The theory of Cosserat elasticity (also known as micropolar or asymmetric elasticity) was introduced by Cosserat brothers [1] and further developed by Eringen [2] to model the mechanical behavior of materials for which the microstructure is significant (see [3] for a review of works in this area and an extensive bibliography). The theory was intended to eliminate discrepancies between the class...

A formulation of the dynamics of a collection of connected simple 1dimensional Cosserat continua and rigid bodies is presented in terms of sections of an SO(3) fibration over a 1-dimensional net. A large class of junction conditions is considered in a unified framework. All the equations of motion and junction conditions are derived as extrema of a constrained variational principle on the net a...

Microcontinuum field theories, including Micromorphic theory, Microstructure theory, Micropolar theory, Cosserat theory, nonlocal theory and couple stress theory, are the extensions of the classical field theories for the applications in microscopic space and time scales. They have been expected to overlap atomic model at microscale and encompass classical continuum mechanics at macroscale. Thi...

-Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocations. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological...

The idea of a material body endowed with both translational and rotational degrees of freedom stems from the seminal work of the Cosserat brothers (Cosserat and Cosserat, 1909). A triad of orthonormal directors (d )i=1,3 is associated to the microstructure of each material point. The material transformation describes the displacement u of the material point and the rotation R∼ with respect to t...

1. Abstract Micropolar field theory represents an extension of the classical Cauchy continuum theory. In this paper, a topology optimization procedure for maximum stiffness is applied to structural elements made of micropolar (Cosserat) solids. Some special problems are dealt with, and particular attention is given to models that refer to structural interfaces. The results are in good agreement...

In this paper, the modelling strategy of a Cosserat rod element (CRE) is addressed systematically for 3-dimensional dynamical analysis of slender structures. We employ the nonlinear kinematic relationships in the sense of Cosserat theory, and adopt the Bernoulli hypothesis. The Kirchoff constitutive relations are adopted to provide an adequate description of elastic properties in terms of a few...

Different from Cauchy elastic materials, generalized continua, and in particular constrained Cosserat materials, can be designed to possess extreme (near a failure of ellipticity) orthotropy properties and in this way to model folding in a three-dimensional solid. Following this approach, folding, which is a narrow zone of highly localized bending, spontaneously emerges as a deformation pattern...

Reticulated open cell polymer foams exhibit substantial size e↵ects in torsion and bending: slender specimens are more rigid than anticipated via classical elasticity. Such size e↵ects are predicted by Cosserat (micropolar) elasticity, which allows points to rotate as well as translate and incorporates distributed moments (couple stresses). The Cosserat characteristic length is larger than the ...