A Method for Elasticity Modulus Calculation in Porous Media with Known Geometry Using the Monte Carlo Technique

Abstract

This study introduces a method for a computational calculus of the Elasticity Modulus (E) of simulated porous media using the Monte Carlo technique. The porous media of known geometry is simulated as an elastic network of central forces, to which a known deformation is applied. The minimum strain energy is calculated applying the Monte Carlo technique. The Elasticity Modulus is obtained from the theoretical relations between the elastic energy of a system and its deformation. The computational method is validated by applying it in systems of known analytic solution and over porous media generated through aggregation algorithm in two dimensions i.e. Random Sequential Aggregation and Diffusion Limited Cluster-Cluster Aggregation (RSA and DLCA respectively). The latter used to simulate the structure of silica aerogels. As for the range of concentrations studied for the DLCA and RSA systems, it was found that the elasticity modulus E decreases as the porosity of the system increases, being the E value higher for the DLCA system with respect to RSA. The method used is able to differentiate the elastic properties for two different aggregation models. Being E values different for equal porosities, the coordination number (Z) was the geometric parameter that best explains the behavior of the Elasticity Modulus.