IGFEM-based shape sensitivity analysis of the transverse failure of a composite laminate

Zhang, X.; Brandyberry, David; Geubelle, Philippe H.

doi:10.1007/s00466-019-01726-y

Cited by 20 publications

(7 citation statements)

References 27 publications

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“…Moreover, IGFEM is stable by means of scaling enrichment functions or a simple diagonal preconditioner (van den Boom et al 2019a;Aragón et al 2020), meaning it has the same condition number as standard FEM. The method has been applied to the modeling of fiber-reinforced composites (Soghrati and Geubelle 2012b), multi-scale damage evolution in heterogeneous adhesives (Aragón et al 2013), microvascular materials with active cooling (Soghrati et al 2012a, b andc, 2013), and the transverse failure of composite laminates (Zhang et al 2019b;Shakiba et al 2019). IGFEM was later developed into the Hierarchical Interface-enriched Finite Element Method (HIFEM) (Soghrati 2014) that allows for intersecting discontinuities, and into the Discontinuity-Enriched Finite Element Method (DE-FEM) (Aragón and Simone 2017), which provides a unified formulation for both strong and weak discontinuities (i.e., discontinuities in the field and its gradient, respectively).…”

Section: Introductionmentioning

confidence: 99%

“…It was shown that IGFEM is optimally convergent under mesh refinement for problems without singularities [6,36], and stable by means of scaling enrichment functions or a simple diagonal preconditioner [7]. The method has been applied to the modeling of fibre-reinforced composites [36], multi-scale damage evolution in heterogeneous adhesives [37], microvascular materials with active cooling [6,36,38,39], and the transverse failure of composite laminate [40,41]. Extensions of IGFEM are found in the Hierarchical Interface-enriched Finite Element Method (HIFEM) [42], that allows for intersecting discontinuities, and in the Discontinuity-Enriched Finite Element Method (DE-FEM) [35], that provides a unified formulation for both weak and strong discontinuities.…”

Section: Introductionmentioning

confidence: 99%

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An interface-enriched generalized finite element method for level set-based topology optimization

Boom

Zhang

Keulen

et al. 2020

Struct Multidisc Optim

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During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A level set description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density-based methods. However, existing enriched methods have drawbacks, including ill-conditioning and difficulties in prescribing essential boundary conditions. In this work, we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks; boundaries are resolved accurately by means of the Interface-enriched Generalized Finite Element Method (IGFEM), coupled to a level set function constructed by radial basis functions. The enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as the standard finite element method with matching meshes, but without the need for remeshing. We derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. We establish that IGFEM-based level set topology optimization generates correct topologies for well-known compliance minimization problems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An interface-enriched generalized finite element method for level set-based topology optimization

Boom

Zhang

Keulen

et al. 2020

Struct Multidisc Optim

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“…41 Beyond the simplicity of the meshing process, the main advantages of adopting the IGFEM in this multiscale shape optimization study resides in the stationary nature of the underlying nonconforming mesh, which simplifies the computation of the shape sensitivities and eliminates issues associated with mesh distortion. 16,[42][43][44] When C −1 enrichments are used to capture the strong discontinuity along the cohesive interfaces, every enrichment node has a corresponding "mirror node" tied by the cohesive failure law, as shown in Figure 2 for the case of a linear tetrahedral element traversed by a single material interface. During the optimization process, it is possible that two adjacent inclusions occupy the same enriched element.…”

Section: Interface-enriched Generalized Finite Element Methodsmentioning

confidence: 99%

Multiscale design of three‐dimensional nonlinear composites using an interface‐enriched generalized finite element method

Brandyberry

Najafi

Geubelle

2020

Numerical Meth Engineering

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A computational framework is developed to model and optimize the nonlinear multiscale response of three-dimensional particulate composites using an interface-enriched generalized finite element method. The material nonlinearities are associated with interfacial debonding of inclusions from a surrounding matrix which is modeled using C −1 continuous enrichment functions and a cohesive failure model. Analytic material and shape sensitivities of the homogenized constitutive response are derived and used to drive a nonlinear inverse homogenization problem using gradient-based optimization methods. Spherical and ellipsoidal particulate microstructures are designed to match a component of the homogenized stress-strain response to a desired constructed macroscopic stress-strain behavior. K E Y W O R D Sanalytic sensitivity, cohesive failure, composites, multiscale modeling, shape optimization 1 2806

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“…The stabilized weak form with the interface traction and separation components expressed in the normal and tangential coordinates is given by (20) resembles the Nitsche stabilized finite element method for frictional contact presented in [65]. Thus, the stabilized weak form remains well-defined in the limiting case of a non-interpenetration (contact) constraint or an extrinsic cohesive law, unlike the standard weak form in (15).…”

Section: Stabilized Weak Formmentioning

confidence: 99%

“…Mesh dependence of the predicted crack path or directional mesh bias can be an issue with CZMs, as cracks can only propagate along finite element edges. To allow the propagation of arbitrary cohesive cracks and/or the inclusion of intra-element cohesive interfaces, various approaches based on the partition of unity concept (including G/XFEM) or virtual/phantom nodes were proposed [14][15][16][17][18][19][20][21]. The performance of the standard FEM to simulate cohesive cracks can be poor with distorted or low quality meshes, so mesh free methods were proposed to alleviate such difficulties [22].…”

Section: Introductionmentioning

confidence: 99%

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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IGFEM-based shape sensitivity analysis of the transverse failure of a composite laminate

Cited by 20 publications

References 27 publications

An interface-enriched generalized finite element method for level set-based topology optimization

An interface-enriched generalized finite element method for level set-based topology optimization

Multiscale design of three‐dimensional nonlinear composites using an interface‐enriched generalized finite element method

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

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