Quantifying the uncertainties in modeling soft composites via a multiscale approach

Abstract

The goal of this paper is to evaluate the uncertainties in soft composites composed of a soft solid as the matrix filled by incompressible liquid inclusions. The surface stresses at the liquid–solid interfaces can significantly impact the elastic deformation of the bulk composite at the macroscale. Depending on the characteristic dimension, a stiffening or softening can happen. We model the elastic behavior employing a stochastic multiscale approach and counting on well established rules for composites. Insights on the mechanics of elasto-capillary coupling are provided considering the heterogeneity at different length scales. Global sensitivity analysis is performed to quantify the effect of variation in the material properties, surface tension, the size, and the random dispersion and agglomerations of the inclusions. The influence of the model choice at the mesoscale on the uncertainty of the response is also taken into account as an additional source of uncertainty. The results show that the relative stiffness is mainly influenced by the uncertainties in the size of liquid inclusions and the surface tension, while the remaining parameters show a significant interaction effects.