NDLI: Granular micromechanics model of anisotropic elasticity derived from Gibbs potential

Content Provider	Springer Nature Link
Author	Misra, Anil Poorsolhjouy, Payam
Copyright Year	2016
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.
Starting Page	1393
Ending Page	1413
Page Count	21
File Format	PDF
ISSN	00015970
Journal	Acta Mechanica
Volume Number	227
Issue Number	5
e-ISSN	16196937
Language	English
Publisher	Springer Vienna
Publisher Date	2016-02-01
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical and Applied Mechanics Classical Continuum Physics Continuum Mechanics and Mechanics of Materials Structural Mechanics Vibration, Dynamical Systems, Control Engineering Thermodynamics, Heat and Mass Transfer
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering Computational Mechanics

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