Microscale thermo-elastic analysis of composite materials by high-order geometrically accurate finite elements

The present work proposes a new approach for conducting thermo-elastic micromechanical analysis. It relies on the use of high-order and geometrically accurate beam finite elements to model the microstructures. The governing equations of the micromechanics models involving the unit cell concept are derived through the Mechanics of Structure Genome (MSG). MSG allows multiscale analysis where global and local scales are decoupled and provides the constitutive information and local fields without needing ad hoc assumptions or requiring different loading steps. The high-order beam elements are derived instead by means of the well-known Carrera Unified Formulation (CUF). These advanced models provide a level of accuracy comparable to conventional solid elements with a fraction of the computational effort. Depending on the problem considered, the cross-section of the refined beam model is modelled by a set of Legendre polynomials, whilst the main direction of the representative unit cell is discretised using one-dimensional (1D) finite elements. Additionally, a non-isoparametric mapping technique allows a perfect description of the microstructural constituents. The present approach enables the resolution of both thermo-elastic homogenisation problems and the recovery of local stress fields through a single run of a CUF-MSG-based code. Several numerical examples compared with numerous other representative solutions of fibre and particle reinforced composites are conducted in order to demonstrate the validity and the efficiency of the presented methodology.