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Absolute and relative size effects within nonlocal strain gradient elastic beam models, II

Castrenze Polizzotto, Paolo Fuschi and Aurora Angela Pisano

Vol. 10 (2022), No. 3, 233–244

The present paper explores the size effects arising in a beam in bending by applying a theory of coherent nonlocal strain gradient (NSG) beam models, i.e., one admitting equivalent integral and differential approaches. Considering shear undeformable Euler–Bernoulli (EB) beams in bending it has been shown that the coherence requisite requires that the constitutive equations incorporate a pair of two-phase local/nonlocal models of which one is driven by strain, and the other by strain gradient. In the present paper a few benchmark beam models in static bending are considered for numerical applications which turn out to be exempt from paradoxical outcomes. Two distinct ways are proposed to evaluate size effects, namely: absolute size effects (with reference to the classic model) and relative size effects (with respect to the equiscale model featured by equal nonlocal and gradient length scale parameters). Absolute and relative size effects coincide only if the equiscale beam behaves as the classical beam (what is generally not true).

nonlocal strain gradient elasticity, absolute size effects, relative size effects, shear undeformable Euler–Bernoulli beams
Mathematical Subject Classification
Primary: 74B99, 74E99
Received: 20 January 2022
Revised: 24 April 2022
Accepted: 29 May 2022
Published: 4 December 2022

Communicated by Francesco dell'Isola
Castrenze Polizzotto
Dipartimento di Ingegneria
University of Palermo
Paolo Fuschi
Dipartimento Patrimonio Architettura Urbanistica
University Mediterranea of Reggio Calabria
Reggio Calabria
Aurora Angela Pisano
Dipartimento Patrimonio Architettura Urbanistica
University Mediterranea of Reggio Calabria
Reggio Calabria