Micromechanics Modeling of Unit Cells Using CUF Beam Models and the Mechanics of Structure Genome

Abstract

A novel approach for the micromechanics analysis of composite structures is developed using refined beam models and the mechanics of structure genome (MSG). The MSG provides a tool to obtain the complete stiffness matrix of general composite materials by asymptotically minimizing the loss of information between the original heterogeneous body and the sought homogenized body. The constitutive information is in this manner extracted from the representative volume without the need of ad-hoc assumptions and in one single loading step. The local fields are then straightforwardly recovered using the same unknowns of the original homogenization problem, with no need of additional analyses. This work proposes the use of higher-order beam models based on the Carrera unified formulation (CUF) to solve the micromechanics problem by means of MSG. The fibers, or equivalent constituents, are discretized along the longitudinal direction with beam elements and the unknown variables are expanded over the remaining two local coordinates making use of Legendre-class polynomial sets, denoted to as Hierarchical Legendre Expansions (HLE). In addition, non-local expansion domains with curved boundaries are defined to capture the exact shape of the constituents independently of the refinement of the model. In this sense, the quality of the approximation is controlled by the polynomial order of the beam model, which is introduced in the analysis as a user input, and the size of the computational problem can be reduced for many typical microstructures with no loss of accuracy.