Authors:
Amirreza Khodadadian | Leibniz University of Hannover | Germany
Nima Noii | Leibniz University of Hannover | Germany
Maryam Parvizi | TU Wien, Vienna University of Technology | Austria
Mostafa Abbaszadeh | Amirkabir University of Technology | Iran, Islamic Republic of
Thomas Wick | Leibniz University of Hannover | Germany
Clemens Heitzinger | TU Wien, Vienna University of Technology | Austria
The variational phase-field formulation is a thermodynamically consistent framework to compute the fracture failure process. This formulation emanates from the regularized version of the sharp crack surface function (know as Hausdorff measure). Herein, the second-order variational phase-field formulation is employed. Additional to that, a second-order stress degradation state function (intacted-fractured transition formulation) is used as a monotonically decreasing function which is lower semi-continuous.
In this work, by using Bayesian inversion, we strive to determine the unknown and effective phase-field fracture parameters, i.e., shear and bulk modulus as well as Griffith’s critical elastic energy release rate. To that end, a reference value (calculated on a sufficiently small mesh) is chosen as a replacement of measurement, and its posterior distribution is obtained. Due to time and mesh dependency of the phase-field problem, the computational cost is prohibitive. By using Bayesian inversion, we solve the problem with a coarser mesh and fit the parameters. The obtained load-displacement curve (as an important characteristic) is matched with the reference value. In spite of using coarser meshes and therefore significantly lower computational costs (CPU time), the accuracy of the solution is reliable; crack initiation and material fracture time are estimated precisely.