Extended Finite Element Methods

Moës, Nicolas; Dolbow, John E.; Sukumar, N.

doi:10.1002/9781119176817.ecm2111

Cited by 3 publications

(4 citation statements)

References 88 publications

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“…3. 6 In the non-equilibrium, or over-stress branch, deformation is assumed to consist of an elastic and an inelastic viscous portion, and the deformation gradient is multiplicatively decomposed into…”

Section: Kinematicsmentioning

confidence: 99%

“…Different from classical finite element approaches (FE), it enables to simulate crack growth without the need for remeshing. Furthermore, complex crack patterns that are not a priori known can be simulated in a straightforward manner, which especially makes the concept attractive compared to alternative approaches such as Cohesive zone elements [5] or the Extended-finite-element-method (X-FEM) [6]. The phase-field fracture approach goes back to the variational formulation of brittle fracture of Francfort and Marigo [7], who recast the Griffith criterion [8] for crack propagation into a variational setting.…”

Section: Introductionmentioning

confidence: 99%

“…For sake of brevity, terms arising from external loads are omitted in(6) and what follows 3. Note that different from[39,61] and in line with e.g [17,36],.…”

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confidence: 99%

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Phase-field modelling and analysis of rate-dependent fracture phenomena at finite deformation

et al. 2023

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Fracture of materials with rate-dependent mechanical behaviour, e.g. polymers, is a highly complex process. For an adequate modelling, the coupling between rate-dependent stiffness, dissipative mechanisms present in the bulk material and crack driving force has to be accounted for in an appropriate manner. In addition, the resistance against crack propagation can depend on rate of deformation. In this contribution, an energetic phase-field model of rate-dependent fracture at finite deformation is presented. For the deformation of the bulk material, a formulation of finite viscoelasticity is adopted with strain energy densities of Ogden type assumed. The unified formulation allows to study different expressions for the fracture driving force. Furthermore, a possibly rate-dependent toughness is incorporated. The model is calibrated using experimental results from the literature for an elastomer and predictions are qualitatively and quantitatively validated against experimental data. Predictive capabilities of the model are studied for monotonic loads as well as creep fracture. Symmetrical and asymmetrical crack patterns are discussed and the influence of a dissipative fracture driving force contribution is analysed. It is shown that, different from ductile fracture of metals, such a driving force is not required for an adequate simulation of experimentally observable crack paths and is not favourable for the description of failure in viscoelastic rubbery polymers. Furthermore, the influence of a rate-dependent toughness is discussed by means of a numerical study. From a phenomenological point of view, it is demonstrated that rate-dependency of resistance against crack propagation can be an essential ingredient for the model when specific effects such as rate-dependent brittle-to-ductile transitions shall be described.

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Section: Kinematicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase-field modelling and analysis of rate-dependent fracture phenomena at finite deformation

et al. 2023

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“…• Extended finite element method (XFEM), where elements are enhanced by discontinuous field through a partition of unity method [106,107,137],…”

Section: Approaches To Fracture Modelingmentioning

confidence: 99%

Brittle fracture of laminated glass structural elements

Schmidt

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Many damage models have been developed over the past decades, but most of them still struggle to simulate damage without additional ad-hoc criteria or the need for difficult implementation. In particular, brittle fracture models that represent a mathematical singularity are not easy to be simulate correctly. Recently discovered phase field models prove to be advantageous in many ways. These are variationally consistent models that show a high degree of robustness. Problems such as tensile cracking, cracking of a specialized structure in 3D, crack branching or crack initiation are all described by the same set of equations. Since the model uses a regularized damage field, its implementation is also efficient. Laminated glass is a material that needs to be investigated even after cracks appear. Undamaged laminated glass is a stunning material itself, but its undisputed advantage is its cohesiveness and load-bearing capacity even in post-breakage domain. And phase-field models are suitable for simulating this residual load capacity, which allow investigating both the initiation of cracks and their branching and the impact on the structural response. This work is supposed to bring the combination of such phenomena - the simulation of laminated glass before and after the appearance of cracks. Models of different degrees of spatial reduction and structures under different loading are investigated. The work first investigates the quasi-static response of the beams, then stochastically investigates the response when the strength changes and is concluded by investigating the low-velocity impact. The paper primarly tries to create fully applicable approaches for engineering practice and reveals the benefits and shortcomings of such an approach for glass modeling.

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An efficient method for the elastic field in a transversely isotropic full space due to arbitrary inclusions

Zhao

Wang

et al. 2020

International Journal of Solids and Structures

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Extended Finite Element Methods

Cited by 3 publications

References 88 publications

Phase-field modelling and analysis of rate-dependent fracture phenomena at finite deformation

Phase-field modelling and analysis of rate-dependent fracture phenomena at finite deformation

Brittle fracture of laminated glass structural elements

An efficient method for the elastic field in a transversely isotropic full space due to arbitrary inclusions

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