A hybrid H1×H(curl) finite element formulation for a relaxed micromorphic continuum model of antiplane shear

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dc.contributor.authorSky, Adam
dc.contributor.authorNeunteufel, Michael
dc.contributor.authorMünch, Ingo
dc.contributor.authorSchöberl, Joachim
dc.contributor.authorNeff, Patrizio
dc.date.accessioned2022-03-18T13:52:10Z
dc.date.available2022-03-18T13:52:10Z
dc.date.issued2021-05-17
dc.description.abstractOne approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric microdistortion in the free energy function. This suggests the existence of solutions not belonging to H1, such that standard nodal H1-finite elements yield unsatisfactory convergence rates and might be incapable of finding the exact solution. Our approach is to use base functions stemming from both Hilbert spaces H1 and H(curl), demonstrating the central role of such combinations for this class of problems. For simplicity, a reduced two-dimensional relaxed micromorphic continuum describing antiplane shear is introduced, preserving the main computational traits of the three-dimensional version. This model is then used for the formulation and a multi step investigation of a viable finite element solution, encompassing examinations of existence and uniqueness of both standard and mixed formulations and their respective convergence rates.en
dc.identifier.urihttp://hdl.handle.net/2003/40812
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-22669
dc.language.isoende
dc.relation.ispartofseriesComputational mechanics;Vol. 68. 2021, pp 1–24
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectRelaxed micromorphic continuumen
dc.subjectEdge elementsen
dc.subjectNédélec elementsen
dc.subjectCurl based energyen
dc.subjectMixed formulationen
dc.subjectCombined Hilbert spacesen
dc.subjectMetamaterialsen
dc.subject.ddc690
dc.titleA hybrid H1×H(curl) finite element formulation for a relaxed micromorphic continuum model of antiplane shearen
dc.typeTextde
dc.type.publicationtypearticlede
dcterms.accessRightsopen access
eldorado.secondarypublicationtruede
eldorado.secondarypublication.primarycitationComputational mechanics. Vol. 68. 2021, pp 1–24en
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1007/s00466-021-02002-8de

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