A new coupled peridynamic-spring approach for modeling ductile cracked steel plates reinforced with composite patch

In this paper, a novel framework is developed to overcome the limitations of the standard ordinary state-based peridynamic (OSB-PD) method in capturing bond-level shear and rotational effects in composite-patch-reinforced cracked steel plates. The bond between two material points is modeled as an Euler-Bernoulli beam, while the additional degrees of freedom associated with shear and rotation are incorporated through a novel rotational spring in the governing equations. The formulation is derived for an isotropic cracked steel plate coupled with an orthotropic composite patch. The equation of motion is enhanced by introducing shear and rotational force terms obtained from the strain-energy derivatives. The total strain energy accounts for the contributions of sub-elements and rotational springs in the steel plate, interface elements, and orthotropic patch material. The accuracy of the proposed model is assessed through validation against finite element simulations and experimental measurements. Parametric studies are conducted to investigate the effects of crack growth path and branching, initial crack type, reinforcement strategy, composite patch material, and delamination on the structural response of the specimens. The proposed formulation provides a balanced compromise between OSB-PD and NOSB-PD, reducing the computational cost of NOSB-PD by a factor of 4.68 while improving the accuracy of OSB-PD by approximately 17% through the incorporation of bond rotation and shear effects. With a prediction error below 6% relative to experimental results, the proposed model shows strong potential for structural repair and rehabilitation applications.