Large size effects are experimentally measured in lattices of triangular unit cells: about a factor of 36 in torsion rigidity and 29 in bending rigidity. This nonclassical phenomenon is consistent with Cosserat elasticity, which allows for the rotation of points and distributed moments in addition to the translation of points and force stress of classical elasticity. The Cosserat characteristic...

Size effects are explored experimentally in a tetragonal lattice structure. Size dependence of rigidity is nonclassical elastic and is interpreted via Cosserat elasticity. The characteristic lengths are about a third the cell size. The Cosserat characteristic length for torsion is `t = 5.6 mm. The characteristic length for bending is `b = 5.4 mm. The size effect in torsion was a factor 4.5 in r...

Abstract In this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from Cosserat material. The dimensional reduction procedure extends methods of classical shell theory case shells. Starting three-dimensional parent model, perform integration over thickness and obtain consistent model order $$ O(h^5) <mml:math xmlns:mm...

On the basis of a “local” principle of equivalence of general relativity, we consider a navigation in a kind of “4D-ocean” involving measurements of conformally invariant physical properties only. Then, applying the Pfaff theory for PDE to a particular conformally equivariant system of differential equations, we show the dependency of any kind of function describing “spacetime waves”, with resp...

We present a novel method to simulate bending and torsion of elastic rods within the position-based dynamics (PBD) framework. The main challenge is that torsion effects of Cosserat rods are described in terms of material frames which are attached to the centerline of the rod. But frames or orientations do not fit into the classical position-based dynamics formulation. To solve this problem we i...

In this study, an inhomogeneous Cosserat rod theory is introduced and compared to the conventional homogeneous for modeling soft manipulators. The inhomogeneity addressed by considering pressure actuation as part of rod's constitutive laws, resulting in shifting neutral axis. This shift investigated a manipulator with three parallel fiber-reinforced actuators. Furthermore, actuator modeled usin...