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Modeling and numerical investigation of damage behavior in pantographic layers using a hemivariational formulation adapted for a Hencky-type discrete model

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Abstract

In this study, a hemivariational formulation is presented for a Hencky-type discrete model to predict damage behavior in pantographic layers. In the discrete model, elastic behavior of pantographic layers is modeled via extensional, bending and shear springs. A damage descriptor is added for each spring type. Such a damage descriptor is non-decreasing function of time, and therefore, the standard variational formulation of the problem is generalized to a hemivariational one providing not only the Euler–Lagrange equations for the evolution of the displacements of all the standard degrees of freedom but also the Karush–Khun–Tucker condition governing the evolution of damage descriptor. The dissipation energy included in the hemivariational formulation depends upon six additional constitutive parameters (two per each spring type), and the mechanical behavior of layer is simulated with an efficient and smart strategy able to solve the nonlinear equilibrium equations coupled with the evolution of damage variables. A metallic pantographic layer which was experimentally investigated in the literature is considered to test the proposed formulation.

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Notes

  1. The hypothesis of pantographic layer with orthogonal beams can easily be removed as proven in [47].

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Authors and Affiliations

  1. International Research Center for the Mathematics and Mechanics of Complex Systems, University of L’Aquila, L’Aquila, Italy

    M. Erden Yildizdag

  2. Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Turkey

    M. Erden Yildizdag

  3. Engineering Faculty, International Telematic University Uninettuno, Rome, Italy

    Luca Placidi

  4. Department of Architecture, Design and Urban Planning, University of Sassari, Alghero, Italy

    Emilio Turco

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  1. M. Erden Yildizdag
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  2. Luca Placidi
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Correspondence to M. Erden Yildizdag.

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Erden Yildizdag, M., Placidi, L. & Turco, E. Modeling and numerical investigation of damage behavior in pantographic layers using a hemivariational formulation adapted for a Hencky-type discrete model. Continuum Mech. Thermodyn. 35, 1481–1494 (2023). https://doi.org/10.1007/s00161-022-01154-z

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