Interplay of liquid particles and interphases on the macroscopic elastic response of Liquid-filled composites

This paper deals with providing the effective elastic response of three-phase composites consist of a matrix filled with a random suspension of liquid-filled capsules firmly bonded to the matrix in the realm of small deformation theory. The capsules shell (interphases) and the matrix are considered to be elastic solids and the liquid is considered ideal. For this purpose, the solution for dilute concentrations of the interphases and the liquid particles are derived analytically. Then, the dilute solution is passed to an iterative technique to generate the non-dilute version of the solution. The non-dilute response is available in terms of a system of two nonlinear-coupled -ODE-initial-value problems. The results are confronted with the results of a 3D full-field FE analysis and experimental data and a good agreement is observed. The solution, provided here for polydisperse microstructures, allows for considering different thicknesses for the interphases and in turn can possibly account for different physical phenomena like the size and the surface tension effects. A comprehensive study on the effects of interphases (capsules shell) thickness and mechanical properties as well as the volume concentration of the capsules and the liquid particles on the overall elastic properties of three-phase liquid-filled composites are carried out. We show that although the addition of liquid particles to the matrix has deteriorating effects on the overall elastic properties of the composites, proper selection of the interphases can compensate for these negative effects.