Abstract This contribution aims at introducing first steps to develop hysteresis operator type inelastic constitutive laws for Cosserat rods the simulation of cables composed complex interior components. Motivated by basic elements rod theory, we a specific approach modelling adapted this application. Afterwards, describe hysteretical behaviour arising from cyclic bending experiments on means P...

A geometrically exact model of a Cosserat rod with nonholonomic constraints is outlined. The constraint forces are derived from the framework of nonholonomic mechanics by using arguments from Cauchy analysis, and a thorough discussion is given concerning the nature of these constraints. By making an additional assumption on the magnitude of the deflections, a simplified model similar to the Eul...

A Γ-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane...

The micropolar continuum theory has attracted enormous attention for studying many mechanical problems specially when the microstructure effects (size scale) could not be ignored like granular materials. This enriched model refers to Cosserat-type theories which take into account independently rotational degrees of freedom (DOF) in addition translational ones. provides essential features media ...

In this paper, we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. framework of linear model, provide a comparison our models with classical Koiter shell model and “best” first-order For all proposed models, show existence uniqueness based on Korn’s inequality for surfaces.

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that classical Navier–Stokes equation does not fully describe motion water. In this article, we propose an approach to dynamics formed chiral, planar and rigid molecules some kind equations for their description. Examples such are water, ozone, carbon dioxide hydrogen cyanide.