Discovering the size effects in nanoporous structures: theoretical analysis and computational investigation

Structures exhibit uncommon physical properties such as ultra-high quality factor, nonlinear damping, and the abrupt change of Young's modulus when their size approaches 1 nm to 100 nm. Such amazing properties upon the length scale is the so-called size effects. Though previous experimental studies reveal that the nanostructures do not comply with the classical continuum theories at nano-scale, their inherent mechanism is still unclear yet. The work in this dissertation aims to develop a computational method to predict the size effects for nanoporous materials and introduce the method of structural topology optimisation into the utilization of size effects in micro/nano-electrical/mechanical system, ultra-high sensitive sensor, lightweight structure and high-strength material. To achieve the aforementioned aims, a framework in terms of the combination of surface elasticity theory and the generalized Young-Laplace equation is established to evaluate the size effects. By modelling the nanoporous gold as a complex cellular architecture in theoretical analysis, the abrupt change in Young's modulus at nano-level is formulated and can be verified in previous experiments. <br><br>Subsequently, an iterative algorithm based on finite element analysis is developed to allow this method applicable to the nanostructures in an arbitrary shape. The proposed computational method clearly shows that size effects are highly dependent on the structural shape and topology at the nanoscale. By assuming the complex structures as a system of interconnected beams, I proposed a beam element to incorporate the size effects in finite element analysis. This general method paves the way to apply the method of structural topology optimization in the design of nanoporous structures. Its versatile and powerful functions will fuel up the utilization of size effects in future.