Computational homogenization of brittle fracture

• Applicant: Professor Dr. Matti Schneider
• Subject Area: Mechanics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 426323259

For modelling materials with complex microstructure multiscale methods are especially important, i.e. to get hands on material properties which are difficult to determine for anisotropic materials. For hardening material behavior, multiscale methods have reached a high level of maturity and sophistication, both in the mean field context and for computational homogenization.The goal of the proposal is to develop simulation technology to computationally homogenize a special class of brittle fracture models. Building upon recent mathematical results on the periodic and stochastic homogenization of the Francfort-Marigo model, which is often approximated by phase field damage models in mechanics, the (anisotropic) parameters of an effective phase field damage models shall be determined by simulations on complex microstructures. In contrast to methods published so far, the proposed methodology ensures a proper scale transition independent of the applied boundary conditions, because the existence of a representative elementary volume is (mathematically) ensured.The effective (anisotropic) critical energy release rate is computed, for prescribed normal, by the fracture surface (through the microstructure) of minimal area. Using an idea of G. Strang the non-convex minimal surface problem can be transformed into a convex program with unique minimal value. In analogy to segmentation methods used in image processing, performing algorithms are to be identified, enabling the computational homogenization of the Francfort-Marigo model for heterogeneous materials of industrial complexity.To demonstrate the power of the proposed technique, the method shall be implemented in the commercial finite element code Abaqus, and enhanced to work for complex parts.The objectives of the proposed project are:- computation of the fracture surface and the effective critical energy release rate for - complex microstructures based on digital volume images - complex synthetic microstructures - materials with locally isotropic and anisotropic material behavior- fast and robust macroscopic solution of an anisotropic phase field damage modelIn case of approval the project will provide insights for users of phase field damage models, which form of the anisotropic phase field model needs to be assumed and how the associated parameters can be robustly and efficiently computed numerically, provided the corresponding parameters on the microscopic scale are available.

• DFG Programme: Research Grants