We generalize substructuring methods to problems for functions f : Ω → M , where Ω is a domain in R and M is a Riemannian manifold. Examples for such functions include configurations of liquid crystals, ferromagnets, and deformations of Cosserat materials. We show that a substructuring theory can be developed for such problems. While the theory looks very similar to the linear theory on a forma...

We illustrate the flow behaviour of fluids with isotropic and anisotropic microstructure (internal length, layering with bending stiffness) by means of numerical simulations of silo discharge and flow alignment in simple shear. The Cosserat theory is used to provide an internal length in the constitutive model through bending stiffness to describe isotropic microstructure and this theory is cou...

We propose a first example of a simple classical field theory with nonholonomic constraints. Our model is a straightforward modification of a Cosserat rod. Based on a mechanical analogy, we argue that the constraint forces should be modeled in a special way, and we show how such a procedure can be naturally implemented in the framework of geometric field theory. Finally, we derive the equations...

This paper uses the special Cosserat theory of hyperelastic shells satisfying Kirchoff's hypothesis and irrotational flow theory to model the interaction between a heavy thin elastic sheet and an infinite ocean beneath it. From a general discussion of three-dimensional motions, involving an Eulerian description of the flow and a Lagrangian description of the elastic sheet, a special case of two...

We study the effect of a magnetic field on the behaviour of a slender conducting elastic structure subject to end forces. Both statical (buckling) and dynamical (whirling) instability are considered and we also compute post-buckling configurations. The theory used is the geometrically exact Cosserat rod theory. We consider two types of boundary conditions: the traditional welded boundary condit...

I present a derivation of the static equations of a granular mechanical interpretation of Cosserat continuum based on a continuum formulated in the intra-granular fields. I assume granular materials with three-dimensional, nonspherical, and deformable grains, and interactions given by traction acting on finite contact areas. Surface traction is decomposed into a mean and a fluctuating part. The...

Usual introductions of the concept of motion are not well adapted to a subsequent, strictly tensorial, theory of elasticity. The consideration of arbitrary coordinate systems for the representation of both, the points in the laboratory, and the material points (comoving coordinates), allows to develop a simple, old fashioned theory, where only measurable quantities —like the Cauchy stress— need...