Abstract: It is universally known that composite materials possess higher specific stiffness and specific modulus than conventional single materials. Therefore, composite materials have become important structural materials in engineering practice. Nevertheless, the mechanism of failure generation and propagation for composite materials is quite complicated. Although, accordant results of the theoretical solution and standard tests concerning the static and quasi-static problems of composite materials can be achieved by traditional continuum mechanics theory (like the finite element method), modification of the continuum theory, as well as additional the criterion of failure and functions are needed when it comes to dynamic problems. However, the traditional method still cannot accurately simulate the propagation of complex cracks, like 3D cracks and group cracks. Fortunately, the peridynamics theory (referred to as PD theory) replaces the differential term in the traditional constitutive equations of continuum mechanics with the integral term, avoiding the singularity of derivative solution caused by the crack. The application of PD theory to fai-lure-propagation simulation presents the following three major advantages. Ⅰ. It can spontaneously simulate the crack generation and propagation without additional failure criterion. Ⅱ. It is capable of modeling issues in different scales by varying the constitutive force function. Ⅲ. It can simultaneously handle the propagation of multiple cracks while considering their interactions under the framework of the same computing system. Unfortunately, the heterogeneity of composite materials and their anisotropy of mechanical properties make it difficult to construct an ideal mat-hematical model because the point-to-point force function in the PD model cannot fully describe the anisotropic behavior of the composites. In addition, the essence of PD theory is to discrete the model into a series of points, and calculate the resultant force of all the other points in the near-field range of one point, which leads to a huge amount of computation of the PD method. Therefore, in recent years, the application of PD theory in the study of composite material failure mainly focus on building a reasonable theoretical model of composite materials and continuous development of the computational efficiency, and a series of results have been achieved. At present, a variety of composite materials PD models have been developed, which can effectively simulate the multiple failure of fiber fracture, matrix crack and delamination. The new algorithm and the solution strategy can greatly speed up the calculation of solution while ensure the accuracy. The PD models that successfully simulated the failure modes of composites include models based on fiber bonds and matrix bonds, and models based on normal bonds and shear bonds. The model based on fiber bonds and matrix bonds is the earliest established PD model of composite materials, which describe the constitutive information of materials by adding appropriate modification items to the constitutive force functions of two material point pairs. For the model based the normal bond and shear bond, the solution of deformation in the constitutive force function is similar to the expression of the strain in the traditional continuum mechanics, and the change of the mechanical parameters can be directly displayed in the final failure result graph. For the sake of improving computational efficiency, dynamic adaptive relaxation techniques and parallel algorithms have been successfully applied to the PD method. In addition, fast algorithms and transformation equations have been developed for the PD mo-del. Moreover, the PD model and the finite element model also have been successfully coupled to solve the problem. The PD model is arranged in the core (failure expansion) area, and the finite element model is arranged in other areas, so as to reduce the calculation amount and improve the calculation efficiency, as well as ensure the accuracy and correctness of the solution. In this article, the progress of PD method in the study of composite failure is summarized. The theoretical framework of the PD method, the PD model of the composite material, the new solution algorithm and solution strategy, and the application of the PD method in the failure of composite materials are introduced respectively. The problems and prospects in the study of composite materials failure are proposed, so as to provide a reference for the further application of PD method in the study of failure mechanism of composite materials.
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2019, Vol. 33 
