Minimum Principles for Interacting Cosserat Elastic Continua

Continua of Minimum Capacity

1. Surfaces containing a given volume. In an endeavour to simplify a proof of Liapounoff [2], to the effect that in the problem of the forms of equilibrium of rotating liquids the sphere would be the only form for a liquid at rest, Poincaré [ l ] was led to the consideration of electric capacities of solids of given volume, and arrived at the result that among such bodies the sphere would have ...

Internally Constrained Mixtures of Elastic Continua

A treatment of internally constrained mixtures of elastic continua at a common temperature is de­ veloped. Internal constraints involving the defonnation gradient tensors and the common mixture temperature are represented by a constraint manifold, and an internally constrained mixture ofelastic continua is associated with each unique equivalence class ofunconstrained mixtures. The example of in...

Stress Concentration in an Elastic Cosserat Plate Undergoing Extensional Deformations

Accuracy Examination of the Multiple Interacting Continua Approximation

This study examines the accuracy of the multiple interacting continua (MINC) model. A regularly shaped rock block with uniform initial conditions and a step change in boundary conditions on the surface is evaluated. The analysis results show that pressures (or temperatures) predicted by MINC approximation may deviate from exact solutions by as much as 10 − 15% at certain points within the block...

CORDE: Cosserat Rod Elements for the Dynamic Simulation of One-Dimensional Elastic Objects

Simulating one-dimensional elastic objects such as threads, ropes or hair strands is a difficult problem, especially if material torsion is considered. In this paper, we present CORDE(french ’rope’), a novel deformation model for the dynamic interactive simulation of elastic rods with torsion. We derive continuous energies for a dynamically deforming rod based on the Cosserat theory of elastic ...