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

Wu, Ling; Becker, Gauthier; Noels, Ludovic

doi:10.1016/j.cma.2014.06.031

Cited by 26 publications

(48 citation statements)

References 58 publications

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“…(90). In order to capture these critical states, a damage-crack transition framework should be used as proposed by Wu et al (2014). Figure 18 shows the distributions of the softening and failure variables leading to the total softening result in Fig.…”

Section: Mesh Objectivitymentioning

confidence: 99%

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

Nguyễn

Lani

Pardoen

et al. 2016

International Journal of Solids and Structures

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A large strain hyperelastic phenomenological constitutive model is proposed to model the highly nonlinear, rate-dependent mechanical behavior of amorphous glassy polymers under isothermal conditions. A corotational formulation is used through the total Lagrange formalism. At small strains, the viscoelastic behavior is captured using the generalized Maxwell model. At large strains beyond a viscoelastic limit characterized by a pressure-sensitive yield function, which is extended from the Drucker-Prager one, a viscoplastic region follows. The viscoplastic flow is governed by a non-associated Perzyna-type flow rule incorporating this pressure-sensitive yield function and a quadratic flow potential in order to capture the volumetric deformation during the plastic process. The stress reduction phenomena arising from the post-peak plateau and during the failure stage are considered in the context of a continuum damage mechanics approach.The post-peak softening is modeled by an internal scalar, so-called softening variable, whose evolution is governed by a saturation law. When the softening variable is saturated, the rehardening stage is naturally obtained since the isotropic and kinematic hardening phenomena are still developing. Beyond the onset of failure characterized by a pressure-sensitive failure criterion, the damage process leading to the total failure is controlled by a second internal scalar, so-called failure variable. The final failure occurs when the failure variable reaches its critical value. To avoid the loss of solution uniqueness when dealing with the continuum damage mechanics formalism, a non-local implicit gradient formulation is used for both the softening and failure variables, leading to a multi-mechanism non-local damage continuum. The pressure sensitivity considered in both the yield and failure conditions allows for the distinction under compression and tension loading conditions. It is shown through experimental comparisons that the proposed constitutive model has the ability to capture the complex behavior of amorphous glassy polymers, including their failure.

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Section: Mesh Objectivitymentioning

confidence: 99%

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

Nguyễn

Lani

Pardoen

et al. 2016

International Journal of Solids and Structures

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“…Following a similar approach than in [35], the free energy associated with the crack surface in a one-dimensional setting is assumed to be stated under the form Ψ surf = Ψ surf ( u ; Z), or in other words, to be dependent on the jump and some internal variables Z. If the material unloading is linear elastic, the closing of the cohesive band follows the same non-dissipative behaviour.…”

Section: One Dimensional Problem Settingmentioning

confidence: 99%

“…Indeed, the decoupling between elements eases parallel implementation. The following lines explain how the non-local DG formalism developed in [35] is extended to the hybrid CDM/CBM scheme.…”

Section: Discontinuous Galerkin Frameworkmentioning

confidence: 99%

“…Such a system of equations has been solved in [35] using a cohesive zone model (instead of a cohesive band model) by assuming that the transition occurs at a damage value close to one. In this paper, a more general solving strategy is developed in order to extract the cohesive band behaviour and to deduce an appropriate band thickness value.…”

Section: Semi-analytical Resolution Of the Localisation Problemmentioning

confidence: 99%

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A damage to crack transition model accounting for stress triaxiality formulated in a hybrid nonlocal implicit discontinuous Galerkin‐cohesive band model framework

Leclerc

Nguyễn

et al. 2017

Numerical Meth Engineering

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SUMMARYModelling the entire ductile fracture process remains a challenge. On the one hand, continuous damage models succeed in capturing the initial diffuse damage stage but are not able to represent discontinuities or cracks. On the other hand, discontinuous methods, as the cohesive zones, which model the crack propagation behaviour, are suited to represent the localised damaging process. However, they are unable to represent diffuse damage. Moreover, most of the cohesive models do not capture triaxiality effect.In this paper, the advantages of the two approaches are combined in a single damage to crack transition framework. In a small deformation setting, a non-local elastic damage model is associated with a cohesive model in a discontinuous Galerkin finite element framework. A cohesive band model is used to naturally introduce a triaxiality-dependent behaviour inside the cohesive law. Practically, a numerical thickness is introduced to recover a 3D-state, mandatory to incorporate the in-plane stretch effects. This thickness is evaluated to ensure the energy consistency of the method and is not a new numerical parameter. The traction-separation law is then built from the underlying damage model.The method is numerically shown to capture the stress triaxiality effect on the crack initiation and propagation.

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“…cohesive damage type interface models see Barenblatt (1962), Needleman (1990Needleman ( , 1992Needleman ( , 2014, van den Bosch et al (2006van den Bosch et al ( , 2007, Mosler and Scheider (2011), Aragón et al (2013), Wu et al (2014) and references therein. -A coherent interface is endowed with its own elastic behavior or more precisely with its own energetic structure.…”

Section: Introductionmentioning

confidence: 99%

Coherent Energetic Interfaces Accounting for In-Plane Degradation

Esmaeili¹,

Javili²,

Steinmann³

2017

Defect and Material Mechanics

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Interfaces can play a dominant role in the overall response of a body. The importance of interfaces is particularly appreciated at small length scales due to large area to volume ratios. From the mechanical point of view, this scale dependent characteristic can be captured by endowing a coherent interface with its own elastic resistance as proposed by the interface elasticity theory. This theory proves to be an extremely powerful tool to explain size effects and to predict the behavior of nano-materials. To date, interface elasticity theory only accounts for the elastic response of coherent interfaces and obviously lacks an explanation for inelastic interface behavior such as damage or plasticity. The objective of this contribution is to extend interface elasticity theory to account for damage of coherent interfaces. To this end, a thermodynamically consistent interface elasticity theory with damage is proposed. A local damage model for the interface is presented and is extended towards a non-local damage model. The non-linear governing equations and the weak forms A. Esmaeili · P. Steinmann (B) Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstrasse 5, 91058 Erlangen, Germany e-mail: paul.steinmann@ltm.uni-erlangen.de A. Esmaeili e-mail: ali.esmaeili@ltm.uni-erlangen.de A. Javili Department of Mechanical Engineering, Bilkent University, 06800 Ankara, Turkey e-mail: ajavili@bilkent.edu.tr thereof are derived. The numerical implementation is carried out using the finite element method and consistent tangents are listed. The computational algorithms are given in detail. Finally, a series of numerical examples is studied to provide further insight into the problem and to carefully elucidate key features of the proposed theory.

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

Cited by 26 publications

References 58 publications

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

A damage to crack transition model accounting for stress triaxiality formulated in a hybrid nonlocal implicit discontinuous Galerkin‐cohesive band model framework

Coherent Energetic Interfaces Accounting for In-Plane Degradation

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