engleski

Residual Control Phase-field Staggered Algorithm for Brittle Fracture Modelling of Heterogeneous Microstructure

The phase-field approach to fracture is a diffusive method based on the variational principle of the free energy minimization. It introduces fracture induced dissipation energy term in the total free energy functional, corresponding to the Griffith’s fracture theory. A scalar damage parameter continuously varies over the domain approximating the sharp crack topology, thus eliminating the need for the numerical tracking of the crack displacement discontinuity inherent to the discrete fracture methods. Consequently, the phase-field approach is successful in solving the complex fracture processes even in the three-dimensional settings [1]. A length scale parameter is introduced to regulate the width of the approximated fracture band and govern the regularization of the free energy functional. Therefore, very fine mesh is required to resolve thin crack approximation. Combination of the thick mesh with the commonly used single-iteration staggered solution scheme for the phase-field fracture problem [1, 2] can be computationally very expensive, due to small loading increment requirement, which is essential to provide an accurate solution. In this work, an iterative staggered phase-field fracture model with the stopping criterion based on the control of the residual norm is implemented in the commercial finite element software Abaqus. It utilizes Abaqus advanced convergence control, automatic incrementation and built-in line search algorithm making the implementation more efficient. The model is verified on the several benchmark tests in terms of robustness, accuracy and computational cost. Moreover, a porous microstructure exhibiting crack nucleation and complex crack paths is analyzed. The proposed implementation demonstrates an improvement in the computational efficiency. Additionally, an accurate solution can be obtained independently of the loading increment size.

Phase-field Fracture, Heterogeneous Mictrostructure, Residual Control

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