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Granular micromechanics based micromorphic model predicts frequency band gaps

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Abstract

Granular materials are typically characterized by complex structure and composition. Continuum modeling, therefore, remains the mainstay for describing properties of these material systems. In this paper, we extend the granular micromechanics approach by considering enhanced kinematic analysis. In this analysis, a decomposition of the relative movements of interacting grain pairs into parts arising from macro-scale strain as well as micro-scale strain measures is introduced. The decomposition is then used to formulate grain-scale deformation energy functions and derive inter-granular constitutive laws. The macro-scale deformation energy density is defined as a summation of micro-scale deformation energy defined for each interacting grain pair. As a result, a micromorphic continuum model for elasticity of granular media is derived and applied to investigate the wave propagation behavior. Dispersion graphs for different cases and different ratios between the microscopic stiffness parameters have been presented. It is seen that the model has the capability to present band gaps over a large range of wave numbers.

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Authors and Affiliations

  1. Civil, Environmental and Architectural Engineering Department, University of Kansas, 1530 W. 15th Street, Learned Hall, Lawrence, KS, 66045-7609, USA

    Anil Misra & Payam Poorsolhjouy

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  1. Anil Misra
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  2. Payam Poorsolhjouy
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Correspondence to Anil Misra.

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Communicated by Victor Eremeyev, Peter Schiavone and Francesco dell’Isola.

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Misra, A., Poorsolhjouy, P. Granular micromechanics based micromorphic model predicts frequency band gaps. Continuum Mech. Thermodyn. 28, 215–234 (2016). https://doi.org/10.1007/s00161-015-0420-y

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