Effective Elastic Moduli of Spherical Particle Reinforced Composites Containing Imperfect Interfaces

Abstract

The effective elastic moduli of composite materials are investigated in the presence of imperfect interfaces between the inclusions and the matrix. The primary focus is on the spherical particle reinforced composites. By admitting the displacement jumps at the particle–matrix interface, the modified Eshelby inclusion problem is studied anew. To derive the modified Eshelby tensor, three approximate methods are presented and compared by emphasizing the existence of a unique solution and computational efficiency. Subsequently, the effective elastic stiffness tensor of the composite is formulated based on the proposed micromechanical framework and homogenization. Specifically, by incorporating imperfect interface, the modified versions of the Mori–Tanaka method, the self-consistent method, and the differential scheme are presented. By comparing these three methods, the effects of interfacial sliding and separation on the degradation (damage) of the effective elastic moduli of composites are analyzed and assessed. Finally, a critical aspect of the presented formulations is specifically addressed.

Multi-scale approach for modeling the transversely isotropic elastic properties of shale considering multi-inclusions and interfacial transition zone

“…This method is based on the analytical expressions of Eshelby's tensor S developed by Withers [53] and the relations between these two tensors [10]. The components of the tensor P for a transversely isotropic medium can be calculated based on the following expressions [10]: 16 16 …”

“…Actually there are many types of inclusions, such as quartz, calcite and dolomite, in the shale rock [9][10][11][12][13][14]. And the inclusions are not perfectly bonded to the matrix phase of shale rock, which implies that there are interfacial transition zones (ITZs) [16][17][18][19]. To address these issues, in this extension we propose a multiscale (from nanoscale to macroscale) predicting framework for the shale rock's transversely isotropic properties considering the multi-inclusion and ITZ effects with a new multilevel micromechanical homogenization scheme.…”

Micro-scaled size-dependence of the effective properties of 0–3 PZT–cement composites: Experiments and modeling

“…where d jm is the Kronecker delta, a and b are the positive compliance coefficients of the interface related to the tangential sliding and normal separation, respectively [39], and c is positive, signifying the electric compliance coefficient. The modified piezoelectric Eshebly tensor S M , which links the average (extended) strain e Gh induced in the inclusion to the uniform eigenstrain e à Mn prescribed in the inclusion through…”

Multiscale Modeling of Polymer–Nanotube Nanocomposites

“…Since the discontinuity of the displacement affects the perturbed strain field caused by the inclusion, the Eshelby tensor that correlates the eigenstrain and perturbed strain is slightly modified. In a recent reformulation of the modified Eshelby tensor, it has been proven that the range of allowable interfacial compliance to account for the weakened interface is inherently narrow, and therefore singularity of the modified Eshelby tensor exists [71]. For a slightly weakened interface condition, Esteva and Spanos [72] demonstrated the negative impact of the transversely isotropic elastic constant of CNT/EPON862 composites using a modified MT model.…”