A finite element implementation of the stress gradient theory

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dc.contributor.authorKaiser, Tobias
dc.contributor.authorForest, Samuel
dc.contributor.authorMenzel, Andreas
dc.date.accessioned2021-03-12T11:28:30Z
dc.date.available2021-03-12T11:28:30Z
dc.date.issued2021-03-02
dc.description.abstractIn this contribution, a finite element implementation of the stress gradient theory is proposed. The implementation relies on a reformulation of the governing set of partial differential equations in terms of one primary tensor-valued field variable of third order, the so-called generalised displacement field. Whereas the volumetric part of the generalised displacement field is closely related to the classic displacement field, the deviatoric part can be interpreted in terms of micro-displacements. The associated weak formulation moreover stipulates boundary conditions in terms of the normal projection of the generalised displacement field or of the (complete) stress tensor. A detailed study of representative boundary value problems of stress gradient elasticity shows the applicability of the proposed formulation. In particular, the finite element implementation is validated based on the analytical solutions for a cylindrical bar under tension and torsion derived by means of Bessel functions. In both tension and torsion cases, a smaller is softer size effect is evidenced in striking contrast to the corresponding strain gradient elasticity solutions.en
dc.identifier.urihttp://hdl.handle.net/2003/40081
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-21958
dc.language.isoende
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectGeneralised continuumen
dc.subjectStress gradient theoryen
dc.subjectStress gradient elasticityen
dc.subjectStrain gradient elasticityen
dc.subjectFinite elementsen
dc.subjectAnalytical solutionsen
dc.subject.ddc620
dc.subject.ddc670
dc.subject.rswkKontinuumsmechanikde
dc.subject.rswkFinite-Elemente-Methodede
dc.subject.rswkAnalytische Lösungde
dc.subject.rswkMindlin-Reissner plate theoryen
dc.titleA finite element implementation of the stress gradient theoryen
dc.typeTextde
dc.type.publicationtypearticlede
dcterms.accessRightsopen access
eldorado.secondarypublicationtruede
eldorado.secondarypublication.primarycitationKaiser, T., Forest, S. & Menzel, A. A finite element implementation of the stress gradient theory. Meccanica (2021).de
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1007/s11012-020-01266-3de

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