Abstract
AbstractThe research of a formulation to model non-local interactions in the mechanical behavior of matter is currently an open problem. In this context, a strong non-local formulation based on fractional calculus is provided in this paper. This formulation is derived from an analogy with long-memory viscoelastic models. Specifically, the same kind of power-law time-dependent kernel used in Boltzmann integral of viscoelastic stress-strain relation is used as kernel in the Fredholm non-local relation. This non-local formulation leads to stress-strain relation based on the space Riesz integral and derivative of fractional order. For unbounded domain, proposed model can be defined in stress- and in strain-driven formulation and in both cases the stress–strain relation represent a strong non-local model. Also, the proposed strain driven and stress driven formulations defined in terms of Riesz operators are proved to be fully consistent each another. Moreover, the proposed model posses a mechanical meaning and for unbounded non-local rod is described and discussed in detail.
Funder
Università degli Studi Mediterranea di Reggio Calabria
Publisher
Springer Science and Business Media LLC
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
10 articles.
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