Gradient-enhanced damage modelling of concrete fracture

Peerlings, Rhj Ron; Borst, de R René; Brekelmans, Wam Marcel; Geers, Mgd Marc

doi:10.1002/(sici)1099-1484(1998100)3:4<323::aid-cfm51>3.0.co;2-z

Cited by 380 publications

(251 citation statements)

References 30 publications

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“…As a consequence, no spurious mesh sensitivity, neither an influence of the direction of the mesh lines will occur. This is exemplified in Figure 18, which shows the damage pattern for the single edge notched beam of Figure 3 at one of the ultimate stages of loading [55].…”

Section: Higher-order Continuum Theoriesmentioning

confidence: 97%

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Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

Borst

Gutiérrez

Wells

et al. 2004

Numerical Meth Engineering

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SUMMARYA concise overview is given of various numerical methods that can be used to analyse localization and failure in engineering materials. The importance of the cohesive-zone approach is emphasized and various ways to incorporate the cohesive-zone methodology in discretization methods are discussed. Numerical representations of cohesive-zone models suffer from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill-posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive-zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition-of-unity property of finite element shape functions. The effectiveness of the approach is demonstrated for some examples at different scales. Moreover, examples are shown how this concept can be used to obtain a proper transition from a plastifying or damaging continuum to a shear band with gross sliding or to a fully open crack (true discontinuum). When adhering to a continuum description of failure, higher-order continuum models must be used. Meshless methods are ideally suited to assess the importance of the higher-order gradient terms, as will be shown. Finally, regularized strain-softening models are used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes.

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Section: Higher-order Continuum Theoriesmentioning

confidence: 97%

“…In the original approach of Peerlings et al [50,51], the non-local strain measure is coupled to the local strain measure˜ =˜ ( ) via: Figure 18. Damage profiles for SEN-beam in one of the ultimate loading stages computed with a gradient-enhanced damage model [55].…”

Section: Higher-order Continuum Theoriesmentioning

confidence: 99%

Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

Borst

Gutiérrez

Wells

et al. 2004

Numerical Meth Engineering

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“…Equation (14) b = 350 represent the relative reduction of the stress as κ → ∞ and the rate at which damage grows respectively. This law has been proposed in Peerlings et al (1998). The equivalent strain ε eq is defined as in De Vree et al (1996),…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…This definition of the equivalent strain has been used in Peerlings et al (1998) to describe concrete structures with a gradient-enhanced damage model. The internal length scale in Equation (11) is l s = 4 mm The specimen, that has a thickness of 50 mm, is discretised into eight-noded, plane-stress finite elements with a 2 × 2 Gauss-Legendre integration quadrature.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Size Sensitivity for the Reliability Index in Stochastic Finite Element Analysis of Damage

Gutiérrez

2006

Int J Fract

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Abstract. The direct differentiation method is applied to the estimation of statistical size effect behaviour in quasi-brittle solids. The scale factor is included in the finite element model and the autocorrelation function. Particular attention is paid to the proper differentiation of the Nataf transformation, which has been chosen to convert the basic random variables into a set of uncorrelated, standard normal variables. The predictive possibilities of the presented algorithm provide a valuable insight in the actual mechanisms responsible for failure. It can be evaluated to what extent the scale factor sensitivity of the failure probability is influenced by the phenomena related to the material disorder or the deterministic size effect.

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“…The objective of this paper is to establish an efficient numerical framework for fracture simulations in which the transition from damage to crack is carried out based on the preservation of dissipated energies. The implicit damage model [5,6,7,8] is chosen as the continuous description since it can simulate the damage evolution and strain softening phenomena. The CZM is integrated in the hybrid DG/ECL to model the discontinuous stage.…”

Section: Introductionmentioning

confidence: 99%

Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework

Becker

Noels

2014

Computer Methods in Applied Mechanics and Engineering

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One current challenge related to computational fracture mechanics is the modeling of ductile fracture and in particular the damage to crack transition. On the one hand, continuum damage models, especially in their non-local formulation which avoids the loss of solution uniqueness, can capture the material degradation process up to the localization of the damage, but are unable to represent a discontinuity in the structure. On the other hand cohesive zone methods can represent the process zone at the crack tip governing the crack propagation, but cannot account for the diffuse material damaging process.In this paper we propose to combine, in a small deformations setting, a non-local elastic damage model with a cohesive zone model. This combination is formulated within a discontinuous Galerkin finite element discretization. Indeed this DG weak formulation can easily be developed in a non-local implicit form and naturally embeds interface elements that can be used to integrate the traction separation law of the cohesive zone model. The method remains thus consistent and computationally efficient as compared to other cohesive element approaches.The effects of the damage to crack transition and of the mesh discretization are respectively studied on the compact tension specimen and on the double-notched specimen, demonstrating the efficiency and accuracy of the method.

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Gradient-enhanced damage modelling of concrete fracture

Cited by 380 publications

References 30 publications

Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

Size Sensitivity for the Reliability Index in Stochastic Finite Element Analysis of Damage

Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework

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