On the consistency of the nonlocal strain gradient elasticity

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dc.contributor.author Zaera, Ramón
dc.contributor.author Serrano, O.
dc.contributor.author Fernández-Sáez, José
dc.date.accessioned 2020-12-18T11:13:17Z
dc.date.available 2020-12-18T11:13:17Z
dc.date.issued 2019-05
dc.identifier.bibliographicCitation Zaera, R., Serrano, Ó., Fernández-Sáez, J. (2019). On the consistency of the nonlocal strain gradient elasticity. International Journal of Engineering Science, 138, 65–81
dc.identifier.issn 0020-7225
dc.identifier.uri http://hdl.handle.net/10016/31639
dc.description.abstract The nonlocal strain gradient elasticity theory is being widely used to address structural problems at the micro- and nano-scale, in which size effects cannot be disregarded. The application of this approach to bounded solids shows the necessity to fulfil boundary conditions, derived from an energy variational principle, to achieve equilibrium, as well as constitutive boundary conditions inherent to the formulation of the constitutive equation through convolution integrals. In this paper we uncover that, in general, is not possible to accomplish simultaneously the boundary conditions, which are all mandatory in the framework of the nonlocal strain gradient elasticity, and therefore, the problems formulated through this theory have no solution. The model is specifically applied to the case of static axial and bending behaviour of Bernoulli-Euler beams. The corresponding governing equation in terms of displacements results in a fourth-order ODE with six boundary conditions for the axial case, and in a sixth-order ODE with eight boundary conditions for the bending case. Therefore, the problems become overconstrained. Three study cases will be presented to reveal that all the boundary conditions cannot be simultaneously satisfied. Although the ill-posedness has been pointed out for an elastostatic 1D problem, this characteristic holds for other structural problems. The conclusion is that the nonlocal strain gradient theory is not consistent when applied to finite structures and leads to problems with no solution in a general case.
dc.description.sponsorship The authors are indebted to the Ministerio de Ciencia e Innovación de España (Projects DPI-2014-57989-P and BES-2015-073720) for the financial support.
dc.format.extent 17
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2019 The Authors
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Nanobeams
dc.subject.other Nonlocal Strain Gradient
dc.subject.other Constitutive Boundary Conditions
dc.subject.other Bending
dc.subject.other Axial
dc.subject.other 2-Phase Integral Elasticity
dc.subject.other Stress-Driven
dc.subject.other Free-Vibration
dc.subject.other Nano-Beams
dc.subject.other Models
dc.subject.other Nanobeams
dc.subject.other Mass
dc.title On the consistency of the nonlocal strain gradient elasticity
dc.type article
dc.subject.eciencia Ingeniería Industrial
dc.subject.eciencia Ingeniería Mecánica
dc.identifier.doi https://doi.org/10.1016/j.ijengsci.2019.02.004
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. DPI2014-57989-P
dc.relation.projectID Gobierno de España. BES-2015-073720
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 65
dc.identifier.publicationlastpage 81
dc.identifier.publicationtitle International Journal of Engineering Science
dc.identifier.publicationvolume 138
dc.identifier.uxxi AR/0000023715
dc.contributor.funder Ministerio de Ciencia e Innovación (España)
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