Development of isogeometric-finite element unified numerical methodology for nonlinear planar instability analysis of dual-phase SiO2-graphene nanoplatetlets reinforced shallow curved microbeams

Abstract

The main intention of the proposed multiscale framework is to employ an isogeometric analysis formulation for the size-dependent nonlinear planar instability analysis of dual-phase nanocomposite shallow curved beams at the microscale. A finite element–based micromechanics model is developed at the representative volume element level to capture the material properties. The homogenized properties obtained from the representative volume element-level finite element analysis are directly incorporated into the isogeometric model. This coupling enables accurate surveying of the small scale-dependent nonlinear in-plane stability characteristics of uniformly laterally loaded dual-phase inhomogeneous shallow curved microbeams reinforced with SiO2 nanoparticles and graphene nanoplatelets, while embracing distinct strain gradient tensors. In this regard, cuboid-shaped representative volume elements are employed. This enables consideration of the interphase between the dual-phase nanofillers and the polymer, as well as the critical role of nanofiller agglomeration, in order to create an accurate multiscale correlation. Additionally, non-uniform rational B-splines are utilized in the relevant discretization process. This process involves distinct microstructural-dependent strain gradient tensors. The numerical results reveal that increasing the SiO2 nanoparticle volume fraction significantly enhances both the upper and lower limit loads by nearly 69.5%. This increase does not markedly affect the axial resultant load or the lateral deflection. Conversely, increasing the SiO2 nanoparticle diameter at a fixed volume fraction notably decreases the load-bearing capacity by about 49.5%. Similarly, a rise in graphene nanoplatelet thickness leads to an approximately 61.1% reduction in the stability limits. The inclusion of the interphase region between the nanofillers and the matrix improves the upper and lower limit loads by around 17.4%, demonstrating its reinforcing influence. Furthermore, aligning nanofillers along the beam's longitudinal direction increases the limit loads by roughly 48.1% compared to the random dispersion case. In contrast, agglomeration has the opposite effect, reducing the load-carrying capacity by about 12.4%. © 2025 Elsevier Ltd