engleski

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

A novel multiscale algorithm based on the higher-order continuum at both micro- and macrostructural levels 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. 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. 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.

Multiscale analysis, second-order computational homogenization, damage, C1 continuity finite element, quasi-brittle material.

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