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Granular micromechanics model of anisotropic elasticity derived from Gibbs potential

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Abstract

This paper presents a Gibbs potential-based granular micromechanics approach capable of modeling materialswith complete anisotropy. The deformation energy of each grain–pair interaction is taken as a function of the inter-granular forces. The overall classical Gibbs potential of a material point is then defined as the volume average of the grain–pair deformation energy. As a first-order theory, the inter-granular forces are related to the Cauchy stress tensor using a modified static constraint that incorporates directional distribution of the grain–pair interactions. Further considering the conjugate relationship of the macroscale strain tensor and the Cauchy stress, a relationship between inter-granular displacement and the strain tensor is derived. To establish the constitutive relation, the inter-granular stiffness coefficients are introduced considering the conjugate relation of inter-granular displacement and forces. Notably, the inter-granular stiffness introduced in this manner is by definition different from that of the isolated grain–pair interactive. The integral form of the constitutive relation is then obtained by defining two directional density distribution functions; one related to the average grain–scale combined mechanical–geometrical properties and the other related to purely geometrical properties. Finally, as the main contribution of this paper, the distribution density function is parameterized using spherical harmonics expansion with carefully selected terms that has the capability of modeling completely anisotropic (triclinic) materials. By systematic modification of this distribution function, different elastic symmetries ranging from isotropic to completely anisotropic (triclinic) materials are modeled. As a comparison, we discuss the results of the present method with those obtained using a kinematic assumption for the case of isotropy and transverse isotropy, wherein it is found that the velocity of surface quasi-shear waves can show different trends for the two methods.

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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

  2. Department of Civil Engineering, Shanghai Jiao Tong Univ., Dong Chuan Rd., Shanghai, 200240, China

    Anil Misra

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  1. Anil Misra
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Misra, A., Poorsolhjouy, P. Granular micromechanics model of anisotropic elasticity derived from Gibbs potential. Acta Mech 227, 1393–1413 (2016). https://doi.org/10.1007/s00707-016-1560-2

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