On the role of material dissipation for the crack-driving force

Tillberg, Johan; Larsson, Fredrik; Runesson, Kenneth

doi:10.1016/j.ijplas.2009.12.001

Cited by 18 publications

(16 citation statements)

References 33 publications

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“…Under this premise, crack growth is driven by the near tip J-integral (c.f. Rice [1]; Gurtin and Podio-Guidugli [2]; Tillberg et al [3]), a quantity that coincides with the energy release rate in the case of elastic materials. In situations involving elastic-plastic solids, it may happen that the calculated near tip J-integral vanishes (Rice [4], Simha et al [5], Brocks et al [6]), which implies that there is no driving force for crack growth.…”

Section: Introductionmentioning

confidence: 99%

A phase-field/gradient damage model for brittle fracture in elastic–plastic solids

Duda

Ciarbonetti

Sánchez

et al. 2015

International Journal of Plasticity

211

106

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The formulation of a phase-field continuum theory for brittle fracture in elastic-plastic solids and its computational implementation are presented in this contribution. The theory is based on a virtual-power formulation in which two additional and independent kinematical descriptors are introduced, namely the phase-field and the accumulated plastic strain. Further, it incorporates irreversibility of both phase-field and plastic strain evolutions by introducing suitable constraints and by carefully heeding the influence of those constraints on the kinetics underlying microstructural changes associated with plasticity and fracture.The numerical implementation employs the finite-element method for spatial discretization and a splitting scheme with sub-stepping for the time integration. To illustrate its potential utility, we apply the model to a number of well known linear, as well as non-linear, fracture mechanics problems.The described phase-field model, coupled with plasticity, provides a feasible technique to analyzing crack initiation and the subsequent crack growth resistance only if the length scale parameter included in the phase-field model is finite and treated as a material parameter which should be properly characterized.

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Section: Introductionmentioning

confidence: 99%

A phase-field/gradient damage model for brittle fracture in elastic–plastic solids

Duda

Ciarbonetti

Sánchez

et al. 2015

International Journal of Plasticity

211

106

View full text Add to dashboard Cite

show abstract

“…In the case of inelastic response, nodal smoothing techniques such as the aforementioned L 2 -projection may turn out insufficient for capturing the steep gradients occurring in the near-tip region, contributing to the "pathological" FE-mesh sensitivity reported in e.g. Tillberg et al [16].…”

Section: Computation Of Configurational Forcesmentioning

confidence: 99%

“…In order to compute the spatial gradient in such a case, it is natural to utilize some sort of smoothing strategy. Such a strategy introduces further discretization errors, especially in crack problems involving steep gradients, see Tillberg et al [16] and Özenç et al [17]. In Özenç et al [17] and Näser et al [18], it is shown that pathindependence of the J -integral for inelasticity is achieved only by including the material dissipation inside the contour.…”

Section: Introductionmentioning

confidence: 99%

“…A previously derived thermodynamically consistent definition of configurational forces, developed by Tillberg et al [16] is thereby used. The coupled primary fields are the displacements along with a so-called micro-stress 2 field, the latter being the stress measure which is energy-conjugated to the spatial gradient of the internal variables.…”

Section: Introductionmentioning

confidence: 99%

“…Namely, smooth gradient fields are obtained, which together with the nodal values of the gradient field 3 , obtained from the solution of the primary problem at hand, provide a rational basis towards computation of configura- 1 The evaluation of spatial gradients of internal variables is performed in order to compute the so-called material dissipation part of the total configurational force, see e.g. Tillberg et al [16]. 2 The respective field, which is properly introduced in Sect.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On configurational forces for gradient-enhanced inelasticity

2017

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In this paper we discuss how configurational forces can be computed in an efficient and robust manner when a constitutive continuum model of gradient-enhanced viscoplasticity is adopted, whereby a suitably tailored mixed variational formulation in terms of displacements and microstresses is used. It is demonstrated that such a formulation produces sufficient regularity to overcome numerical difficulties that are notorious for a local constitutive model. In particular, no nodal smoothing of the internal variable fields is required. Moreover, the pathological mesh sensitivity that has been reported in the literature for a standard local model is no longer present. Numerical results in terms of configurational forces are shown for (1) a smooth interface and (2) a discrete edge crack. The corresponding configurational forces are computed for different values of the intrinsic length parameter. It is concluded that the convergence of the computed configurational forces with mesh refinement depends strongly on this parameter value. Moreover, the convergence behavior for the limit situation of rate-independent plasticity is unaffected by the relaxation time parameter.

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An implicit adaptive node‐splitting algorithm to assess the failure mechanism of inelastic elastomeric continua

Özenç

Kaliske

2014

Numerical Meth Engineering

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SUMMARYThis contribution presents a mesh adaptive crack propagation scheme for the evaluation of the viscoelastic fracture response of elastomers at large strains and up to high loading rates. The approach accounts for micromechanical based features of both elastic and viscoelastic bulk responses of idealized polymer networks. To this end, the Bergstörm–Boyce model is considered to introduce hyperelastic and nonlinear finite viscoelastic responses. Moreover, the crack driving force and the crack driving direction are predicted by the material force approach. A consistent thermodynamic framework for the combined configurational motion in viscoelastic continua at finite strain regime is discussed.The fracture toughness of non‐strain‐crystallizing elastomers shows strong rate dependency and the energy release rate versus the rate of tearing to be a fundamental material property. Therefore, in this contribution, a dynamic fracture criterion, which is a function of the rate of crack growth, is shown to be adequate in numerical simulations. The use of the presented method enables to study fracture behaviour of any material nonlinearity within the implicit time integration. Main feature of the proposed algorithm is restructuring the overall discrete system by duplication of crack front DOFs based on minimization of the overall energy via the Griffith criterion. Copyright © 2014 John Wiley & Sons, Ltd.

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On the role of material dissipation for the crack-driving force

Cited by 18 publications

References 33 publications

A phase-field/gradient damage model for brittle fracture in elastic–plastic solids

A phase-field/gradient damage model for brittle fracture in elastic–plastic solids

On configurational forces for gradient-enhanced inelasticity

An implicit adaptive node‐splitting algorithm to assess the failure mechanism of inelastic elastomeric continua

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