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

Abstract 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.