Locking‐free interface failure modeling by a cohesive discontinuous Galerkin method for matching and nonmatching meshes

Abstract

Summary In this work, modeling of brittle failure of the interface for a linear elastic material is presented. The idea is to integrate a novel extrinsic cohesive zone model into the incomplete interior penalty Galerkin variant of the discontinuous Galerkin (DG) method. As a result, the initial stiffness in the prefailure regime is omitted without having to remesh the crack path during the crack propagation. The interface model is used in combination with different discretization techniques, including matching and nonmatching meshes. This is possible due to the DG method's weak continuity constraint. Moreover, the locking problem in the bulk is cured by the application of a reduced Gaussian integration scheme on the boundary terms. The performance of the new cohesive discontinuous Galerkin elements with different integration schemes is compared with one of the standard intrinsic cohesive models. Due to the elimination of locking, crack initiation at the interface can be realistically displayed.

Extended general interfaces: Mori–Tanaka homogenization and average fields

“…al. [118] elastic interface Gurtin and Murdoch [51,52,119], Gao et al [120,121], Caillerie [122], Benveniste and Miloh [32], Rubin and Benveniste [123], Rizzoni et al [43], Fried and Gurtin [124], Dingreville and Qu [125,126], Sharma et al [127,128], Yang [129], Sun et al [130], Duan et al [73,74,[131][132][133], Huang and Wang [134], Monteiro et al [135], Huang and Sun [136], He [137], Le-Quang and He [138][139][140], Mogilevskaya et al [141][142][143][144], Kushch et al [145][146][147], Muskhelishvili [148], Kushch and Sevostianov [149], Benveniste and Miloh [150], Gao et al [121], Monchiet and Bonnet [151], Kushch [152] Sharma and Wheeler [153], Chen and Dvorak [154], Chen et al [155], Fischer and Svoboda …”

Homogenization of Composites with Extended General interfaces: Comprehensive Review and Unified Modeling

“…For further computational studies on applications of cohesive interfaces in fracture and failure in composites see Refs. [479,[491][492][493][494][495], and [497][498][499][500][501][502][503][504][505][506][507][508][509][510][511], among others.…”

About the influence of neglecting locking effects on the failure behavior at the interface

“…This is denoted by α = 1. In this stage, the cohesive tractions are computed by a traction separation law (TSL) [5] which is given in equation 2.…”

“…Discontinuous Galerkin methods [1] are used in various engineering applications ranging from fluid and solid mechanics [2,3] to the modeling of damage. The latter is attracting significant attention in the failure modeling of the interfaces [4,5]. This is mainly due the inherent non-conformity of the DG methods.…”