A stabilized finite element method for enforcing stiff anisotropic cohesive laws using interface elements

Ghosh, Gourab; Duddu, Ravindra; Annavarapu, Chandrasekhar

doi:10.1016/j.cma.2019.02.007

Cited by 16 publications

(13 citation statements)

References 71 publications

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“…In this section, we briefly review the Nitsche-inspired stabilized finite element method originally proposed in [7] for enforcing stiff cohesive laws. We will begin with a description of the strong form of the governing equations followed by the anisotropic bilinear cohesive law for mixed-mode loading.…”

Section: Governing Equations and Weak Formulationsmentioning

confidence: 99%

“…In this paper, we illustrate the ability of the stabilized FEM of Ghosh et al [7] in alleviating traction oscillations at interlaminar interfaces in multi-directional orthotropic composite laminates under different loading conditions. A specific aim is to illustrate its robustness for composite delamination analysis, with regard to the choice of the cohesive stiffness and the structure of the finite element mesh (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Simple engineering solutions [5] may mitigate numerical issues with the standard finite element method (FEM) on a case-by-case basis, but they are not robust and introduce parametric uncertainty [6]. We recently illustrated that a Nistche-based stabilized FEM is robust and accurate for enforcing stiff cohesive laws and simulating fracture propagation in isotropic, homogeneous elastic materials [7]. The purpose of this article is to investigate the numerical stability and accuracy of standard FEM and weighted Nitsche-based stabilized FEM for delamination analysis of composites using cohesive elements, especially at anisotropic and dissimilar interlaminar interfaces.…”

Section: Introductionmentioning

confidence: 99%

“…Nitsche's method has been extended for modeling frictionalsliding on embedded interfaces [64,65] and small-sliding contact on frictional surfaces, including stick?slip behavior [66]. Inspired by the work of [67], we recently extended the Nitsche's method to cohesive fracture problems, and developed a stabilized FEM that alleviates traction oscillations with stiff, anisotropic cohesive laws [7].…”

Section: Introductionmentioning

confidence: 99%

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A Stabilized Finite Element Method for Modeling Mixed-mode Delamination of Composites

Ghosh¹,

Annavarapu²,

Jiménez³

et al. 2017

American Society for Composites 2017

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Delamination of composite materials is commonly modeled using intrinsic cohesive zone models (CZMs), which are generally incorporated into the standard finite element (FE) method through a zero-thickness interface (cohesive) element; however, intrinsic CZMs exhibit numerical instabilities when the cohesive stiffness parameters is assumed to be large relative to the elastic stiffness of the composite material. To address this numerical instability issue, we propose a stabilized finite element method by combining the traditional penalty method with the Nitsche's method that is equally effective for any specified initial stiffness of the cohesive (traction-separation) law. The key advantage of the proposed method is that it generalizes the Nitsche's method to any tractionseparation law with arbitrary large values of initial stiffness and provides a unified way to treat cohesive fracture problems in a variationally consistent and stable manner. We implemented the stabilized method in the commercial finite element software Abaqus via the user element subroutine and simulated benchmark tests for mode I and mixed-mode delamination in isotropic materials to establish the viability of the approach. Ongoing work is aimed at extending the method to model delamination in transversely isotropic laminated composites.

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Section: Governing Equations and Weak Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Stabilized Finite Element Method for Modeling Mixed-mode Delamination of Composites

Ghosh¹,

Annavarapu²,

Jiménez³

et al. 2017

American Society for Composites 2017

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“…Aduloju and Truster developed a DG formulation for modeling dynamic debonding in composite materials. Ghosh et al generalized Nitsche's method to enforce stiff anisotropic cohesive laws. In this way, the problem of oscillations due to spurious tractions could be overcome.…”

Section: Introductionmentioning

confidence: 99%

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

Bayat

Rezaei

Brepols

et al. 2020

Numerical Meth Engineering

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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.

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Spatial and temporal constraints of the cohesive modeling: A unified criterion for fluid‐driven fracture

Wang

et al. 2023

Numerical Meth Engineering

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We present a unified criterion for cohesive modeling of fluid-driven fracture based on the dimensional analysis to simultaneously provide the constraint for cohesive element and time step sizes. Complicated by the nonlinear interaction between solid deformation and fluid flow, the underlying correlation between discretization and physical parameters of fluid-driven fracture is still unclear. This work studies this correlation through the dimensionless process of the governing equations that associate the cohesive element and time step sizes in a discrete regime. Three characteristic parameters (i.e., related to crack opening, fluid pressure, and fracture length) are introduced in the derivation, and two dimensionless parameters are proposed to construct the unified criterion. The criterion is validated by numerical tests of toughness-dominated fracture with various conditions including the modulus of solid, injection rate of fluid, fracture energy, and in-situ stress. The proposed criterion determines the spatial and temporal constraints of the cohesive zone model for modeling fluid-driven fracture, which is often treated empirically in previous practices.

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A stabilized finite element method for enforcing stiff anisotropic cohesive laws using interface elements

Cited by 16 publications

References 71 publications

A Stabilized Finite Element Method for Modeling Mixed-mode Delamination of Composites

A Stabilized Finite Element Method for Modeling Mixed-mode Delamination of Composites

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

Spatial and temporal constraints of the cohesive modeling: A unified criterion for fluid‐driven fracture

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