Coupling of peridynamics and inverse finite element method for shape sensing and crack propagation monitoring of plate structures

A novel structural health monitoring approach is developed by coupling the inverse finite element method (iFEM) and peridynamic theory (PD) for real-time shape sensing analysis and crack propagation monitoring of plate structures. This hybrid method, called iFEM-PD, can account for deformation, stress, and damage states of any sensor-equipped structure in real time without the need for loading knowledge and regardless of the complexity of structural topology or boundary conditions. The integrated iFEM-PD approach first reconstructs continuous (full-field) deformations from discrete strain measurements and then utilizes them to obtain full-field strains within the structure. Subsequently, iFEM-reconstructed strains are employed with a suitable damage diagnosis index to quantify the critical (possibly damaged/cracked) zone of the structural domain. Next, this critical zone is modelled by populating PD material points and establishing non-local interactions between the material points. Enforcing the real-time deformations predicted by iFEM to the boundary material points of the PD domain as displacement boundary conditions, the deformations of the material points located internal to the damaged zone is recalculated through PD analysis. During this simulation, the damage prognosis is achieved by precisely modelling structural discontinuities (crack etc.) and analyzing crack propagation based on non-local particle interactions. The shape sensing and damage monitoring capabilities of the iFEM-PD method are numerically verified for crack monitoring problems of composite structures subjected to various static/dynamic loads. Also, the high accuracy of the iFEM-PD formulation is experimentally validated by comparing the numerical results with those of digital image correlation. Overall, the merits of the new approach are revealed for precise crack growth monitoring in composite structures