A nanocomposites computational tool for all ages and seasons


Nanocomposite materials are finding new applications in diverse areas owing to the potential offered by their unique properties. This is driven by continuously improving fabrication techniques that enable precise realization of material microstructures at the nanoscale (1-20 nm). Hence the investigation of structure-property relationship of these materials is an ongoing endeavor. Knowledge of the elastic material properties and local stress fields is important as they affect the overall functionality of these materials.

Current approaches for the determination of homogenized moduli and local stress fields in nanocomposites are based on well-established classical micromechanics models which neglect adjacent pore or inclusion interactions, thereby producing inaccurate stress fields at higher porosity/inclusion content. Finite-volume and finite-element solutions of periodic nanocomposites provide accurate estimates of local stress fields, but come at much higher computational costs due to tedious input data construction, including unit cell discretization. Hence it is not efficient to employ these approaches in parametric studies and identification of structure-property relationship, which motivates an ongoing search for alternative approaches.

Elasticity-based approaches motivated by the seminal work of Nemat-Nasser and co-workers for periodic heterogeneous materials are attractive alternatives, but have not been widely implemented because of intrinsic solution complexities. The development of the locally-exact homogenization theory (LEHT) at the University of Virginia during the past ten years by Dr. Anthony Drago and recently by Dr. Guannan Wang (presently at Texas Tech University) working with Professor Marek-Jerzy Pindera overcomes many of these limitations due to a novel implementation of periodic boundary conditions which results in an efficient and robust homogenization tool for periodic materials with rectangular, square and hexagonal unit cells characterized by transversely isotropic or radially/circumferentially orthotropic phases. Most recently, Dr. Wang in collaboration with the University of Virginia researchers Qiang Chen, Zhelong He and Professor Pindera, extended the LEHT to enable analysis of nanocomposites by incorporating surface elastic effects based on the Gurtin-Murdoch model, reported in Composites Part B.

The authors demonstrated that the theory provides accurate local stress fields and homogenized moduli for hexagonal and square arrays of nanoporosities in a wide range of pore volume fractions, and pore radii even below 1 nm where most theories break down because of numerical instabilities. The extended theory enables efficient execution of parametric studies owing to the quick convergence and stability of the solution approach, and hence efficient identification of the structure-property relationship even by researchers with little mechanics background due to the simplicity of input data construction (less than half minute). The attached movie illustrates the automated calculation of the transverse Young’s modulus of a hexagonal array of porosities characterized by three sets of surface elastic moduli (A,B,C) as a function of pore content, with the majority of time consumed by the calculation and graphing of local stress fields. The study also has revealed differences in potential failure modes of nanocomposites with different pore arrays which are highly influenced by surface elastic moduli and loading type.

The accuracy of the extended LEHT model has been validated through comparison with other approaches in the determination of local stress concentrations and homogenized moduli in nonoporous aluminum, including classical micromechanics, semi-analytical, numerical and competing elasticity-based methods. The published results provide a convincing proof that the extended LEHT is an accurate and efficient tool in understanding the structure-property relationship in nanoporous materials with substantial surface elasticity effects. The extended theory is also useful in establishing the limits of applicability of the widely-used classical micromechanics approaches with surface effects based on the Gurtin-Murdoch model.


Wang, G., Chen, Q., He, Z., & Pindera, M. (2018). Homogenized moduli and local stress fields of unidirectional nanocomposites. Composites Part B: Engineering138, 265-277.

Go To Composite Part B: Engineering

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