Towards Viscoplastic Constitutive Models for Cosserat Rods

Abstract

Flexible, slender structures like cables, hoses or wires can be described by the geometrically exact Cosserat rod theory. Due to their complex multilayer structure, consisting of various materials, viscoplastic behavior has to be expected for cables under load. Classical experiments like uniaxial tension, torsion or three-point bending already show that the behavior of e.g. electric cables is viscoplastic. A suitable constitutive law for the observed load case is crucial for a realistic simulation of the deformation of a component. Consequently, this contribution aims at a viscoplastic constitutive law formulated in the terms of sectional quantities of Cosserat rods. Since the loading of cables in applications is in most cases not represented by these mostly uniaxial classical experiments, but rather multiaxial, new experiments for cables have to be designed. They have to illustrate viscoplastic effects, enable access to (viscoplastic) material parameters and account for coupling effects between different deformation modes. This work focuses on the design of such experiments.

Geometrically exact elastoplastic rods: determination of yield surface in terms of stress resultants

“…For the case of geometrically nonlinear beams, we refer to [9][10][11][12]. Attempts towards a direct approach to model viscoplastic and thermoelastoplastic rods are, e.g., [13] and [14,15], respectively. There, the assumption is made that the strain prescriptors (the rod's translational strains and curvatures) split additively into elastic and plastic parts.…”

Two-scale off-and online approaches to geometrically exact elastoplastic rods

“…The key components of modeling elastoplastic rods are briefly presented here. The strain prescriptors are assumed to decompose into an elastic and a plastic part as follows: [16,23,31].…”

Nonlinear computation of cables with high order solid elements using an anisotropic material model

“…In Fig. 1 the results of two experiments with a coaxial cable (top right) [1] and the results of corresponding simulations can be seen. On the left-hand side the force-displacement curve of a simple tension experiment is pictured.…”

“…Fig.1: Experimental data of a coaxial cable (top right)[1] and simulation results for the anisotropic material model: tension test on the left, torsion test in the middle, and deformation of FE model under torsion on the right bottom.…”