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...

Cosserat rods are models for long slender objects. Let SE(3) = R3 SO(3) be the 13 group of orientation-preserving rigid body motions of R3 (the special Euclidean 14 group). A configuration of a Cosserat rod is a map φ : [0,1] → SE(3). For each 15 s ∈ [0,1], the value φ(s) = (φr(s),φq(s)) is interpreted as the position φr(s)∈R and 16 orientation φq(s)∈ SO(3) of a rigid rod cross section. Strain ...

This paper provides an extension to Cosserat mechanics of a recently proposed version of hypoplasticity [1], and this extension is achieved economically by means of a novel complex-variable formulation of Cosserat theory. The present work represents a compact synthesis and theoretical framework for both non-polar and polar hypoplasticity, and it encompasses various special cases considered in t...

The Cosserat theory of elastic rods has been used in a wide range of application domains to model and simulate the elastic deformation of thin rods. It is physically accurate and its implementations are efficient for interactive simulation. However, one requirement of using Cosserat rod theory is that the tubular object must have rigid cross-sections that are small compared to its length. This ...

This brief article provides an independent derivation of a formula given by Kafadar and Eringen (1971) connecting two distinct Cosserat spins. The first of these, the logarithmic spin represents the time rate of change of the vector defining finite Cosserat rotation, whereas the second, the instantaneous spin, gives the local angular velocity representing the infinitesimal generator of that rot...

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...

In this paper we investigate the application of bounding volume hierarchies in collision detection among densely packed fiber assemblies like hair strands or cable looms. In particular, we glance at collision detection algorithms with sub-quadratic upper bound and their practicability and performance in complex dynamic hair scenes. Unlike common collision detection techniques our approach explo...