No abstract

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 C 1 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 C 1 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.

An overview of the modelling of quasi-brittle as well as ductile damage is given. The multiscale procedure employing the nonlocal continuum theory is described in more detail. The softening is introduced at the microlevel in the microstructural volume element and after that the homogenization procedure state variables are mapped at the macrolevel material point via the scale transition approach. In the case of quasi-brittle softening the C1 continuous finite element discretization is applied at both micro- and macrolevel. At the modelling of ductile damage response, the macrolevel is also discretized by the C1 finite element formulation, while the microscale utilizes quadrilateral mixed finite elements employing the nonlocal equivalent plastic strain and gradient-enhanced elastoplasticity. All approaches presented are verified in the standard examples.

Abstract. The present study deals with the modeling of quasi-brittle softening phenomena

No abstract