Micromechanics of periodically heterogeneous materials using higher-order beam theories and the mechanics of structure genome

A novel approach for the micromechanical analysis of periodically heterogeneous composite materials is proposed in this paper. It is based on the use of refined beam theories for the modeling of the microstructure and the mechanics of structure genome (MSG) for the derivation of the governing equations of the unit cell problem. On the one hand, MSG is recalled to decouple the multiscale problem into global and local analysis, providing the constitutive information and the local fields with no need of ad hoc assumptions, nor multiple loading steps. On the other hand, the Carrera Unified Formulation (CUF) is employed to generate higher-order beam models that show the same accuracy as conventional solid elements with reduced computational efforts. Accordingly, the main direction of the constituents (e.g. the fibre direction) is discretized by means of one-dimensional finite elements whereas the cross-section is hierarchically enriched with a set of Legendre-based polynomials with non-local capabilities. In addition, the implementation of a non-isoparametric mapping technique permits the representation of the exact geometry of the constituents with no additional costs. The validity and efficiency of the proposed model is assessed through comparison with several benchmark solutions of fibre reinforced and particle reinforced composites.