Particle inverse method for full-field displacement and crack propagation monitoring from discrete sensor measurements

This study presents the Particle Inverse Method (PIM), a novel structural health monitoring technique for real-time, full-field monitoring of deformations and damages/cracks in structures using discrete sensor data. Towards this end, the PIM mathematically unifies the concepts of the inverse finite element method and peridynamics differential operator for the first time, thus creating a fully meshless approach that relies solely on particle discretization of the physical domain to solve the inverse problem of shape sensing. Utilizing a least squares variational principle, the PIM matches experimental measurements with numerical strains derived through interactions among particles in a non-local framework. This innovative principle allows the reconstruction of continuous deformations in the physical domain (for every particle) from discrete strain data. Additionally, the PIM uses a local damage parameter for each particle, dependent on the integrity of its bonds, to monitor crack development and propagation in real time. Crucially, PIM does not require information about loading or material properties for effective shape sensing and structural health monitoring. The method is applicable even if the crack continues to propagate in the physical domain. The accuracy of PIM is validated through comparative numerical analyses on benchmark problems involving both intact and cracked isotropic plates under tension and shear. Despite the limited number of sensors, PIM demonstrates its ability to accurately map full-field deformations and monitor crack dynamics effectively, highlighting its significant potential for future experimental applications.