Data-driven enhancement of fracture paths in random composites

A data-driven framework for the enhancement of fracture paths in random heterogeneous microstructures is presented. The approach relies on the combination of manifold learning, introduced to explore the geometrical structure exhibited by crack patterns and achieve efficient dimensionality reduction, and a posteriori crack path reconstruction, defined through a Markovianization. The proposed methodology enables the generation of new crack patterns, the underlying structure and dynamical properties of which are consistent, by construction, with those obtained from high-fidelity computations. These sampled cracks can subsequently be used to enrich datasets and perform uncertainty quantification at multiple scales, at a fraction of the computational cost associated with full-scale simulations. A numerical example where the initial dataset is obtained from a recently developed gradient damage formulation is provided to demonstrate the effectiveness of the method. While the methodology is presently applied to digital data, it can also be deployed on experimental measurements.