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.
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