A review on the size-dependent bulking, vibration and, wave propagation of nanostructures

Size effect is a typical characteristic of micro-/nano-materials, which can contribute to a variety of size-dependent behaviors, phenomena, and properties, such as stiffness softening, deformation springback, etc. The intrinsic causes of size effects are micro-structural properties of materials, and the sensitivity of microstructural properties of materials is closely related to the smallest structural unit of the crystal, crystal defects and geometric dimensions, and is heavily influenced by the material's field conditions. The modeling method based on non-local theory and gradient theory in the model is not only consistent with experimental and molecular dynamics simulation results, but also provides a solid explanation for the size effect underlying 'softening' and 'hardening' behaviors. Taking this as a basic point, this paper further considers the real working environment of materials, and systematically reviews the static and dynamic mechanical behavior cases of various nano-structures, mainly involving bulking, vibration and wave propagation of micro-beams and plates under different theories. A description and discussion of the differences in mechanical properties resulting from size effects under various theoretical frameworks and three key bottleneck problems are provided: the selection of kernel functions, the determination of size parameters, and the physical meaning of boundary conditions at higher orders. A summary is provided of the possible avenues and potentials for size effect models in future research. Many studies have shown that size parameters have a significant impact on the mechanical behavior of micro-/nano-structures, and these effects will increase as the size of the structure decreases. Nevertheless, different theories have varying scopes of application and size effects, and further research is needed to develop a unified size-dependent theory with universal applicability. A major focus of this paper is on the size effect of micro-/nano-structures, as well as provides the necessary data support to resolve the bottleneck problem associated with the size effect in the processing and manufacturing industries, and realizes the design and optimization of micro-scale parts based on their size.