Size dependent and micromechanical modeling of strain gradient-based nanoparticle composite plates with surface elasticity

• The bending and the free vibration behaviors of strain gradient-based nanocomposite plates with surface elasticity are investigated.
• The plate is modeled according to the modified strain gradient theory and Gurtin and Murdoch surface theory.
• The plate is made of a composite material with a nanocrystalline matrix and nanoparticles reinforcement.
• A multi-phase size-dependent micromechanical model for materials with nano-inhomogeneities is developed.
• Effects of the plate's size and material structure on the deflection and natural frequencies of the plate are investigated.

The bending and free vibration behaviors of strain gradient-based Kirchhoff plates made of nanoparticle composites are investigated with the incorporation of the plate's surface effects. The modified strain gradient theory is used to capture the first-order deformation of the material structure while the impacts of the surface energy and surface tension are represented according to Gurtin and Murdoch surface elasticity theory. The plate is made of a composite material with nanocrystalline matrix and nanoparticles reinforcement. A size-dependent micromechanical model for multi-phase materials is developed to estimate the elastic moduli of the composite plate. This model has the merit to account for the effects of the surface energy of the inhomogeneities inside the composite structure. In addition, the impacts of the interface, grain size of the nanocrystalline matrix, porosity, and size of the reinforcing particles are incorporated into the micromechanical model. A simply supported composite plate consisting of nanocrystalline-silicon as the matrix and Al2O3-nanoparticles as the reinforcement is considered to study the influences of the size of the Si-grains, Al2O3-particles, voids, strain gradient deformation, and plate surface energy and tension on the deflection and natural frequencies of the plate. The results show that a decrease in the plate's thickness is accompanied with a decrease in the plate's deflection and an increase in the plate's natural frequency. Furthermore, the plate's strain gradient and surface tension contribute to its stiffness through a hardening effect while the interface and porosities inside the material structure affect the plate's stiffness with a softening mechanism. The plate's surface energy could stiffen or soften the plate depending on the values of the surface Lame constants. The surface energy of the inhomogeneities inside the material structure may increase or decrease the plate's stiffness, deflection, and natural frequencies depending on the inhomogeneities' sizes, their bulk material parameters, their surface material parameters, and their volume fractions.