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Homogenization of the Mooney-Rivlin coefficients of graphene-based soft sandwich nanocomposites

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Abstract

This paper presents an investigation into the homogenization of the nonlinear behavior of graphene-based soft sandwich nanocomposites via the rule of mixtures (ROM). These composites consist of soft polymers embedded with large contiguous graphene films with unit atomic thickness. They have a representative volume element with a sandwich construction exhibiting in-plane isotropy. Their unique characteristic is that they consist of a matrix and reinforcement which both behave nonlinearly. In this work, the in-plane mechanical behavior of both constituents as well as the composite is modeled via the compressible Mooney-Rivlin (MR) constitutive model. Two approaches to homogenize this nonlinear behavior are considered. The first approach, referred to as the linear ROM, applies the ROM to the initial tangent moduli of the constituents, and derives the composite’s MR coefficients from the homogenized initial tangent modulus. The second approach, referred to as the nonlinear ROM, builds on Ogden’s bounds on the strain energy density, and applies the ROM directly to the MR coefficients of the constituents to derive the composite’s MR coefficients. The predictions from both approaches are compared to the embedded element (EE) technique in Abaqus which enforces a kinematic constraint between the explicitly modeled constituents resulting in a parallel model. It is demonstrated that the nonlinear ROM approach properly homogenizes the entire nonlinear stress-stretch curve (both normal and shear), including the nonlinear Poisson effects, and embodies the correct strain energy density (SED). The linear ROM predicts reasonably the normal stress-stretch curve and the SED, but it does not capture Poisson’s ratio and the shear response well and therefore is not recommended. The nonlinear ROM is found to work for a wide range of stretch values, various reinforcement volume fractions, and loading conditions, especially for high stiffness ratios. For lower stiffness ratios (i.e., for a stiffer matrix), the nonlinear stress-stretch curves (normal and shear) and the SED are captured well by the nonlinear ROM, but not the out of plane Poisson effects, due to the assumed isotropy in the Mooney-Rivlin model. Finally, an analogous approach to determine the variational Hashin-Shtrikman bounds on the homogenized Mooney-Rivlin constants is proposed. These variational bounds are found to be tighter compared to the Voigt and Reuss bounds as expected.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors would like to acknowledge Profs. Matthew Eisaman and Toshio Nakamura of Stony Brook University for their invaluable review of this study.

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This work was supported by Stony Brook University’s Germination Space Funding Award.

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  1. Department of Mechanical Engineering, Stony Brook University, 112 Light Engineering, Stony Brook, NY, 11794, USA

    Mersim Redzematovic & Kedar Kirane

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All authors contributed to the study. Conceptualization: (Kedar Kirane). Methodology: (Mersim Redzematovic and Kedar Kirane). Formal analysis and investigation: (Mersim Redzematovic and Kedar Kirane). Writing — original draft preparation: (Mersim Redzematovic). Writing — review and editing: (Kedar Kirane). Funding acquisition: (Kedar Kirane). Resources: (Kedar Kirane). Supervision: (Kedar Kirane)

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Redzematovic, M., Kirane, K. Homogenization of the Mooney-Rivlin coefficients of graphene-based soft sandwich nanocomposites. Mech Soft Mater 3, 6 (2021). https://doi.org/10.1007/s42558-021-00036-9

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