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Modeling of Material Deformation Responses Using Gradient Elasticity Theory

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Multiscale Modeling of Heterogeneous Structures

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 86))

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Abstract

Realistic description of material deformation responses demands more accurate modeling at both macroscopic and microscopic scales. Multiscale techniques employing several homogenization schemes are mostly used, in which a transition between nonlocal and local continuum formulations has been performed. Therein the transition of state variables is not defined fully consistently. In the present contribution a novel multiscale approach is proposed, where the same nonlocal theories at both scales are coupled, and discretisation is performed only by means of the \(C^{1}\) finite element based on the strain gradient theory. The advantage of the new computational procedure is discussed in comparison with the approach using a local concept at microlevel. Employing the strain gradient continuum theory, a damage model for quasi-brittle materials is proposed and embedded into the \(C^{1}\) continuity triangular finite element. The softening response of homogeneous materials under assumption of isotropic damage law is considered. The regularization superiority over the conventional implicit gradient enhancement procedure is demonstrated.

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Acknowledgements

This work has been supported by the Alexander von Humboldt Foundation, Germany, as well as by the Croatian Science Foundation.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000, Zagreb, Croatia

    Jurica Sorić, Tomislav Lesičar, Filip Putar & Zdenko Tonković

Authors
  1. Jurica Sorić
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  2. Tomislav Lesičar
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  3. Filip Putar
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  4. Zdenko Tonković
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Correspondence to Jurica Sorić .

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Editors and Affiliations

  1. University of Zagreb, Zagreb, Croatia

    Jurica Sorić

  2. Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

    Peter Wriggers

  3. LMT Cachan, Cachan, France

    Olivier Allix

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Sorić, J., Lesičar, T., Putar, F., Tonković, Z. (2018). Modeling of Material Deformation Responses Using Gradient Elasticity Theory. In: Sorić, J., Wriggers, P., Allix, O. (eds) Multiscale Modeling of Heterogeneous Structures. Lecture Notes in Applied and Computational Mechanics, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-65463-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-65463-8_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-65462-1

  • Online ISBN: 978-3-319-65463-8

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