Application of the mixed formulation method to eliminate shear-locking phenomenon in the Peridynamic Mindlin plate model

Accurately predicting crack propagation in structures remains a key challenge within the finite element method (FEM) framework. Despite developing the local method to mitigate the challenges encountered in the FEM, this method is computationally demanding and inadequate for accurately modeling fracture processes in actual structures. Recently, a powerful nonlocal method, Peridynamics (PD), has been proposed by employing integral equations rather than differential equations to address various discontinuous problems. This study introduces the classical Peridynamic Mindlin plate theory (classical PD) to characterize the kinematics of thick plates. However, the application of the classical PD to extremely thin plate structures results in a shear-locking phenomenon, causing inaccuracies in the solutions. Although the reduced integration with a single-point rule provides an alternative solution to address the shear-locking problem, its sensitivity to the point number in the horizon becomes especially pronounced in the case of discontinuities. To ensure stability and broad applicability, this paper presents a more general mixed formulation method (mixed PD) that can yield accurate results ranging from very thick to thin plate configurations. The efficacy of the mixed PD is demonstrated via several numerical cases.