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A singular ES-FEM for plastic fracture mechanics. (English) Zbl 1230.74183
Summary: The stress and strain fields around the crack tip for power hardening material, which are singular as $r$ approaches zero, are crucial to fracture and fatigue of structures. To simulate effectively the strain and stress around the crack tip, we develop a seven-node singular element which has a displacement field containing the HRR term and the second order term. The novel singular element is formulated based on the edge-based smoothed finite element method (ES-FEM). With one layer of these singular elements around the crack tip, the ES-FEM works very well for simulating plasticity around the crack tip based on the small strain formulation. Two examples are presented with detailed comparison with other methods. It is found that the results of the presented singular ES-FEM are closer to reference solution, which demonstrates the applicability and the effectiveness of our method for the plastic field around the crack tip.
##### MSC:
 74S05 Finite element methods in solid mechanics 74R20 Anelastic fracture and damage 74G70 Stress concentrations, singularities
XFEM