A nonlinear shell augmented finite element method for geometrically nonlinear analysis of multiple fracture in thin laminated composites

Highlights

• A nonlinear shell augmentation scheme is proposed to account for the multiple fractures in composites.

• Propose a Newton-Raphson based algorithm for the nonlinear considerations process.

• A shell-like cohesive zone model is developed for the nonlinear fracture of composites.

Abstract

A nonlinear shell augmented finite element method (NS-AFEM) is proposed in this paper to account for the multiple fractures and their interactive evolutions in thin laminated composites with large deformations. This NS-AFEM employed a nonlinear elemental condensation algorithm based on Newton-Raphson method, which explicitly treated the strong discontinuity of a cracked element without the need of extra nodes. In addition, an improved geometrically nonlinear shell-like cohesive zone model (CZM) was developed and integrated into the NS-AFEM to represent the nonlinear fracture processes of composites, including matrix cracking in tension/compression, fiber tensile rupture and fiber compressive kinking, and interface delamination. The high-fidelity simulations in open-hole tension and three-point-bending tests of composite laminates demonstrate that the proposed method is capable of dealing with the geometrically nonlinear coupled crack system in thin laminated composites, which is of particular challenge in other alternative numerical methods.

Introduction

Currently, advanced composites have been increasing rapidly as primary load-bearing structures on aerospace and transportation communities due to their excellent mechanical performance, such as high stiffness- and strength-to-weight ratios [1]. However, failure in composites is a complex phenomenon which includes multiple failure mechanisms, such as fiber/matrix debonding, matrix cracking, fiber rupture/kinking, delamination between plies, and their interactions between each other. The multiple cracks of above fracture modes can be observed in a three-point-bending test of the composite laminate, as shown in Fig. 1. The accurate prediction of such failure events in composites is of great importance and it is in urgent need of an advanced modeling strategy for such purpose with regard to the safety and durability of the composite structures.

In the past decades, extensive numerical studies focused on the damage or fracture behavior of laminated composites. For example, the continuum damage mechanics (CDM), as a sophisticated theory, was used to simulate the progressive damage behavior in composites. Various damage modes were involved in CDM based on the phenomenological characterization of the real failure mechanisms. The successful use of CDM was reported for the damage modeling of the unidirectional [[2], [3], [4], [5],[6], [7], [8]] and textile composites [9,10]. However, some studies revealed that the smeared crack representation in CDM might cause the loss of key information on the multiple fracture process in composites [11,12].

To overcome the limitations of CDM, the partition-of-unity (PoU) based finite element method (FEM) was recently developed for the modeling of arbitrary discrete discontinuities in composite laminates, including the generalized FEM (G-FEM) [13], extended FEM (X-FEM) [14,15,16] and phantom node method (PNM) [17,18]. Other recent alternative methods include the phantom node based augmented FEM (A-FEM) [19] and the improved A-FEM [20] for the fracture simulation in laminated or textile composites, the phase field method [21] for failure analyses of open hole laminates under tension, and the floating node method [22,23] for modeling matrix cracking and delamination in composites.

The above studies mainly focused on the 2D and 3D fracture simulations of composite laminates under in-plane loading sceneries. However, the composite component is generally modeled as shell structures, basically due to the thin thickness of each composite ply and the composite components are usually made into thin-walled structures that are stacked together by a number of thin plies with specific fiber orientations. As far as we know, only a few CDM based shell formulations have been proposed and used for composite damage analyses. For example, A. Sabik [24] incorporated the CDM into a 6-field nonlinear shell theory for the progressive damage analysis in the laminated cantilever and plate under out-of-plane loading; Pigazzini et al. [25] proposed a gradient-enhanced damage model in Kirchhoff-Love shells for the failure analyses of laminates under impact loading. Unfortunately, few studies reported the fracture simulation of composites with shell elements, due to the significant challenges such as the dimension-reduced kinematics coupled with the elemental discontinuity caused by a crack, as well as tracing the propagation of multiple interactive cracks especially under large deformation conditions (flexure or twist, etc.).

For this purpose, in this study we develop a nonlinear shell augmented finite element method (NS-AFEM) that can account for multiple crack initiation and propagation in thin laminated composites under large deformation. The proposed NS-AFEM extends the original A-FEM [26] by introducing a Newton-Raphson based nonlinear elemental condensation algorithm with the aim to deal with geometric nonlinear coupled shell fracture problems. This new elemental condensation strategy also provides the advantage of without the need of additional nodal DoFs in treating the crack propagation, which improves the numerical efficiency when accounting for multiple cracks in composites. Besides, the orthotropic shell kinematics is introduced into the NS-AFEM, which is based on the Mindlin-Reissner theory and featured with large deformation formulations. An improved geometrically nonlinear shell-like CZM is further established and integrated into the NS-AFEM to describe the crack propagation in composite shells. Typical fracture mechanisms, including transverse matrix cracking, interface delamination, fiber rupture in tension or fiber kinking in compression, are all incorporated in the NS-AFEM. Specifically, the modeling scheme is achieved by coupling the NS-AFEM for intralaminar fracture with the cohesive elements for interface delamination. The NS-AFEM’s predictive capability on multiple fracture systems is demonstrated through the high-fidelity simulations of the open-hole tension tests and three-point-bending tests of composite laminates.