Computational algorithm for the solution of 2D and 3D dynamic problems of the Cosserat elasticity theory using multiprocessor computer systems is worked out. The algorithm is based on the two-cyclic splitting method with respect to the spatial variables in combination with the explicit monotone finite-difference ENO–scheme for solving 1D problems adapted for the calculation of discontinuities. ...

This paper presents a geometric discretization of elasticity when the ambient space is Euclidean. This theory is built on ideas from algebraic topology, exterior calculus, and the recent developments of discrete exterior calculus. We first review some geometric ideas in continuum mechanics and show how constitutive equations of linearized elasticity, similar to those of electromagnetism, can be...

Cosserat rod theory proved efficient modeling performances in robotics, especially the context of continuum robots, past decade. The implementation such is far from being unique and straightforward. We consider illustrative example multisegment, general routing tendon actuated robots their nominal static operating regime. This article details two main approaches based on modeling, namely, Newto...

The principle underlying cloaking theory is the transformation method whereby the material properties of the cloak are defined by a (singular) spatial transformation. For elastodynamics, Milton et al. [1] concluded that the transformed materials are described by the Willis model, involving coupling between stress and velocity, in addition to anisotropic inertia. For a restricted transformation,...

This paper investigates the Hamiltonian structure and Poisson bracket formulation of a higher-order, geometrically-exact Cosserat type beam with deforming cross-section in terms canonically conjugate variables.

Unlike rigid actuators, soft actuators can easily adapt to complex environments. Understanding the relationship between deformation of and external factors such as pressure would enable rapid designs based on specific requirements, flexible, compliant endoscopes. An effective model is demonstrated that predicts a actuator virtual work principle geometrically exact Cosserat rod theory. The proce...

In the present contribution anisotropic structure of two-dimensional linear Cosserat elasticity is investigated. The symmetry classes this model are derived and detailed in a synthetic way. Particular attention paid to specific features Elasticity which sensitivity non-centrosymmetry as well chirality. These aspects important for application continuum theory mechanical modelling lattices metama...

Ce document présente et discute de certains concepts de base de la mécanique du continuum de façon à permettre d'envisager des applications dans le domaine de la géophysique. Il aborde en particulier les concepts tels que les milieux de Cosserat, la répartition continue d’hétérogénéités et le rôle des symétries matérielles. Dans l'esprit de notre communication orale, la présentation garde un st...