Abstract
In this work, we modeled the brittle fracture of shell structure in the framework of Peridynamics Mindlin-Reissener shell theory, in which the shell is described by material points in the mean-plane with its drilling rotation neglected in kinematic assumption. To improve the numerical accuracy, the stress-point method is utilized to eliminate the numerical instability induced by the zero-energy mode and rank-deficiency. The crack surface is represented explicitly by stress points, and a novel general crack criterion is proposed based on that. Instead of the critical stretch used in common peridynamic solid, it is convenient to describe the material failure by using the classic constitutive model in continuum mechanics. In this work, a concise crack simulation algorithm is also provided to describe the crack path and its development, in order to simulate the brittle fracture of the shell structure. Numerical examples are presented to validate and demonstrate our proposed model. Results reveal that our model has good accuracy and capability to represent crack propagation and branch spontaneously.
Highlights
Dynamic damage and failure process of shell structure is very challenging in the computational community for its special geometric features which requires the numerical method to be capable of representing material characteristics and discontinuity in finite deformation and large rigid rotations [1]
Because the intrinsic nature of the discontinuities emerges from the damage area of interest, numerical approaches based on classical continuum mechanics have to handle the discontinued displacement field and the singularity in stress field at the crack tip, where partial-differential equations become unsolvable
There is no requirement for the continuity of the displacement field since the domain is discretized in terms of material points and described by the integral equation of motion
Summary
Dynamic damage and failure process of shell structure is very challenging in the computational community for its special geometric features which requires the numerical method to be capable of representing material characteristics and discontinuity in finite deformation and large rigid rotations [1]. Bazazzadeh et al study fatigue crack propagation in structural materials by developing a new computational tools which is based on peridynamic theory [8,9]. When it is extended to plate or shell structures, it is very hard to achieve reasonable results with high accuracy since the system have to use very fine discretizations to satisfy the precision requirement along the thickness direction To address this issue, several peridynamics membrane approaches have been proposed based on various kinematic assumptions to improve the computational efficiency [11–13]. Peng et al developed the Reproducing Kernel Particle method (RKPM) to the simulation of the large deformation of a curved shell in the Mindlin-Reissner shell theory [21], which can address large deformations without mesh distortion By using this method, the dynamic response of the ship cabin and real ship structure under impact load are numerically predicted [22]. The accuracy, convergence, and stability of this work will be discussed in the last section
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