Abstract In Continuum Mechanics a widely cited formula, due to Nanson (Mess Math 7:182–185, 1878), contributes the relation between product of area and unit normal vectors relevant corresponding surfaces in two configurations 3D body. A geometric treatment provides equivalent expressions formula by direct elaborations on Euler – Jacobi volume change formula. Meaning limits are underlined. liter...

We propose a geometrical approach to the mechanics of continuous media equipped with inner structures and give basic (Navier–Stokes, mass conservation energy conservation) equations their motion.

this paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. the graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. nonlocal governing equations of motion for this double-layer graphene s...