An Improved Local Damage Model with Adaptive Mesh Refinement for Quasi-Brittle Materials: Fid-Bau Portal

An Improved Local Damage Model with Adaptive Mesh Refinement for Quasi-Brittle Materials

Van Pham, Manh / Nguyen, Minh Ngoc / Bui, Tinh Quoc

In this paper, an adaptive mesh refinement scheme is utilized to further enhance the local damage model (shortly as the local model) for quasi-brittle materials, for e.g., concrete or limestone. The novelty here is twofold: (i) introduction of an alternative equivalent strain for a local damage model and (ii) incorporation of the proposed model with adaptive mesh refinement. Compared to non-local models, a local damage model is advantageous in term of low computational cost. By taking the characteristic length of element and the material fracture energy into account during calculation of damage parameter, the issue of mesh-dependency being inherent to traditional local models is here mitigated. Based on the so-called bi-energy norm concept, the equivalent strain can be split into tension and compression parts to better model the behavior of materials that exhibit higher compressive strength than tensile strength, like concrete and limestone. Here, the split operator is based on the Mazars model for concrete, resulting in an equivalent strain that has only one parameter for calibration (instead of four parameters as in the Mazars model), yet the accuracy is sufficient. For efficient computation, adaptive mesh refinement is conducted, i.e., the mesh is only updated (refined) in the vicinity of the damage zone. The damage parameter, representing the deterioration of a material point from its initial state to total failure on a scale from 0 to 1, can serve as an indicator for mesh refinement as well. The refinement task is conducted such that each quadrilateral element is divided into four new elements. The issue of hanging nodes is avoided by the employment of polygonal elements instead of the traditional four-node quadrilateral based on Lagrange shape functions. The accuracy and efficiency of the proposed model are demonstrated and analyzed via various numerical examples, in which comparison with results available from experiments and other numerical methods is studied.