Structural health monitoring of precracked structures using an in-plane inverse crack-tip element

This study investigates the application of the inverse finite element method (iFEM) in fracture mechanics by developing a novel two-dimensional six-node triangular inverse crack-tip element. With its simplified formulation, the proposed inverse element is computationally efficient and ensures strain singularity at the crack tip by repositioning midside nodes. Its displacement-based stress intensity factor (SIF) computation methodology integrates seamlessly with the existing iFEM framework, making it highly suitable for real-time health assessment of structures with pre-existing cracks. The inverse element has been rigorously validated for shape-sensing and mixed-mode SIF calculations by considering various crack geometries and mixed-mode loading conditions. The triangular inverse element demonstrates superior flexibility in handling structured and unstructured discretizations in mapping regular and complex geometries, particularly high-stress gradient areas like crack tips. The study also explores the variational least squares method for optimal sensor placement within the inverse element domain, ensuring accurate shape-sensing and SIF computations with fewer onboard strain sensors. The proposed inverse formulation, with its accurate shape-sensing capabilities and precise reconstruction of fracture parameters, represents a significant advancement in the real-time Structural Health Monitoring of engineering structures with pre-existing cracks.