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Three-Dimensional Lattice Approach to Fractional Generalization of Continuum Gradient Elasticity |
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PP: 243-258 |
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doi:10.18576/pfda/010402
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Author(s) |
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Vasily E. Tarasov,
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Abstract |
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| A relationship between discrete and continuous fractional-order nonlocal elasticity theory is discussed. As a discrete system
we consider three-dimensional lattice with long-range interactions that are described by fractional-order lattice operators.We prove that
the continuous limit of suggested three-dimensional lattice equations gives continuum differential equations with the Riesz derivatives
of non-integer orders. The proposed lattice models give a new microstructural basis for elasticity of materials with power-law type of
non-locality. Moreover these lattice models allow us to have a unified microscopic description for fractional and usual (non-fractional)
gradient elasticity continuum. |
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