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On Ductile Damage Modelling of Heterogeneous Material Using Second-Order Homogenization Approach

Computer Modeling in Engineering & Sciences 2021年第3期126卷 915-934页

作者： Jurica Soric tomislav lesicar Zdenko Tonkovic Faculty of Mechanical Engineering and Naval Architecture University of ZagrebZagreb10000Croatia

The paper deals with the numerical modelling of ductile damage responses in heterogeneous materials using the classical second-order homogenization *** scale transition methodology in the multiscale framework is *** structure at the macrolevel is discretized by the triangular C^(1) finite elements obeying nonlocal continuum theory,while the discretization of microstructural volume element at the microscale is conducted by means of the mixed type quadrilateral finite element with the nonlocal equivalent plastic strain as an additional nodal *** ductile damage evolution at the microlevel is modelled by using the gradient enhanced *** macrolevel softening is governed by two criterions expressed by the increase in homogenized damage variable and the threshold of the local equivalent *** softening at each material point at the macrolevel is detected by the critical value of the homogenized damage,where homogenization of the damage variable is performed onlywithin softening *** to the nonlocal continuumtheory applied,a realistic softening behaviour is demonstrated after the damage initiation,compared to the widely used first-order homogenization *** algorithms derived have been embedded into the finite element code ABAQUS by means of the user subroutines and verified on the standard benchmark *** damage evolution at both microlevel and macrolevel has been demonstrated.

关键词： Ductile damage second-order homogenization multiscale approach C1 finite element

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

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Computer Modeling in Engineering & Sciences 2019年第7期120卷 123-156页

作者： Filip Putar Jurica Soric tomislav lesicar Zdenko Tonkovic Faculty of Mechanical Engineering and Naval Architecture University of ZagrebIvana Lucica 5Zagreb 10000Croatia

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 ***,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 *** C^1 continuity finite element employing a modified case of Mindlin’s form II strain energy density is derived for the softening *** 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 *** 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 *** 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 *** 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 *** employing the conventional second-order computational homogenization,the microstructural material constitutive response is averaged over the whole RVE *** 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 *** derived finite element formulation,as well as the multiscale damage algorithm,are implemented into the finite element program *** capabilities of the presented multiscale scheme to capture the effects of the deformat

关键词： Multiscale analysis second-order computational homogenization damage,C^(1) continuity finite element quasi-brittle material

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