An XFEM/CZM implementation for massively parallel simulations of composites fracture

Abstract

Because of their widely spread use in many industries, composites are the subject of many research campaigns. More particularly, the development of both accurate and flexible numerical models able to capture their intrinsically multiscale modes of failure is still a challenge. The standard finite element method typically requires intensive remeshing to adequately capture the geometry of the cracks and high accuracy is thus often sacrificed in favor of scalability, and vice versa. In an effort to preserve both properties, we present here an extended finite element method (XFEM) for large scale composite fracture simulations. In this formulation, the standard FEM formulation is partially enriched by use of shifted Heaviside functions with special attention paid to the scalability of the scheme. This enrichment technique offers several benefits, since the interpolation property of the standard shape function still holds at the nodes. Those benefits include (i) no extra boundary condition for the enrichment degree of freedom, and (ii) no need for transition/blending regions; both of which contribute to maintain the scalability of the code.Two different cohesive zone models (CZM) are then adopted to capture the physics of the crack propagation mechanisms. At the intralaminar level, an extrinsic CZM embedded in the XFEM formulation is used. At the interlaminar level, an intrinsic CZM is adopted for predicting the failure. The overall framework is implemented in ALYA, a mechanics code specifically developed for large scale, massively parallel simulations of coupled multi-physics problems. The implementation of both intrinsic and extrinsic CZM models within the code is such that it conserves the extremely efficient scalability of ALYA while providing accurate physical simulations of computationally expensive phenomena. The strong scalability provided by the proposed implementation is demonstrated. The model is ultimately validated against a full experimental campaign of loading tests and X-ray tomography analyses for a chosen very large scale.

A shell element for the prediction of residual load‐carrying capacities due to delamination

“…This also holds for the thickness normal stress and the shear stress. It is important to note that stress r is only obtained with the curvature termw in Equation (27). Asw is taken from the last load increment, the computation must be done in two steps.…”

“…Due to the plane strain boundary conditions, the stresses are independent of y. Without the curvature term w in (27), one obtains the linear solution for z . The deformed configuration for load factor = 5 is plotted in Figure 12.…”

“…26 The extended finite element method (XFEM) is enlarged for delamination problems in other works. [27][28][29][30][31] Delamination initiation analyses are often based on stress criteria. Especially, the interlaminar stresses as driving forces for this type of failure mode must be known.…”

A study of composite laminates failure using an anisotropic gradient-enhanced damage mean-field homogenization model

“…This is achieved by multiplying the bulk strong form (6)(7)(8) by the trial functions (wū, wp) ∈ C 0 (Ω i ), and by integrating by parts on each ply Ω i instead of performing this integration on the whole domain Ω as it is usually performed. Using the boundary conditions (8-10, 13 and 17) and definitions (11) of the jump and average operators across the interface Γ L i+1 i between the surfaces Γ Li and Γ Li+1 , see …”

“…The use of cohesive zones within the plies using the extended finite element method, see e.g. [8], or the phantom node method [9] does not suffer from the loss of solution uniqueness.…”