Strain Gradient Elasticity-Based Method for Homogenization of Multiphase Composites
Hemei Ma (Zodiac Aerospace Corporation), Xin-Lin Gao (University of Texas at Dallas)
Prager Medal Symposium in honor of George Weng: Micromechanics, Composites and Multifunctional Materials
Wed 9:00 - 10:30
MacMillan 117
Homogenization methods based on Eshelby’s fourth-order strain transformation tensor, including the Mori-Tanaka method and the self-consistent method, have been playing an important role in composite design and modeling [1,2]. However, these homogenization methods cannot account for size effects experimentally observed in particle-matrix composites at the micron and nano-meter scales, since Eshelby’s original formulation [3] is based on classical elasticity. In this study, a homogenization method is developed for predicting effective elastic properties of multiphase composites using the Eshelby tensors based on a simplified strain gradient elasticity theory (SSGET) (e.g., [4,5]). The macroscopic behavior of such a heterogeneous material is characterized by a homogeneous elastic medium that obeys the constitutive relations in the SSGET. An effective elastic stiffness tensor and an effective material length scale parameter are obtained for the composite. Both of them are found to be dependent not only on the volume fractions and shapes of the inhomogeneities (i.e., phases other than the matrix) but also on the inhomogeneity sizes, unlike what is predicted by the existing homogenization methods based on classical elasticity. The effective elastic stiffness tensor is analytically derived by applying the Mori-Tanaka method and Eshelby’s equivalent inclusion method. It is illustrated that the inhomogeneity size has a large influence on the effective Young’s moduli when the inhomogeneity size is small (at the micron scale). Also, the composite becomes stiffer when the inhomogeneities get smaller. References [1] Weng, G. J., 1984, Int. J. Eng. Sci. 22, 845-856. [2] Weng, G. J., 1990, Int. J. Eng. Sci. 28, 1111-1120. [3] Eshelby, J. D., 1957, Proc. R. Soc. Lond. A 241, 376-396. [4] Gao, X.-L. and Ma, H. M., 2010, Proc. Royal Soc. A 466, 2425-2446. [5] Gao, X.-L. and Ma, H. M., 2010, J. Mech. Phys. Solids 58, 779-797.