Abstract
In Continuum Mechanics a widely cited formula, due to Nanson (Mess Math 7:182–185, 1878), contributes the relation between the product of area and unit normal vectors relevant to corresponding surfaces in two configurations of a 3D body. A geometric treatment provides equivalent expressions of Nanson formula by direct elaborations on Euler–Jacobi volume change formula. Meaning and limits of Nanson formula are underlined. In the literature this formula has been improperly assumed to be expedient for attempts of imposing equilibrium in a reference shape of the body. A critical revision shows recourse to scaling and parallel transport of surface and bulk forces is impassable in assessing alleged referential equilibrium. A variational formulation of evolutive equilibrium in spacetime is developed and finite step elastic problems guided by control algorithms in computational procedures are illustrated. Step-by-step iterative methods of solution of nonlinear structural problems and simple counterexamples should help in convincing referential equilibria are not conceivable in Nonlinear Continuum Mechanics.
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