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Structural Engineering and Mechanics
  Volume 89, Number 2, January25 2024 , pages 199-211

Ductile fracture simulation using phase field approach under higher order regime
Nitin Khandelwal and Ramachandra A. Murthy

    The loading capacity of engineering structures/components reduces after the initiation and propagation of crack eventually leads to the final failure. Hence, it becomes essential to deal with the crack and its effects at the design and simulation stages itself, by detecting the prone area of the fracture. The phase-field (PF) method has been accepted widely in simulating fracture problems in complex geometries. However, most of the PF methods are formulated with second order continuity theoryinvolving C0 continuity. In the present study, PF method based on fourth-order (i.e., higher order) theory, maintaining C1 continuity has been proposed for ductile fracture simulation. The formulation includes fourth-order derivative terms of phase field variable, varying between 0 and 1. Applications of fourth-order PF theory to ductile fracture simulation resulted in novelty in this area. The proposed formulation is numerically solved using a two-dimensional finite element (FE) framework in 3-layered manner system. The solutions thus obtained from the proposed fourth order theory for different benchmark problems portray the improvement in the accuracy of the numerical results and are well matched with experimental results available in the literature. These results are also compared with second-order PF theory and a comparison study demonstrated the robustness of the proposed model in capturing ductile behaviour close to experimental observations.
Key Words
    finite element method; fourth order theory; phase field method; second order theory; user-defined element
Nitin Khandelwal and Ramachandra A. Murthy: CSIR-Structural Engineering Research Centre, Taramani, Chennai, 600113, India

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