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Abstract:
A comprehensive finite element-meshfree multiscale numerical framework is developed to investigate the size-dependent nonlinear asymmetric instability behavior of carbon nanofiber (CNF)-silicon carbide (SiC) nano-particle hybrid reinforced micro-arches subjected to radial concentrated loads applied at different positions. At the nanoscale, a finite-element-based homogenization strategy employing 3D periodic representative volume elements (RVEs) is developed to compute the effective elastic properties of nanocomposites reinforced with SiC nanoparticles and cylindrical CNFs, accounting for interphase characteristics. These homogenized material constants are subsequently incorporated into a nonlocal strain gradient theory (NSGT)-based radial point interpolation meshfree formulation, enhanced with an adaptive background decomposition integration approach to capture load location-sensitive nonlinear stability responses accurately. Numerical results demonstrate a pronounced multiscale coupling effect: increasing the CNF volume fraction from 1% to 4% results in approxi-
mately a 52% enhancement in all critical limit point loads, while increasing the SiC nanoparticle content from 1% to 5% increases them by nearly 29%. The relative interphase thickness provides a moderate gain of approximately 4.8%, and increasing the CNF aspect ratio strengthens the instability resistance by about 12.8%.
Conversely, increasing the SiC nanoparticle diameter results in a nearly 10.9% reduction in load-carrying capacity, indicating the superior reinforcing efficiency of smaller nanoparticles at a fixed volume fraction. Overall, the proposed framework successfully captures the highly nonlinear, curvature-sensitive, and size-dependent
instability characteristics of hybrid CNF-SiC micro-arches, offering a powerful predictive tool for the optimal design of advanced micro-scale structural components

Keywords:
Nonlinear stability, Meshfree approach, Size dependency, Finite element method, Hybrid composites