Rot-free mixed finite elements for gradient elasticity at finite strains

  • Through enrichment of the elastic potential by the second-order gradient of deformation, gradient elasticity formulations are capable of taking nonlocal effects into account. Moreover, geometry-induced singularities, which may appear when using classical elasticity formulations, disappear due to the higher regularity of the solution. In this contribution, a mixed finite element discretization for finite strain gradient elasticity is investigated, in which instead of the displacements, the first-order gradient of the displacements is the solution variable. Thus, the C\(^{1}\) continuity condition of displacement-based finite elements for gradient elasticity is relaxed to C\(^{0}\). Contrary to existing mixed approaches, the proposed approach incorporates a rot-free constraint, through which the displacements are decoupled from the problem. This has the advantage of a reduction of the number of solution variables. Furthermore, the fulfillment of mathematical stability conditions is shown for the corresponding small strain setting. Numerical examples verify convergence in two and three dimensions and reveal a reduced computing cost compared to competitive formulations. Additionally, the gradient elasticity features of avoiding singularities and modeling size effects are demonstrated.

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Author:Johannes RiesselmannORCiDGND, Jonas W. KettelerGND, Mira SchedensackGND, Daniel BalzaniORCiDGND
Parent Title (English):International journal for numerical methods in engineering
Place of publication:Weinheim
Document Type:Article
Date of Publication (online):2024/03/07
Date of first Publication:2020/11/26
Publishing Institution:Ruhr-Universität Bochum, Universitätsbibliothek
Tag:finite strains; gradient elasticity; higher-order gradients; mixed finite elements; size effects
First Page:1602
Last Page:1628
Dieser Beitrag ist auf Grund des DEAL-Wiley-Vertrages frei zugänglich.
Institutes/Facilities:Lehrstuhl für Kontinuumsmechanik
Dewey Decimal Classification:Technik, Medizin, angewandte Wissenschaften / Ingenieurbau, Umwelttechnik
open_access (DINI-Set):open_access
faculties:Fakultät für Bau- und Umweltingenieurwissenschaften
Licence (English):License LogoCreative Commons - CC BY 4.0 - Attribution 4.0 International