The paper examines the properties that constraint manifolds possess as Riemannian submanifolds of the Euclidean space of all second-order tensors and have implications on the description of mechanical behavior of internally constrained bodies. It is shown that constraint manifolds corresponding to some usual internal constraints have non-zero curvature and, hence, possess a non-Euclidean structure that has to be taken into account when the active and reactive parts of the Piola-Kirchhoff stress are differentiated with respect to deformation gradient. -
Lembo, M. (2009). On the geometry of constraint manifolds. MECCANICA, 44(6), 635-651 [10.1007/s11012-009-9201-7].
On the geometry of constraint manifolds
LEMBO, Marzio
2009-01-01
Abstract
The paper examines the properties that constraint manifolds possess as Riemannian submanifolds of the Euclidean space of all second-order tensors and have implications on the description of mechanical behavior of internally constrained bodies. It is shown that constraint manifolds corresponding to some usual internal constraints have non-zero curvature and, hence, possess a non-Euclidean structure that has to be taken into account when the active and reactive parts of the Piola-Kirchhoff stress are differentiated with respect to deformation gradient. -I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
