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...

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...

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 ...

The physical meaning of Cosserat, void, and microstretch elastic constants is analyzed and interpreted. Various torsion experiment designs provide a clear path to extract Cosserat elastic constants independently of any dilatation gradient sensitivity the material may have. For void elasticity (with sensitivity to dilatation gradients) there is no known quasi-static modality to demonstrate pheno...

Department of Engineering Physics, Department of Materials Science University of Wisconsin, 1500 Engineering Drive, Madison, WI 53706-1687, USA preprint adapted from Lakes, R. S., Reduced warp in torsion of reticulated foam due to Cosserat elasticity: experiment, Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP), 67(3), 1-6 (2016). Abstract Warp of cross sections of square section bars i...

In a previous publication the authors proposed a continuous model for describing the mechanical behaviour of ‘Running Bond’ masonry walls. Here a different masonry structure is considered. This structure is ‘bi-atomic’ in the sense that its pattern consists in two kind of blocks with different. The homogenization by differential expansions technique is used for obtaining an equivalent Cosserat ...

Pure bending experiments on prismatic bars of square cross-section composed of reticulated polymer foam exhibit deformation behavior not captured by classical elasticity theory. Perhaps the clearest example of this is the observed sigmoidal deformation of the bars’ lateral surfaces, which are predicted by classical elasticity theory to tilt but remain planar upon pure moment application. Such f...

A generalized theory of elasticity, taking into account the rotational degrees of freedom of point bodies constituting a continuum, was proposed at the beginning of the twentieth century by the Cosserat brothers. We report the experimental observation of coupled rotational-translational modes in a noncohesive granular phononic crystal. While absent in the classical theory of elasticity, these e...

Negative Poisson’s ratio polymer foams derived from reticulated open cell foams exhibit large size effects in torsion and bending. Effective moduli increase as diameter decreases in contrast to the prediction of classical elasticity. Size effects of this sort are predicted by Cosserat (micropolar) elasticity in which points can rotate as well as translate and distributed moments are incorporate...