Extracting interfacial interactions using elastic field decomposition and a deep complex neural network

Extracting the nonlinear interactions across interfaces for cohesive zone modeling has always been challenging, yet critically important. Experimentally, obtaining displacement fields near discontinuities can be difficult, and tractions must be inferred, subject to assumptions that cannot always be met. The inverse extraction of cohesive laws often relies on forward modeling via the finite element method, which can be computationally cumbersome, particularly when iterative procedures that require many simulations are used in the extraction process. In this paper, a complex-valued neural network with an embedded displacement field solver that enables elastic field decomposition is developed. Furthermore, this inverse approach requires a limited amount of far-field data. With the full-field solution provided by the neural network, the near-tip fracture behavior of the interface is extracted in terms of cohesive laws. Specifically, the pseudo-elastic field surrounding the nonlinear fracture process zone is constructed with complex potentials represented by Jacobi polynomials with unknown coefficients. Subsequently, known probing fields, the interactive J-integral, and the Maxwell-Betti reciprocal work theorem are used to construct equations to solve for the coefficients of the Jacobi polynomials, thereby enabling the extraction of cohesive laws. Following successful validation that employed analytically known fields, the robustness of the developed approach is demonstrated using experimental data collected from laminated beams with a range of interactions between them. The results confirm that interfacial interactions can be efficiently probed using elastic field decomposition, interactive integrals, and a deep complex neural network.