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Strain-Gradient Elasticity Theory for the Mechanics of Fiber Composites Subjected to Finite Plane Deformations: Comprehensive Analysis

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Abstract

A general model for the mechanics of fiber-reinforced composites is delivered in finite-plane elastostatics. Within the framework of the nonlinear strain-gradient theory, we obtain the Euler equilibrium equations and admissible boundary conditions. In particular, we present a third gradient continuum model and associated formulations. Soft composite materials are also considered by employing the Mooney-Rivlin energy potential. The presented model can be used as an alternative two-dimensional Cosserat theory of nonlinear elasticity.

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Acknowledgements

This work was supported by the Natural Sciences and Engineering Research Council of Canada via Grant #RGPIN 04742 and the University of Alberta through a start-up grant. The author would like to thank Dr. David Steigmann for discussions concerning the underlying theory.

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  1. Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canada

    Chun Il Kim

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Kim, C.I. Strain-Gradient Elasticity Theory for the Mechanics of Fiber Composites Subjected to Finite Plane Deformations: Comprehensive Analysis. Multiscale Sci. Eng. 1, 150–160 (2019). https://doi.org/10.1007/s42493-019-00015-3

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