Mechanical effects of circular liquid inclusions inside soft matrix: role of internal pressure change and surface tension

Abstract

The mechanical effects of dilute liquid inclusions on the solid-liquid composite are explored, based on an analytical circular inclusion model incorporating the internal pressure change of the liquid and the surface tension of the interface. Several simple explicit dependences of the stress field and effective stiffness on the bulk modulus and the size of the liquid, the surface tension, and Poisson’s ratio of the matrix are derived. The results show that the stresses in the matrix are reduced, and the stiffness of the solid-liquid composite is enhanced with the consideration of either the surface tension or the internal pressure change. Particularly, the effective Young’s modulus predicted by the present model for either soft or stiff matrices agrees well with the known experimental data. In addition, according to the theoretical results, it is possible to stiffen a soft solid by pressured gas with the presence of the surface tension of the solid-gas interface.