Multi-parameter optimization of layered WS2-polymer nanocomposite under mechanical loading

Abstract

The aim of the study is to determine the optimal geometry and magnitude of the applied load to ensure safety and prevent delamination in a three-layered nanocomposite structure under axial mechanical loading. The structure consists of a layer of the nanomaterial tungsten disulfide (WS₂) and a substrate layer of poly(methyl methacrylate) (PMMA), which are adhesively bonded using SU-8 glue. To achieve this aim, a multi-parameter optimization problem (MOP) is formulated. It includes a two-dimensional stress function model that describes stress transfer in the considered three-layer structure. Two types of analytical solutions for the interface shear stress (ISS) are derived, featuring real and complex roots. The decision variables in MOP include the external load, layer thicknesses, and structure length. The optimization criterion is defined as the minimization of the difference between the model ISS and ultimate shear stress (USS) in the adhesive layer to assure no delamination occurs in the nanocomposite structure. A genetic algorithm and alternative optimization approach developed within the framework of “Mathematica” are implemented for the optimization of both model solutions. As a result, optimal values for the given external load, layer thicknesses, and structure length are obtained for considered nanostructure. For the case of an ISS model solution with real roots, the optimization procedures ensure optimal geometries that physically correspond to thinner structural layers, but they are limited at lower possible loads. In contrast, for the case of a model solution for the ISS with complex roots, solutions for the optimal geometries of the nanostructures were obtained with thicker layers requiring higher loads, than thinner ones, but delamination does not occur.