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Higher gradient expansion for linear isotropic peridynamic materials

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    0475571 - MÚ 2018 RIV DE eng J - Journal Article
    Šilhavý, Miroslav
    Higher gradient expansion for linear isotropic peridynamic materials.
    Mathematics and Mechanics of Solids. Roč. 22, č. 6 (2017), s. 1483-1493. ISSN 1081-2865
    Institutional support: RVO:67985840
    Keywords : peridynamics * higher-grade theories * non-local elastic-material model * representation theorems for isotropic functions
    Subject RIV: BA - General Mathematics
    OBOR OECD: Applied mathematics
    Impact factor: 2.545, year: 2017

    Peridynamics is a non-local continuum mechanics that replaces the differential operator embodied by the stress term div S in Cauchy's equation of motion by a non-local force functional L to take into account long-range forces. The resulting equation of motion reads If the characteristic length delta of the interparticle interaction approaches 0, the operator L admits an expansion in delta i that, for a linear isotropic material, reads Where lambda and mu are the LamE moduli of the classical elasticity, and the remaining higher-order corrections contain products of the type T(s)u := Theta(s) . del(2s)u of even-order gradients del(2s)u (i. e., the collections of all partial derivatives of u of order 2s) and constant coefficients Theta(s) collectively forming a tensor of order 2s. Symmetry arguments show that the terms T(s)u have the form where lambda(s) and mu(s) are scalar constants.
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