Geometrically exact micropolar Timoshenko beam and its application in modelling sandwich beams made of architected lattice core

Abstract

Abstract With a view towards modelling nonlinear elastic response of sandwich beams made of architected lattice core, a geometrically exact formulation for micropolar Timoshenko beam is developed. Starting with the assumed deformation field that reflects the classical hypothesis of shear deformable Timoshenko beam theory, a systematic dimensional reduction is carried out without any further approximation in the definition of strain measures and thus follows the phrase geometrically exact . Proposed beam model is then used to investigate the mechanics of sandwich beams made of architected lattice core. We establish that the new beam formulation is capable of representing the nonlinear mechanical behaviour of such sandwich structures through an equivalent single layer beam theory. Two-scale computational homogenization approach based on the FE 2 formalism is adopted to obtain the constitutive behaviour of the proposed single layer beam. A set of numerical simulations is carried out to investigate the nonlinear behaviour of the proposed beam as well as to attest to the effectiveness of the homogenized beam formulation. While the present theory is applicable for planar deformation alone, it has no restriction over the finiteness of deformation and micro/macro-rotation of the beam.