A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si20.gif" display="inline" overflow="scroll"><mml:mi>J</mml:mi></mml:math>-integral-based arc-length solver for brittle and ductile crack propagation in finite deformation-finite strain hyperelastic solids with an application to graphene kirigami

Barbieri, Ettore; Ongaro, Federica; Pugno, Nicola

doi:10.1016/j.cma.2016.10.043

Cited by 13 publications

(11 citation statements)

References 52 publications

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“…Notice that, in previous definitions, we supposed that the elemental discontinuity splits Ω e into two sub-elements Ω + e and Ω − e such that vector n is inward Ω + e . By substituting definition (16) into (14), and exploiting the properties of the Dirac's delta function, one obtains the following local/discontinuity-scale momentum balance equation:…”

Section: Statically and Kinematically Optimal Nonsymmetric (Skon) Formentioning

confidence: 99%

“…Since the pioneering work of [6], many algorithms were proposed in the literature to overcome these limitations. Among them, one should mention path-following constraints on the rate of variation of selected sets of DOFs [6,7], on strain measures [8,9,10] or on variables directly associated with the energy dissipation occurring in the system during damage propagation [11,12,13,14,15,16]. Hybrid geometric-dissipative arc-length methods were also proposed (see e.g.…”

Section: Introductionmentioning

confidence: 99%

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Discontinuity-scale path-following methods for the embedded discontinuity finite element modeling of failure in solids

Rastiello¹,

Riccardi²,

Richard

2019

Computer Methods in Applied Mechanics and Engineering

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The initiation and propagation of cracks in solids often leads to unstable structural responses characterized by snap-backs. Path-following procedures allow finding a solution to the algebraic system of equations resulting from the numerical formulation of the considered problem. Accordingly, the boundary value problem is supplemented by a novel global unknown, namely, the loading factor, which should comply with a dedicated equation, the so-called path-following constraint equation. In this contribution, path-following methods are discussed within the framework of the Embedded Finite Element Method (E-FEM). Thanks to the enhanced kinematic description provided by the E-FEM, we show that it is possible to formulate constraint equations where the prescribed quantities are directly related to the dissipative process occurring at the strong discontinuity level. After introducing the augmented E-FEM formulation, three discontinuity-scale path-following constraints and their numerical implementation (using an operator-splitting method) are described. Simple quasi-static strain localization problems characterized by unstable structural responses exhibiting multiple snap-backs are numerically simulated. A comparison with several well-known constraint equations (commonly used in non-linear finite element computations) is finally established. This allows for illustrating the main features of the proposed methods as well as their efficiency in controlling highly unstable embedded discontinuity finite element simulations.

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Section: Statically and Kinematically Optimal Nonsymmetric (Skon) Formentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discontinuity-scale path-following methods for the embedded discontinuity finite element modeling of failure in solids

Rastiello¹,

Riccardi²,

Richard

2019

Computer Methods in Applied Mechanics and Engineering

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“…The only boundary conditions that can be applied when adopting Riks solvers are tractions or body forces which, when integrated over the boundary of volume of the domain, manifest themselves as equivalent nodal forces. This limits the physical problems that can be modelled using arc-length methods to those where it is appropriate to load the analysed structure via nodal forces, however non-zero displacement constraints 3 are often more appropriate especially when analysing the response of experimental tests where rigid constraints are imposed on the boundary of loaded specimens. While the initial literature on arc-length techniques is quite old, there is much evidence of their recent use in many new structural areas such as the following.…”

Section: Introductionmentioning

confidence: 99%

“…Turco et al [38], and Findeisen et al [20]; and Brittle materials suffering damage (e.g. May et al [30], and Gao and Bower [21]) , bones [9], laminated composites [1],and graphene kirigami [3].…”

Section: Introductionmentioning

confidence: 99%

A displacement-controlled arc-length solution scheme

Pretti

Coombs

Augarde

2022

Computers & Structures

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Tracing load-displacement paths in structural mechanics problems is complicated in the presence of critical points of instability where conventional load-or displacement control fails. To deal with this, arc-length methods have been developed since the 1970s, where control is taken over increments of load at these critical points, to allow full transit of the load-displacement path. However, despite their wide use and incorporation into commercial finite element software, conventional arc-length methods still struggle to cope with non-zero displacement constraints. In this paper we present a new displacement-controlled arc-length method that overcomes these shortcomings through a novel scheme of constraints on displacements and reaction forces. The new method is presented in a variety of serving suggestions, and is validated here on six very challenging problems involving truss and continuum finite elements. Despite this paper's focus on structural mechanics, the new procedure can be applied to any problems that involve nonhomogeneous Dirichlet constraints and challenging equilibrium paths.

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“…The basic J-integral definition assumes that calculations are conducted along a contour around the crack tip in a two-dimensional case. A number of applications have been proposed within many scientific settings for elastic [4], hyperelastic [5], composite [6] and viscoelastic materials [7], generalized to accommodate a crack growth model [8]. The J-integral concept has now been generalized for complex loadings with coupling friction effects [9], transverse loadings [10], mixed-mode configurations [11][12], and fatigue applications [13].…”

Section: Introductionmentioning

confidence: 99%

A new analytical generalization of the J and G-theta integrals for planar cracks in a three-dimensional medium

Kabir

Dubois

Pitti

et al. 2018

Theoretical and Applied Fracture Mechanics

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International audienceThis paper focuses on the theoretical and numerical development of the J-integral concept for three-dimensional problems. A new integral parameter, developed for the real three-dimensional case, computes the combined energy release rate for an arbitrary crack front. A path-independent integral is verified in both the static and crack propagation cases. Generalization of the í µí°½ "#-integral toward its í µí°º % "# implementation form is performed. The efficiency of this proposed integral is then compared with a number of í µí°½ integrals available in the literature. Lastly, the paper offers a finite element implementation along with its numerical validation

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AJ-integral-based arc-length solver for brittle and ductile crack propagation in finite deformation-finite strain hyperelastic solids with an application to graphene kirigami

Cited by 13 publications

References 52 publications

Discontinuity-scale path-following methods for the embedded discontinuity finite element modeling of failure in solids

Discontinuity-scale path-following methods for the embedded discontinuity finite element modeling of failure in solids

A displacement-controlled arc-length solution scheme

A new analytical generalization of the J and G-theta integrals for planar cracks in a three-dimensional medium

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