Coupled peridynamic model for geometrically nonlinear deformation and fracture analysis of slender beam structures

Abstract

AbstractSlender beam structures can experience large displacements, large rotations and fractures, even if the structures are only subjected to small loads. A coupling model of peridynamics (PD) and classical continuum mechanics (CCM) for beam fracture analysis in geometrically nonlinear deformations is developed in this study. Firstly, the formulations of virtually nonlinear strain energy density of each incremental step are obtained by using the updated Lagrangian (UL) formulation and von Karman beam theory, then the nonlinear PD beam parameters are established on the geometrically nonlinear micro‐beam bonds via the principle of virtual work and homogenization. Secondly, the coupling model of PD and CCM for geometrically nonlinear beams is proposed, for which the morphing method is applied to create a balance between the stiffness of geometrically nonlinear CCM beam model and the weighted coefficients of geometrically nonlinear PD beam model. Thirdly, a new fracture criterion for PD beam models considering the effect of geometrical nonlinearity is adopted. Finally, the large deformation and fracture analysis of straight beam, spiral slender beam and complex frame subjected to different loading conditions illustrate the validity and accuracy of the proposed PD‐CCM coupling model.