular curves in the resultant thermomechanics of shells

Some geometric and kinematic relations associated with the curve moving on the shell base surface are discussed. The extended surface transport relation and the extended surface divergence theorems are proposed for the piecewise smooth tensor fields acting on the regular and piecewise regular surfaces. The recently formulated resultant, two-dimensionally exact, thermodynamic shell relations – the balances of mass, linear and angular momenta, and energy as well as the entropy inequality – are completed by the corresponding jump conditions at the moving (non-material) and stationary (material) singular surface curve.