Nonlocal strain gradient-based isogeometric analysis of graphene platelets-reinforced functionally graded triply periodic minimal surface nanoplates

Recent developments in additive manufacturing (AM) technologies have empowered the design and fabrication of intricate bioinspired engineering structures at the nano/micro scale. However, mathematical modeling and computation of these structures are still challenging. The main target of this study is to address an efficient computational approach for predicting the mechanical behavior of graphene platelets (GPLs)-reinforced functionally graded triply periodic minimal surface (FG-TPMS) nanoplates. The computational model integrates both nonlocal elasticity and strain gradient effects into the NURBS-based isogeometric analysis of these small-scale structures. We establish advanced nanoplate models by combining three sheet-based TPMS architectures with two new porosity distribution patterns and three distribution patterns of GPLs across the thickness direction. Moreover, the present work makes a pioneering attempt to elucidate how the stiffness-hardening and stiffness-softening mechanisms influence FG-TPMS nanoplates reinforced with GPLs. Compared with two common cellular solids, the superiority of TPMS architectures' mechanical performance is demonstrated. Among all, P and IWP TPMS types along with symmetric porosity and GPLs distributions exhibit outstanding behaviors under static bending, free vibration, and dynamic instability. Furthermore, we conducted a performance analysis for the first time, showcasing the superior capabilities of TPMS architectures under dynamic in-plane compressive loads, especially when compared to isotropic plates of equal weight. The findings of this study greatly enhance our understanding of the intricate mechanical responses of GPLs-reinforced TPMS architectures at the small-scale level, contributing to future interdisciplinary applications.