An intrinsic geometric formulation of Hyper-elasticity, pressure potential and non-holonomic constraints

Boris Kolev (1) , Rodrigue Desmorat (1)

1 LMT - Laboratoire de mécanique et technologie

Isotropic hyper-elasticity, altogether with the equilibrium equation and the usual boundary conditions, are formulated directly on the body B, a three-dimensional compact and orientable manifold with boundary equipped with a mass measure. Pearson-Sewell-Beatty pressure potential is formulated in an intrinsic geometric manner. It is shown that Poincaré's formula extended to infinite dimension, provides, in a straightforward manner, the optimal (non-holonomic) constraints for such a pressure potential to exist.

Mots clés: Manifold of Riemannian metrics; Potential for boundary conditions; Poincaré formula; Non-holonomic constraints; Finite strain theory

Domaines: Mécanique des solides [physics.class-ph]

Boris Kolev, Rodrigue Desmorat. An intrinsic geometric formulation of Hyper-elasticity, pressure potential and non-holonomic constraints. Journal of Elasticity, In press, ⟨10.1007/s10659-021-09853-5⟩. ⟨hal-03168412v1⟩