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Two-dimensional strain gradient damage modeling: a variational approach

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Abstract

In this paper, we formulate a linear elastic second gradient isotropic two-dimensional continuum model accounting for irreversible damage. The failure is defined as the condition in which the damage parameter reaches 1, at least in one point of the domain. The quasi-static approximation is done, i.e., the kinetic energy is assumed to be negligible. In order to deal with dissipation, a damage dissipation term is considered in the deformation energy functional. The key goal of this paper is to apply a non-standard variational procedure to exploit the damage irreversibility argument. As a result, we derive not only the equilibrium equations but, notably, also the Karush–Kuhn–Tucker conditions. Finally, numerical simulations for exemplary problems are discussed as some constitutive parameters are varying, with the inclusion of a mesh-independence evidence. Element-free Galerkin method and moving least square shape functions have been employed.

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Acknowledgements

This work was supported by a grant from the Government of the Russian Federation (Contract No. 14.Y26.31.0031)

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Authors and Affiliations

  1. Faculty of Engineering, International Telematic University Uninettuno, C.so Vittorio Emanuele II, 39, 00186, Rome, Italy

    Luca Placidi

  2. Civil, Environmental and Architectural Engineering Department, The University of Kansas, 1530 W. 15th Street, Lawrence, KS , 66045-7609, USA

    Anil Misra

  3. Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma “La Sapienza”, Via Eudossiana, 18, 00184, Rome, Italy

    Emilio Barchiesi

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  1. Luca Placidi
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Placidi, L., Misra, A. & Barchiesi, E. Two-dimensional strain gradient damage modeling: a variational approach. Z. Angew. Math. Phys. 69, 56 (2018). https://doi.org/10.1007/s00033-018-0947-4

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