A geometrically regularized gradient-damage model with energetic equivalence

Wu, Jian‐Ying

doi:10.1016/j.cma.2017.09.027

Cited by 162 publications

(66 citation statements)

References 70 publications

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“…For this so-called smeared crack approach, classical methods were developed by [1][2][3][4][5]. More recently, nonlocal constitutive models [6], gradient enhanced [7,8] and phase field techniques [8][9][10][11][12] have also been considered within the continuous approach.…”

Section: Introductionmentioning

confidence: 99%

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Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy

2017

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The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-017-1438-8This paper discusses the finite element modeling of cracking in quasi-brittle materials. The problem is addressed via a mixed strain/displacement finite element formulation and an isotropic damage constitutive model. The proposed mixed formulation is fully general and is applied in 2D and 3D. Also, it is independent of the specific finite element discretization considered; it can be equally used with triangles/tetrahedra, quadrilaterals/hexahedra and prisms. The feasibility and accuracy of the method is assessed through extensive comparison with experimental evidence. The correlation with the experimental tests shows the capacity of the mixed formulation to reproduce the experimental crack path and the force–displacement curves with remarkable accuracy. Both 2D and 3D examples produce results consistent with the documented data. Aspects related to the discrete solution, such as convergence regarding mesh resolution and mesh bias, as well as other related to the physical model, like structural size effect and the influence of Poisson’s ratio, are also investigated. The enhanced accuracy of the computed strain field leads to accurate results in terms of crack paths, failure mechanisms and force displacement curves. Spurious mesh dependency suffered by both continuous and discontinuous irreducible formulations is avoided by the mixed FE, without the need of auxiliary tracking techniques or other computational schemes that alter the continuum mechanical problem.Peer ReviewedPostprint (author's final draft

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Section: Introductionmentioning

confidence: 99%

“…A clear physical interpretation and direct link between the length parameter in the model and the characteristic length of the material is arguable [40]. An alternative geometrical interpretation has been proposed by [12].…”

Section: Introductionmentioning

confidence: 99%

Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy

2017

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“…To avoid using an auxiliary field, level set methods have also been utilized . Other approaches, which set out to model cohesive fracture rather exploit the variational phase‐field approach to brittle fracture and attempt to obtain a cohesive‐like fracture behavior by modifying the assumed phase‐field distribution perpendicular to the center of the crack, the degradation function, or attempt to reconstruct the crack opening from the phase field …”

Section: Introductionmentioning

confidence: 99%

Considerations on a phase‐field model for adhesive fracture

Motlagh

Borst

2020

Numerical Meth Engineering

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Summary A recently proposed phase‐field model for cohesive fracture is examined. Previous investigations have shown stress oscillations to occur when using unstructured meshes. It is now shown that the use of nonuniform rational B‐splines (NURBS) as basis functions rather than traditional Lagrange polynomials significantly reduces this oscillatory behavior. Moreover, there is no effect on the global structural behavior, as evidenced through load‐displacement curves. The phase‐field model imposes restrictions on the interpolation order of the NURBS used for the three different fields: displacement, phase field, and crack opening. This holds within the Bézier element, but also at the boundaries, where a reduction to 𝒞0‐continuity yields optimal results. Application to a range of cases, including debonding of a hard fiber embedded in a soft matrix, illustrates the potential of the cohesive phase‐field model.

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“…The UPM solves the coupled transport equations one after another and transfers the field states among different physical/chemical fields back and forth, avoiding strong coupled description of the multi-fields such as [53][54][55][56][57]. Moreover, the simulations of crack initiation and propagation are not considered, avoiding complex models presented in such as [58][59][60][61][62][63][64][65][66]. The UPM transforms 3D complicated fractures and porous medium into 1D artificial connected pipes in domain space and it uses the equivalent pipe networks to simulate the mass/energy transport processes within a 3D fractured porous medium.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Effectiveness of CO2 Sequestration Using Portland Cement in Geological Reservoir Based on Unified Pipe-network Method

Yan

Sun

et al. 2020

Energies

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In this paper, we first recapitulate some basic notions of the CO 2 sequestration and numerical model. Next, a mixed model is employed into the CO 2 sequestration framework, for simulating CO 2 geological sequestration processes. The last part of the paper makes extensions to evaluation of the effectiveness of CO 2 sequestration with respect to atmospheric pressure, formation temperature, the initial reactant concentration, fracture aperture, and fracture dip. The results show that reactive Portland cement has a great impact on the effectiveness of CO 2 sequestration, while the proposed mixed model is robust in simulation.

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A geometrically regularized gradient-damage model with energetic equivalence

Cited by 162 publications

References 70 publications

Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy

Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy

Considerations on a phase‐field model for adhesive fracture

Evaluation of Effectiveness of CO2 Sequestration Using Portland Cement in Geological Reservoir Based on Unified Pipe-network Method

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