Homogenization of composites with extended general interfaces: comprehensive review and unified modeling

Interphase regions that form in heterogeneous materials through various underlying mechanisms such as poor mechanical or chemical adherence, roughness, and coating, play a crucial role in the response of the medium. A well-established strategy to capture a finite thickness interphase behavior is to replace it with a zero-thickness interface model characterized by its own displacement and/or traction jumps, resulting in different interface models. The contributions to date dealing with interfaces commonly assume that the interface is located in the middle of its corresponding interphase. This paper revisits this assumption and introduces an extended general interface model, wherein a unifying approach to the homogenization of heterogeneous materials embedding interfaces between their constituents is developed within the framework of linear elasticity. Through utilizing a weighted average operator, we demonstrate that the assumption of enforcing the interface to coincide with the midlayer is not required and thereby develop a new class of interfaces where the interface is allowed to take any arbitrary position between its bulk neighbors. The proposed novel interface model can recover any of the classical interface models. Next, via incorporating this extended general interface model into homogenization, we develop bounds and estimates for the overall moduli of fiber-reinforced and particle-reinforced composites as functions of the interface position and properties. Finally, we carry out a comprehensive numerical study to highlight the influence of interface position, stiffness ratio, and interface parameters on the overall properties of composites. The developed interface-enhanced homogenization framework also successfully captures size effects, which are immediately relevant to emerging applications of nanocomposites due to their pronounced interface effects at small scales.