Non-standard Timoshenko beam model for chiral metamaterial: Identification of stiffness parameters

Abstract

In the literature of granular micromechanics it is standard to achieve, at the macro scale, non-standard enhanced continuum models [1–2]. Among a panoply of exotic behaviors, these models predict that granular materials can show chirality for a specific grain-pair interaction. To verify these predictions, a granular system with a specific grain-pair interaction has been designed and its mechanical behavior under different types of loading has been evaluated via numerical simulations. The resulting granular system, which can be referred to as a granular beam, is a linear array of grains connected via the chosen grain-pair interaction law [1]. The chiral behavior of such mechanical system has been observed experimentally during tensile test. To describe the experimental evidence and numerical results, a continuous one-dimensional beam model has been defined and the four constitutive parameters, which characterize this specific strain energy function, have been identified. The numerical simulations on this granular system, modeled as a 2D deformable-body, have been performed employing the commercial finite element software COMSOL Multiphysics to have a reference data set for the identification process. Comparisons between the results obtained from this 2D FE model and the predictions of the same system analyzed via a specific non standard Timoshenko 1D beam model show an astonishing agreement.