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A procedure for the experimental identification of the strain gradient characteristic length

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Abstract

The aim of this paper is to propose an experimental procedure for determining the characteristic length of a strain gradient model. The identification problem is studied through a virtual pull-out test of a rigid bar along the symmetry axis of a cylindrical strain gradient elastic domain. To allow an accurate parameter identification based on measured data, we investigate the effect of the characteristic length on the mechanical fields for this problem. We see a significant sensitivity of the inflection point of the displacement profile evaluated on the cross section of the cylinder, with respect to the characteristic length. By adjusting the characteristic length of the strain gradient such that the theoretical models match best with experimental measurements of the surface displacement fields, the characteristic length of the strain gradient can be estimated. In order to allow for more efficient analysis and an almost real-time parameter identification, the initial three-dimensional (3D) problem is reduced to a one-dimensional (1D) problem by exploiting the cylindrical symmetry of the problem. As will be shown, an accurate 1D finite element method (FEM) strain gradient solution can be obtained for this simplified problem. Since the cylindrical symmetry is only true in an infinitely long cylinder, specific boundary conditions are constructed on a cylinder of finite length, which is then used for the comparison of the 1D and 3D problems. Results show, however, that the structural response at the inflection point is insensitive to whether the specific boundary conditions are considered or not, which is why the 1D model can be used for parameter identification. Since the proposed approach is methodological, it can be applied to any material. As a prototype problem in this paper, we consider the case of a bar embedded in Portland cement concrete.

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Funding

Erasmus+ (2020-1-IT02-KA103-078163), Deutsche Forschungsgemeinschaft (DFG) (392564687).

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Authors and Affiliations

  1. Faculty of Engineering, International Telematic University UNINETTUNO, Corso Vittorio Emanuele II 39, 00186, Rome, Italy

    Nasrin Rezaei & Luca Placidi

  2. Università degli Studi Niccolò Cusano, Rome, Italy

    Nasrin Rezaei

  3. Ruhr-University Bochum, University street 150, 44801, Bochum, Germany

    Johannes Riesselmann & Daniel Balzani

  4. Department of Civil and Environmental Engineering, Florida International University, Miami, USA

    Anil Misra

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  1. Nasrin Rezaei
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  5. Luca Placidi
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Contributions

NR wrote the main manuscript text in consultation with JR, DB, and AM. LP and AM conceived the original idea. Luca Placidi supervised the project. The results were discussed, and the manuscript was commented on by all authors.

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Correspondence to Nasrin Rezaei.

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Rezaei, N., Riesselmann, J., Misra, A. et al. A procedure for the experimental identification of the strain gradient characteristic length. Z. Angew. Math. Phys. 75, 80 (2024). https://doi.org/10.1007/s00033-023-02181-9

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  • DOI: https://doi.org/10.1007/s00033-023-02181-9

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