TY - JOUR
T1 - Eshelby tensors and overall properties of nano-composites considering both interface stretching and bending effects
AU - Huang, Yezeng
AU - Yan, Peng
AU - Wang, Junbo
AU - Dong, Leiting
AU - Atluri, Satya N.
N1 - Publisher Copyright:
© 2022 World Scientific Publishing Company.
PY - 2022/3/1
Y1 - 2022/3/1
N2 - In this study, analytical micromechanical models are developed for nanocomposites with both interface stretching and bending effects. First, the interior and exterior Eshelby tensors for a spherical nano-inclusion, with an interface defined by the Steigmann-Ogden (S-O) model, subjected to an arbitrary uniform eigenstrain are derived. Correspondingly, the stress/strain concentration tensors for a spherical nano-inhomogeneity subjected to arbitrary uniform far-field stress/strain loadings are also derived. Using the obtained concentration tensors, the effective bulk and shear moduli are derived by employing the dilute approximation and the Mori-Tanaka method, respectively, which can be used for both nano-composites and nano-porous materials. An equivalent interface curvature parameter reflecting the influence of the interface bending resistance is found, which can significantly simplify the complex expressions of the effective properties. In addition to size-dependency, the closed form expressions show that the effective bulk modulus is invariant to interface bending resistance parameters, in contrast to the effective shear modulus. We also put forward a characteristic interface curvature parameter, near which the effective shear modulus is affected significantly. Numerical results show that the effective shear moduli of nano-composites and nano-porous materials can be greatly improved by an appropriate surface modification. Finally, the derived effective modulus with the S-O interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.
AB - In this study, analytical micromechanical models are developed for nanocomposites with both interface stretching and bending effects. First, the interior and exterior Eshelby tensors for a spherical nano-inclusion, with an interface defined by the Steigmann-Ogden (S-O) model, subjected to an arbitrary uniform eigenstrain are derived. Correspondingly, the stress/strain concentration tensors for a spherical nano-inhomogeneity subjected to arbitrary uniform far-field stress/strain loadings are also derived. Using the obtained concentration tensors, the effective bulk and shear moduli are derived by employing the dilute approximation and the Mori-Tanaka method, respectively, which can be used for both nano-composites and nano-porous materials. An equivalent interface curvature parameter reflecting the influence of the interface bending resistance is found, which can significantly simplify the complex expressions of the effective properties. In addition to size-dependency, the closed form expressions show that the effective bulk modulus is invariant to interface bending resistance parameters, in contrast to the effective shear modulus. We also put forward a characteristic interface curvature parameter, near which the effective shear modulus is affected significantly. Numerical results show that the effective shear moduli of nano-composites and nano-porous materials can be greatly improved by an appropriate surface modification. Finally, the derived effective modulus with the S-O interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.
KW - Eshelby tensors
KW - Papkovich-Neuber solution
KW - Steigmann-Ogden interface model
KW - effective modulus
KW - spherical nano-inhomogeneity
UR - http://www.scopus.com/inward/record.url?scp=85124252780&partnerID=8YFLogxK
U2 - 10.1142/S2424913021420091
DO - 10.1142/S2424913021420091
M3 - Article
AN - SCOPUS:85124252780
SN - 2424-9130
VL - 7
SP - 49
EP - 59
JO - Journal of Micromechanics and Molecular Physics
JF - Journal of Micromechanics and Molecular Physics
IS - 1
ER -