A nonlocal contact formulation for confined granular systems
Marcial Gonzalez and Alberto Cuitino
Journal of the Mechanics and Physics of Solids, Vol. 60, 333-350, 2012
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Abstract
We present a nonlocal formulation of contact mechanics that accounts for the interplay of deformations due
to multiple contact forces acting on a single particle. The analytical formulation considers the effects
of nonlocal mesoscopic deformations characteristic of confined granular systems and, therefore, removes the
classical restriction of independent contacts. This is in sharp contrast to traditional contact mechanics
theories, which are strictly local and assume that contacts are independent regardless the confinement of
the particles. For definiteness, we restrict attention to elastic spheres in the absence of gravitational
forces, adhesion or friction. Hence, a notable feature of the nonlocal formulation is that, when nonlocal
effects are neglected, it reduces to Hertz theory. Furthermore, we show that, under the preceding
assumptions and up to moderate macroscopic deformations, the predictions of the nonlocal contact formulation
are in remarkable agreement with detailed finite-element simulations and experimental observations, and in
large disagreement with Hertz theory predictions---supporting that the assumption of independent contacts
only holds for small deformations. The discrepancy between the extended theory presented in this work and
Hertz theory is borne out by studying periodic homogeneous systems and disordered heterogeneous systems.
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