Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds

Gao, Hangshan; Klein, Patrick A.

doi:10.1016/s0022-5096(97)00047-1

Cited by 302 publications

(165 citation statements)

References 23 publications

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“…We can quote Gao and Klein (1999) Rabczuk and Samaniego (2008), besides the earlier references Needleman and Tvergaard (1994a,b), Belytschko and Tabbara (1996), and Zhou et al (1996b). The challenge is to accurately capture the experimentally observed failure mode transition from ductile to brittle failure as the impact velocity reduces, as well as the critical value of the impact velocity where this transition occurs.…”

Section: Failure Mode Transition In Ductile Materialsmentioning

confidence: 99%

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

2009

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This paper presents the extension of some finite elements with embedded strong discontinuities to the fully transient range with the focus on dynamic fracture. Cracks and shear bands are modeled in this setting as discontinuities of the displacement field, the so-called strong discontinuities, propagating through the continuum. These discontinuities are embedded into the finite elements through the proper enhancement of the discrete strain field of the element. General elements, like displacement or assumed strain based elements, can be considered in this framework, capturing sharply the kinematics of the discontinuity for all these cases. The local character of the enhancement (local in the sense of defined at the element level, independently for each element) allows the static condensation of the different local parameters considered in the definition of the displacement jumps. All these features lead to an efficient formulation for the modeling of fracture in solids, very easily incorporated in an existing general finite element code due to its modularity. We investigate in this paper the use of this finite element formulation for the special challenges that the dynamic range leads to. Specifically, we consider the modeling of failure mode transitions in ductile materials and crack branching in brittle solids. To illustrate the performance of the proposed formulation, we present a series of numerical simulations of these cases with detailed comparisons with experimental and other numerical results reported in the literature. We conclude that these finite element methods handle well these dynamic problems, still maintaining the aforementioned features of computational efficiency and modularity.

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Section: Failure Mode Transition In Ductile Materialsmentioning

confidence: 99%

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

2009

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“…To model failure mechanisms in nanomaterials, we have developed a virtual internal bond (VIB) (22,23) method, which incorporates an atomic cohesive force law into the constitutive model of materials. Fig.…”

mentioning

confidence: 99%

Materials become insensitive to flaws at nanoscale: Lessons from nature

Gao

Jäger

et al. 2003

Proc. Natl. Acad. Sci. U.S.A.

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1,668

1,231

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Natural materials such as bone, tooth, and nacre are nanocomposites of proteins and minerals with superior strength. Why is the nanometer scale so important to such materials? Can we learn from this to produce superior nanomaterials in the laboratory? These questions motivate the present study where we show that the nanocomposites in nature exhibit a generic mechanical structure in which the nanometer size of mineral particles is selected to ensure optimum strength and maximum tolerance of flaws (robustness). We further show that the widely used engineering concept of stress concentration at flaws is no longer valid for nanomaterial design.

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“…They are motivated, in large part, by introducing a lengthscale (absent in classical elasticity) by augmenting the displacement field with supplementary fields (e.g., rotations) that provide information about fine-scale kinematics, by using higher-order gradients of the displacement field, by averaging local strains and/or stresses, or by introducing a notion of a field into molecular dynamics. We also mention the papers [15,23] where variational principles for the generalized continua are described useful for finite element based discretizations, and [21] where the classical theory is augmented with internal bonds.…”

Section: Generalized Continuamentioning

confidence: 99%

Blending Methods for Coupling Atomistic and Continuum Models

Bochev¹,

Lehoucq²,

Parks³

et al. 2009

Multiscale Methods

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In this paper we review recent developments in blending methods for atomisticto-continuum (AtC) coupling in material statics problems. Such methods tie together atomistic and continuum models by using a bridge domain that connects the two models. There are several reasons why AtC coupling methods (of which blending methods are a subset) are important and have been subject to an increased interest in the recent years. Despite tremendous increases in computational power, fully atomistic simulations on an entire model domain remain computationally infeasible for many applications of interest. As a result, attention has focused on hybrid schemes where in all regions with well-behaved solutions, the atomistic (microscopic) model is replaced by a (macroscopic) continuum model enabling a more efficient computational scheme (see [14,29,9] for general information). The main challenge is the synthesis of the two distinct models in a manner that minimizes, or altogether eliminates, undesirable artifacts such as ghost forces, unphysical solutions let alone supporting mathematical analysis. Notable AtC coupling methods include the quasicontinuum method [39], the bridging scale decomposition [41], and [24] where atomistic and continuum models are overlapped (see the latter two references, and those mentioned above for numerous citations to the literature). The numerical analysis of AtC methods has lagged in comparison to the number of methods proposed; see the recent papers [2,3,17,31,26,27] for analyses of the quasicontinuum method.Blending methods couple atomistic/continuum modes via a dedicated blending, or bridge, region inserted between the atomistic and continuum subdomains. The atomistic and continuum models are tied together by using a suitable "continuity" condition (or balance law) for the atomistic and continuum positions or displacements in this region. A complicating factor is that the atomistic and (classical) continuum elastic models rely on nonlocal and local models of force interaction, respectively. In the (classical) elastic context, the "local force" is that exerted on a body by contact forces occurring on the surface (of the body). In contrast, in the atomistic model, forces are summed from atoms separated by a finite distance. The incompatibility arising from coupling local and nonlocal force models is intrinsic. The goal of our paper is threefold. First, we review how blending approaches attempt to ameliorate the various negative effects by relying on an interface between the two models. Second, we discuss the beginnings of a JFISH: "CHAP06" -2009/6/4 -17:33 -PAGE 166 -#2 166Blending methods for coupling atomistic and continuum models numerical analysis by discussing consistency of the resulting numerical schemes. Third, we suggest how the intrinsic limitation associated with coupling nonlocal and local mechanical theories may be avoided by replacing the classical elastic theory with a nonlocal elastic theory.The use of a bridge domain in blending methods bears a resemblance to conventional overlapping...

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Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds

Cited by 302 publications

References 23 publications

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

Materials become insensitive to flaws at nanoscale: Lessons from nature

Blending Methods for Coupling Atomistic and Continuum Models

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