A stable non‐ordinary state‐based peridynamic model for laminated composite materials

Abstract

Non-ordinary state-based peridynamics (NOSBPD) has instability issue due to zero-energy modes during nodal integration. A zero-energy mode controlling scheme of NOSBPD for laminated composite materials is derived by using the linearized bond-based peridynamics, which forms a stable force state formulation corresponding to the non-uniform deformation. The proposed controlling scheme does not include any controlling parameter to avoid the complex parametric adjustment. A critical stretch continuously varying with the angle between fiber and bond directions is further proposed for the failure analysis of laminated composite materials with arbitrary fiber angles. The improved NOSBPD model adopts the explicit integration method to solve static problems. Several numerical examples are conducted to validate the proposed scheme suppressing the oscillation caused by zero-energy modes. K E Y W O R D S failure analysis, laminated composite materials, non-ordinary state-based peridynamics, stabilization, zero-energy modes 1 INTRODUCTION Peridynamics (PD) is a powerful non-local theory using integro-differential equations for differential equations. 1-5 The damage at any position in materials initiates spontaneously and can propagate along any paths. Based on these characteristics, PD has been widely used in damage and failure analysis of materials. 6-9 Generally, PD formulations have three types: bond-based peridynamics (BBPD), 10-13 ordinary state-based peridynamics (OSBPD), 14-16 and non-ordinary state-based peridynamics (NOSBPD). 17,18 BBPD has the restriction on the Poisson's ratio, and cannot distinguish the distortional and volumetric deformations. 4,19 OSBPD removes the restriction on the Poisson's ratio. Furthermore, NOSBPD uses the non-local approximate deformation gradient tensor to define strain. However, NOSBPD has inherent instability issues on displacement, stress, and strain fields due to zero-energy modes. 20,21 Recently, several zero-energy modes controlling methods have been developed for NOSBPD. 20-29 Littlewood 22 proposed a penalty approach to control zero-energy modes, in which the penalty force is proportional to the difference

An Ordinary State-Based Peridynamic Model of Unidirectional Carbon Fiber Reinforced Polymer Material in the Cutting Process

“…Due to the complex construction, determining the critical stretch value for laminated material is usually difficult. In recent investigations, there have been many approaches to determine the failure of PD bonds [ 31 , 32 , 33 , 34 , 35 , 36 , 37 ]. In this paper, the failure prediction is based on a relatively convenient approach, which is calculated by the mechanical strengths of a lamina [ 33 , 34 , 35 ].…”

Fatigue damage assessment of complex railway turnout crossings via Peridynamics-based digital twin

“…Consequently, various crack problems from stationary single crack to dynamic multiple cracks as well as fatigue cracks were examined in numerous studies earlier 35 – 40 . Furthermore, PD has also been found to be suitable to utilize many material models such as elastic, plastic, composites, polycrystalline, etc 41 – 45 .…”