Alleviation of shear locking in the Peridynamic Timoshenko beam model using the developed mixed formulation method

• Published in: Computational particle mechanics 2023-06, Vol.10 (3), p.627-643
• Main Authors: Bai, Ruqing, Naceur, Hakim, Liang, Guan, Zhao, Jinglei, Yi, Jin, Li, Xueping, Yuan, Shujin, Pu, Huayan, Luo, Jun
• Format: Article
• Language: English
• Subjects: Classical and Continuum Physics; Computational Science and Engineering; Continuum mechanics; Differential equations; Engineering; Integral equations; Kinematics; Locking; Shear deformation; Theoretical and Applied Mechanics; Timoshenko beams
• ISSN: 2196-4378; 2196-4386
• DOI: 10.1007/s40571-022-00517-2

Peridynamics (PD) differs from classical continuum mechanics (CCM) and other nonlocal theories that do not involve spatial derivatives of the displacement field. Peridynamics is based on the integral equation instead of differential equations to handle discontinuities and other singularities. In this paper, the standard Peridynamic Timoshenko beam model (standard Peridynamics) accounting for the shear deformation is chosen to describe the thick beam kinematics. Unfortunately, when applied to very thin beam structures, the standard Peridynamics encounters shear locking phenomenon, leading to incorrect solutions. This shear locking can be successfully alleviated using the developed mixed formulation method, especially in nonlinear problems involving plasticity and damage. In particular, this technique has been implemented in the standard Peridynamics, which allows an accurate result for a wide range of slenderness from very thin ( L / t > 10 3 ) to thick ( L / t ∼ 10 ) beam structures. Several numerical examples are solved to demonstrate the effectiveness of the proposed method for modeling beam structures.