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Higher gradient expansion for linear isotropic peridynamic materials
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SYSNO ASEP 0475571 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Higher gradient expansion for linear isotropic peridynamic materials Author(s) Šilhavý, Miroslav (MU-W) RID, SAI, ORCID Source Title Mathematics and Mechanics of Solids. - : Sage - ISSN 1081-2865
Roč. 22, č. 6 (2017), s. 1483-1493Number of pages 11 s. Language eng - English Country DE - Germany Keywords peridynamics ; higher-grade theories ; non-local elastic-material model ; representation theorems for isotropic functions Subject RIV BA - General Mathematics OECD category Applied mathematics Institutional support MU-W - RVO:67985840 UT WOS 000402887700015 EID SCOPUS 85020387341 DOI 10.1177/1081286516637235 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2018
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