Stochastic second-gradient continuum theory for particle-based materials: part II

This article is the second part of a previous article devoted to the deterministic aspects. Here, we present a comprehensive study on the development and application of a novel stochastic second-gradient continuum model for particle-based materials. An application is presented concerning colloidal crystals. Since we are dealing with particle-based materials, factors such as the topology of contacts, particle sizes, shapes, and geometric structure are not considered. The mechanical properties of the introduced second-gradient continuum are modeled as random fields to account for uncertainties. The stochastic computational model is based on a mixed finite element (FE), and the Monte Carlo (MC) numerical simulation method is used as a stochastic solver. Finally, the resulting stochastic second-gradient model is applied to analyze colloidal crystals, which have wide-ranging applications. The simulations show the effects of second-order gradient on the mechanical response of a colloidal crystal under axial load, for which there could be significant fluctuations in the displacements.