A robust identification procedure for phase field fracture mechanics parameters

The classical Phase Field (PF) model for fracture mechanics of brittle materials based on the finite element method involves three parameters in addition to the Poisson ratio v: the Young's modulus E, the fracture toughness Gc, and the internal length scale 1c. The latter is mathematically conceived as a numerical regularization parameter that should tend to zero to recover linear elastic fracture mechanics (LEFM) predictions. To address this issue, a robust algorithm is implemented in MATLAB, which combines Particle Swarm Optimization (PSO) and the Phase Field (PF) approach to fracture based on the finite element method. The algorithm has been applied to a series of uni-axial tensile tests (with E and 1c to be identified) and to three-point bending tests (with E, 1c and also Gc to be identified) on specimens made of ABS material. Results show that the optimal values of E and Gc are consistent in both tests, while 1c presents a significant dependency upon the test type. Therefore, different values of the internal length scale should be identified and used to match the experimental responses under uni-axial tension or bending.