A second strain gradient damage model with a numerical implementation for quasi-brittle materials with micro-architectures
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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.
|Number of pages||32|
|Journal||MATHEMATICS AND MECHANICS OF SOLIDS|
|Publication status||E-pub ahead of print - 4 Nov 2019|
|MoE publication type||A1 Journal article-refereed|
- 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