Asymptotics for thin elastic fibers in unilateral contact



What is the contact condition in a 1D beam-model and is it possible to obtain the frictional moments and forces from the 3D traction? If it is possible does the cross-section of the beams influence these values? These questions motivate to study the dimension reduction of a 3D contact problem for beams. This paper is a continuation of [1]. In [1] the asymptotic dimension reduction of a Robin-type elasticity boundary value problem was presented. In this work the explicit relation between a 3D contact problem and a 3D Robin-type elasticity boundary value problem are established and the 1D equations derived in [1] are interpreted as 1D contact conditions, further some numerical examples are shown. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)