Homogenization of Composites with Extended General interfaces: Comprehensive Review and Unified Modeling

Abstract

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. We revisit this assumption and introduce a universal interface model, wherein a unifying approach to the homogenization of heterogeneous materials embedding interfaces between their constituents is developed. The proposed novel interface model is universal in the sense that it can recover any of the classical interface models. Next, via incorporating this universal 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. Furthermore, we elaborate on the computational implications of this interface model. 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, where an excellent agreement between the analytical and computational results is observed. The developed interface-enhanced homogenization framework also successfully captures size effects, which are immediately relevant to emerging applications of nano-composites due their pronounced interface effects at small scales.

Anisotropic imperfect interface in elastic particulate composite with initial stress

“…To be specific, we consider a composite with the volume fraction c of inhomogeneities imperfectly bonded to the matrix. In this case, the equivalent inhomogeneity is a sphere of radius R * (R c /R * ) 3 = c with the unknown effective properties k * and α * , perfectly bonded to the matrix. Continuity of the radial displacement and stress fields…”

“…The unit cell of this structure is a cube with side length a, containing a single inhomogeneity. The volume fraction of inhomogeneities is c = V 1 /V , where V = a 3 and V 1 = 4πR 3 1 /3 are the volumes of the unit cell and the inhomogeneity, respectively. Consideration of the many-particle representative unit cell model follows the same pattern [59].…”

“…Thus, formulations of the models that accurately and efficiently describe the effects of interphases and interfaces on thermomechanical behavior of micro-and nanostructured solids are of utmost importance in the mechanics of materials. In view of this, there exists a large body of literature in which the interphase and interface models have been proposed and extensively studied in the context of heat conduction, elasticity, and thermoelasticity; see comprehensive reviews in [1][2][3][4].…”

“…More elaborately, the so-called general interface models allow for jumps in both displacement and traction fields. Development of phenomenological models started as early as in 1940s, see, for example, [15]; the history of development and a long list of references on the topic can be found in [3,4,[16][17][18][19].…”

“…In search of tools that can adequately model nanoscale phenomena, researchers turned their attention to the theory of material surfaces developed in the 1970s by Gurtin and Murdoch [29] and generalized in the 1990s by Steigmann and Ogden [30]. Both Gurtin-Murdoch (G-M) and Steigmann-Ogden (S-O) theories became very popular and were extensively used to study composite materials with nanosized reinforcements, see the reviews in [3,31,32]. In the context of particulate composites with spherical reinforcements, analytical solutions for a single spherical particle with the G-M interface were obtained and used to model the elastic fields [33][34][35][36][37] and effective properties [10,38,39] of particulate nanocomposites.…”