The present work investigates the influence of embedding spherical and spheroidal capsules containing the healing agent within the base polymers to create a self-healing effect on the overall mechanical properties of the entire medium, using numerical and analytical homogenization approaches. The effects of geometrical and mechanical parameters, including capsule shape, the healing agent volume concentration, the capsules shell thickness, and mechanical properties on the overall responses of the self-healing composites are studied. A square-array configuration is assumed for the distribution of the capsules. This idealization enables computing the behavior of such composites computationally via FE analysis and variationally using Hashin-Shtrikman upper bound by taking a unit cell composed of a cube of the matrix with a perfectly bonded capsule at its center. The boundary conditions on the unit cell are applied in a way that the deformation of the unit cell captivates the overall mechanical responses of the entire medium. Our results show a general decrease in the overall properties of the composites, which can be alleviated by increasing the thickness of the capsules shell or using a stiffer shell. Additionally, we show that the geometry of the capsule shell plays a role in reducing the drop in the overall properties of the composite.

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