A second strain gradient damage model with a numerical implementation for quasi-brittle materials with micro-architectures

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Abstract

In this paper, a quasi-brittle damage model for micro-architectural materials is presented within the framework of isogeometric analysis to exploit the high-order continuity of the non-uniform B-spline basis functions. The constitutive relation depends not only on the strain field, but also on their first and second strain gradient terms. The simplified second-gradient elasticity formulation from Mindlin's theory is employed with corresponding micro-architecture-related length scales to capture the material nonlocality and size effects. The strain-based damage is modelled by a nonlocal independent field coupled to the displacement field. Influences of the two types of nonlocalities (manufactured micro-architectures and damage-induced micro-defects) on the response of structures, as well as the damage initiation and propagation, are analysed through numerical experiments. A formula to determine the micro-defect-related length scale from macroscopic measurements is proposed, boosting the accuracy and applicability of the model. In addition, relevant open problems and further developments of this damage model are discussed.

Details

Original languageEnglish
Article number1081286519884695
Number of pages32
JournalMATHEMATICS AND MECHANICS OF SOLIDS
Publication statusE-pub ahead of print - 4 Nov 2019
MoE publication typeA1 Journal article-refereed

    Research areas

  • Fracture, continuum damage, strain localization, strain gradient elasticity, quasi-brittle materials, isogeometric analysis, FINITE-ELEMENT-METHOD, PHASE-FIELD MODELS, ISOGEOMETRIC ANALYSIS, CHARACTERISTIC LENGTH, FRACTURE, ELASTICITY, FAILURE, FORMULATIONS, CRACKS, LOCALIZATION

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