A new thermoelastic model for agglomerated and randomly-oriented CNT-reinforced bio-inspired materials: Temperature-dependent free vibration analysis of FG-CNTR-TPMS plates

A new thermoelastic model is introduced to reveal equivalent mechanical and thermal properties of randomly oriented (RO), agglomerated carbon nanotube (CNT) inclusions within a matrix material. Thereafter, a bio-inspired FG-CNTR-TPMS material model is established through three typical triply periodic minimal surfaces (TPMS) microstructures reinforced with CNTs and functionally graded (FG) schemes. The free vibration behavior of macro-scale plates made from FG-CNTR-TPMS materials under thermal effects and material temperature dependencies is then devised. A new higher-order shear deformation (HSDT) five-variable plate theory incorporated with isogeometric analysis (IGA) is proposed to show its reliability and efficiency. Various material conditions have been thoroughly studied, emphasizing the influence of CNT reinforcement states and environment temperatures. While increasing the CNT volume fraction ($f_r$) greatly improves the plate frequencies, the temperature rise ($\Delta T$) leads to an opposite influence. These properties can amplify or weaken the effects of porosity distributions on the plate’s natural frequencies both beneficial and unfavorable aspects. Notably, the outstanding elastic modulus of IWP-type TPMS enlarges the initial thermal stress and ratio between mechanical and thermal stiffness, causing greater impacts on plate behaviors in the thermal environment. In some exceptional cases, FG-CNTR-TPMS plates with P-type can exceed isotropic plates in stiffness-to-weight ratios, which is an extraordinary characteristic of porous structures. In various scenarios of CNT agglomeration, this natural phenomenon shows noticeable reductions in plate frequencies up to 40% when considering temperature changes. Bridging the gap between TPMS-based lattice structures and CNT-reinforced composites, this study contributes to advancing the knowledge of advanced bio-inspired materials. The findings from this work can revolutionize their potential applications in various engineering areas, particularly biomedical devices, energy storage, flexible electronics, advanced textiles, and soft robotics, where lightweight, high-strength, and temperature-resistant structural components are critical.