Solids containing spherical nano-inclusions with interface stresses: Effective properties and thermal–mechanical connections

This work examines the overall thermoelastic behavior of solids containing spherical inclusions with surface effects. Elastic response is evaluated as a superposition of separate solutions for isotropic and deviatoric overall loads. Using a variational approach, we construct the Euler–Lagrange equation together with the natural transition (jump) conditions at the interface. The overall bulk modulus is derived in a simple form, based on the construction of neutral composite sphere. The transverse shear modulus estimate is derived using the generalized self-consistent method. Further, we show that there exists an exact connection between effective thermal expansion and bulk modulus. This connection is valid not only for a composite sphere, but also for a matrix-based composite reinforced by many randomly distributed spheres of the same size, and can be viewed as an analog of Levin’s formula for composites with surface effects.