The embedded finite element method (E-FEM) for multicracking of quasi-brittle materials

Hauseux, Paul; Roubin, Emmanuel; Colliat, Jean‐Baptiste

doi:10.1016/b978-0-08-100781-5.00008-7

Cited by 7 publications

(11 citation statements)

References 36 publications

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“…However, they have the evident advantage of their simplicity and numerical solution speed, as the system to solve for [|u|] becomes a single algebraic equation. As simple as it is, this kind of formulation has been successfully used for the modeling of complex fracture phenomena in heterogeneous, quasi-brittle materials [22,23,24]. It has granted satisfactory results for the global strength prediction and overall crack position of actual test specimens under tensile and compressive loads, even when considering triaxial confinement preloading conditions [25].…”

Section: Single Mode Formulationsmentioning

confidence: 99%

General consistency of strong discontinuity kinematics in Embedded Finite Element Method (E-FEM) formulations

Laborin¹,

Malécot²,

Roubin³

et al. 2021

Preprint

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This paper discusses the consistency of the theoretical basis behind the kinematic models of strong discontinuity methods for local fracture simulations using the Embedded Finite Element Method (E-FEM). A brief review is made on the elemental enhancement functions from the current E-FEM literature and how previous works managed to model mode I (normal) and mode II (parallel) fracture kinematics in multiple dimensions. Further analysis is made on how these approaches also introduce unintended mesh dependencies and basic kinematic inconsistencies of the fracture model with respect to its hosting element. Notable work from a few authors discussing some of these issues and their contributions to resolve them is reviewed as well. Based on this analysis, a new proposal of strong discontinuity enhancement functions is introduced to ensure a broader kinematic coherence within the element and to avoid the observed theoretical faults. This is done by making a more extensive use of the flexibility granted by the Hu-Washizu variational principle and by introducing new algebraic constraints that will ensure more correct fracture kinematics without compromising the acknowledged simplicity of the whole E-FEM framework. Element-level simulations are done to compare the outputs within a group of selected formulation approaches, including the novel proposal. Simulations show that the new element formulation grants a wider level of basic kinematic coherence between the local fracture outputs and element kinematics themselves, demonstrating an increase in robustness that might drive the usefulness and competitiveness of E-FEM techniques for fracture simulations to a higher level.

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Section: Single Mode Formulationsmentioning

confidence: 99%

General consistency of strong discontinuity kinematics in Embedded Finite Element Method (E-FEM) formulations

Laborin¹,

Malécot²,

Roubin³

et al. 2021

Preprint

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“…Figure 2 illustrates a typical dual material partition for a 4-node tetrahedral element in domains Ω + , Ω − with a boundary ∂Ω and having a plane Γ d as an interface. The base work in [14,35] considers linear elastic properties for each domain such as Young moduli E + , E − and Poisson ratios ν + , ν − . A local coordinate system (n,t,m) defines the orientation of the material interface, havingn as the unit vector normal to Γ d .…”

Section: Theoretical Foundations and Consistency Analysismentioning

confidence: 99%

An analysis of embedded weak discontinuity approaches for the finite element modelling of heterogeneous materials

Laborin¹,

Malécot²,

Roubin³

et al. 2021

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This paper analyses in detail the use of the Embedded Finite Element Method (E-FEM) to simulate local material heterogeneities. The work starts by a making a short review on the evolution of weak discontinuity models within the E-FEM framework to discuss how they account for the presence of multiple materials within a single element structure. A theoretical basis is introduced through some mathematical weak discontinuity definitions and the Hu-Washizu variational principle, for then establishing a set of requirements for retaining variational and kinematic consistency for any weak discontinuity enhancement proposal. From a general definition of a displacement enhancement field, two particular enhancement functions are derived by considering different consistency requirements: one which has been typically used in previous works and other which truly possesses variational consistency. A discussion is held on enhancement stability properties and the impact to global finite element solution processes. In the end, numerical simulations are made to assess the performance of each of these enhancements on the task of modelling a classical bi-material layered 3D tension problem. The final discussion evaluates both model performance and ease of implementation.

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“…This leads to the simultaneous creation of multiple local cracks that, by the mere mechanism of stiffness damaging and internal force redistribution, will tend to favour a spontaneous coalescence phenomenon giving rise to a larger scale fracture without explicitly aiming for it. While nonlocal crack continuity within the E-FEM framework has already been well studied and implemented in multiple applications for homogeneous material simulations [39,31,40], the line of research currently discussed ( [38,12,41,8,42]) intentionally keeps the locally discontinuous nature of the E-FEM models to favour this behaviour in the context of complex heterogeneous materials. This decision is supported by multiple studies that favour the hypothesis of multi-cracks at smaller scales contributing to the emergence of larger fracture processes in such materials [43,44].…”

Section: Evolution Of the E-fem Framework Approaching Composite Quasi-brittle Failure Problemsmentioning

confidence: 99%

“…Hauseux [41] later achieved the simulation of fracture sliding modes (mode II) with the same framework in the context of simulations of excavations of geomaterials. The strong discontinuity model was still based on a single fracture mode, but it considered mode II local fracture kinematics activated by means of a Mohr-Coulomb localisation criterion, followed by a discrete exponential traction-separation law.…”

Section: Evolution Of the E-fem Framework Approaching Composite Quasi-brittle Failure Problemsmentioning

confidence: 99%

“…Thus, a localisation criterion can objectively determine the orientation but not the exact location of the local fracture. On this matter, the authors of this study have decided to take the approach followed in [12,41] and make Γ d to pass through the centroid of the element reaching localisation. For all heterogeneous elements, it has been already stated that the crack plane will be made perfectly coincident with the material interface plane.…”

Section: Localisation Criteriamentioning

confidence: 99%

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Modelling of triaxial fracture processes in heterogeneous quasi-brittle materials using the Embedded Finite Element Method (E-FEM)

Laborin¹,

Malécot²,

Roubin³

et al. 2021

Preprint

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This paper studies the use of the Embedded Finite Element Method (E-FEM) for the numerical modelling of triaxial fracture processes in non-homogeneous quasi-brittle materials. The E-FEM framework used in this study combines two kinematics enhancements: a weak discontinuity allowing the model to account for material heterogeneities and a strong discontinuity allowing the model to represent local fractures. The strong discontinuity features enriched fracture kinematics that allow the modelling of all typical fracture modes in three dimensions. A brief review is done of past work using similar enriched finite element frameworks to approach this problem. The work continues by establishing the theoretical basis of each kind of discontinuity formulation and their superposition through the Hu-Washizu variational principle. Afterwards, two groups of simulations have been done for discussing the performance of this combined E-FEM model: homogeneous simulations and simple heterogeneous simulations. Simple homogeneous material simulations aim to test the capabilities of the strong discontinuity model featuring full 3-D kinematics. Simple heterogeneous simulations show numerical applications of the model to the problem of a single spherical inclusion embedded into a homogeneous matrix. Comparisons will be made with another E-FEM model considering a single local fracture mode approach to discuss the differences on the representation of fracture physics under all explored conditions. A concluding statement is made on the benefits and complications identified for the E-FEM framework in this kind of applications.

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The embedded finite element method (E-FEM) for multicracking of quasi-brittle materials

Cited by 7 publications

References 36 publications

General consistency of strong discontinuity kinematics in Embedded Finite Element Method (E-FEM) formulations

General consistency of strong discontinuity kinematics in Embedded Finite Element Method (E-FEM) formulations

An analysis of embedded weak discontinuity approaches for the finite element modelling of heterogeneous materials

Modelling of triaxial fracture processes in heterogeneous quasi-brittle materials using the Embedded Finite Element Method (E-FEM)

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