Configurational forces and the basic laws for crack propagation

An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

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“…Besides approaches based on configurational forces [286][287][288][289] there are four major cracking criteria in LEFM.…”

Section: Fracture Mechanics-based Criteriamentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

162

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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

210

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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“…in Miehe and Gürses [34] and Miehe et al [35], the constitutive relation (27) is introduced as a postulate, and the balance law of material forces Equation (36) and the balance law of physical forces Equation (16) are necessary conditions for non-negative dissipation. In Gurtin and PodioGuidugli [42,43], the balance law of material forces Equation (36) is also obtained as a postulate, additionally to the postulate of balance of physical forces. Furthermore, Makowski et al [46] analyze the dissipative process of crack evolution in brittle and ductile materials.…”

Section: Power Of Mechanical Forcesmentioning

confidence: 99%

“…As noted in Gurtin and Podio-Guidugli [42,43] the power of the distributed reaction forces r·n on *R[t] in Figure 2 should account for the power performed in the addition and removal of material at the boundary *R[t] and for the change in material structure as the crack tip evolves. Classically, the standard stress r expends power over the material velocityu.…”

Section: Power Of Mechanical Forcesmentioning

confidence: 99%

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Geometry update driven by material forces for simulation of brittle crack growth in functionally graded materials

Mahnken

2008

Numerical Meth Engineering

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SUMMARYFunctionally graded materials (FGMs) are advanced materials that possess continuously graded properties, such that the growth of cracks is strongly dependent on the gradation of the material. In this work a thermodynamic consistent framework for crack propagation in FGMs is presented, by applying a dissipation inequality to a time-dependent migrating control volume. The direction of crack growth is obtained in terms of material forces as a result of the principle of maximum dissipation. In the numerical implementation a staggered algorithm-deformation update for fixed geometry followed by geometry update for fixed deformation-is employed within each time increment. The geometry update is a result of the incremental crack propagation, which is driven by material forces. The corresponding mesh is generated by combining Delaunay triangulation with local mesh refinement. Furthermore a Newton algorithm is proposed, taking into account mesh transfer of displacements for crack propagation in incremental elasticity. In two numerical examples brittle crack propagation in FGMs is investigated for various directions of strength gradation within the structures.

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Configurational forces and the basic laws for crack propagation

Cited by 139 publications

References 12 publications

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

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

Geometry update driven by material forces for simulation of brittle crack growth in functionally graded materials

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