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A Multiscale Method for Damage Analysis of Quasi-Brittle Heterogeneous Materials

Filip Putar1, Jurica Sorić1,*, Tomislav Lesičar1, Zdenko Tonković1

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

* Corresponding Author: Jurica Sorić. Email: .

Computer Modeling in Engineering & Sciences 2019, 120(1), 123-156.


A novel multiscale algorithm based on the higher-order continuum at both micro- and macrostructural level is proposed for the consideration of the quasi-brittle damage response of heterogeneous materials. Herein, the microlevel damage is modelled by the degradation of the homogenized stress and tangent stiffness tensors, which are then upscaled to govern the localization at the macrolevel. The C1 continuity finite element employing a modified case of Mindlin’s form II strain energy density is derived for the softening analysis. To the authors’ knowledge, the finite element discretization based on the strain gradient theory is applied for the modeling of damage evolution at the microstructural level for heterogeneous materials for the first time. The advantage of the novel C1 finite element formulation in comparison with the standard finite element discretization in terms of the regularization efficiency as well as the objectivity has been shown. An isotropic damage law is used for the reduction of the constitutive and nonlocal material behaviour, which is necessary for the physically correct description of the localization formation in quasi-brittle materials. The capabilities of the derived finite element to capture the fully developed localization zones are tested on a random representative volume element (RVE) for several different loading cases. By employing the conventional second-order computational homogenization, the microstructural material constitutive response is averaged over the whole RVE area. In order to model the loss of structural integrity when sharp localization is formed across RVE, the specific conditions which detect a completely formed localization zone are developed. A new failure criterion at the microstructural level has been proposed. The derived finite element formulation, as well as the multiscale damage algorithm, are implemented into the finite element program ABAQUS. The capabilities of the presented multiscale scheme to capture the effects of the deformation localization are demonstrated by few benchmark numerical examples.


Cite This Article

Putar, F., Sorić, J., Lesičar, T., Tonković, Z. (2019). A Multiscale Method for Damage Analysis of Quasi-Brittle Heterogeneous Materials. CMES-Computer Modeling in Engineering & Sciences, 120(1), 123–156.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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