On Dynamics of Elastic Networks With Rigid Junctions Within Nonlinear Micro-Polar Elasticity

Abstract

Within the nonlinear micropolar elasticity we discuss effective dynamic (kinetic) properties of elastic networks with rigid joints. The model of a hyperelastic micropolar continuum is based on two constitutive relations, i.e. static and kinetic ones. They introduce a strain energy density and a kinetic energy density, respectively. Here we consider three-dimensional elastic network made of three families of elastic fibers connected through massive rigid joints. So effective elastic properties are inherited from the geometry and material properties of fibers, whereas the kinetic (inertia) properties are determined by the both fibers and joints. Formulae for microinertia tensors are given.