A non-local fracture model for composite laminates and numerical simulations by using the FFT method

Abstract

a b s t r a c tIn this paper, we present a fracture model for composite laminates and its numerical solution by using the Fast Fourier Transforms (FFTs). The FFT-based formulation initially proposed for seeking the average behaviour of linear and non-linear composites by means of the homogenisation procedures [1,2] was adapted to evaluate the damage growth in brittle materials. A non-local damage model based on the maximal principal stress criterion was proposed to assess the failure in the matrix and the fibres. This non-local model was then connected to the Griffith-Irwin criterion in the aim of predicting crack growth. In order to assess the matrix/fibre interface delamination, we have adapted the cohesive model developed by Li [3] for accounting the mixed-mode dependent interface failure. To this end, the interfaces between the matrix and the fibres are replaced by a thin layer of interphase with the purpose of facilitating the FFT simulations. By using the proposed model, we carried out several numerical simulations on fracture process in different specimens. From these studies, we can conclude that the present FFTbased analysis is capable to deal with crack initiation and crack growth in composite laminates with high accuracy and efficiency, especially in the cases of matrix/fibre interface debonding and of multi-crack growth.

A non-local approach to crack process modeling in ceramic materials subjected to thermal shock

“…In this paper, the ideas described in Li et al [40,41] were essentially followed. However, the FFT modeling is appropriate only for analyses of periodic structures under periodic loading; Moreover, the criterion proposed in Li et al [40,41] is capable to forecast the position, but not the orientation and length of the new crack.…”

“…However, the FFT modeling is appropriate only for analyses of periodic structures under periodic loading; Moreover, the criterion proposed in Li et al [40,41] is capable to forecast the position, but not the orientation and length of the new crack. In the present work, this model is improved and implemented to a finite element code.…”

“…However, these analyses were suitable only for individual crack formation and evolution. On the basis of the finite fracture mechanics concept, Li et al [40,41] developed a Fast Fourier Transform (FFT) code, which is capable to simulate multiple crack onset and crack growth in brittle materials.…”

Direct numerical simulations on crack formation in ceramic materials under thermal shock by using a non-local fracture model

“…[21][22][23][24] However, multi-cracking phenomenon such as that observed in thermal shock experiments is always an intrinsically difficult problem to deal with. In this paper, a non-local failure criterion was proposed and implemented into a finite element code.…”

Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields

“…In recent years, Fourier-based methods, originally introduced by Moulinec et al [1], have become ubiquitous for computing numerically the properties of composite materials, with applications in domains ranging from linear elasticity [2], viscoplasticity [instead of 'thermoplasticity'] [3], and crack propagation [4] to thermal and electrical [5,6] and also optical properties [7]. The success of the method resides in its ability to cope with arbitrarily complex and often very large microstructures, supplied as segmented images of real materials, for example, multiscale [instead of 'multistage'] nanocomposites [8], austenitic steel [9], granular media [5] or polycrystals [instead of 'polycrystal'] [10,11,12].…”