Elastostatic Cracks

Broberg, K. B.

doi:10.1016/b978-012134130-5/50005-2

Cited by 56 publications

(106 citation statements)

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“…While a number of scenarios for the nucleation of such modes have been suggested [149,199,200,208], it is not yet entirely clear how the transition from sub-Rayleigh to super-shear ruptures comes about. A common theme among these different scenarios is that sufficient elastic energy becomes available in close proximity to a frictional interface.…”

Section: Fig 12mentioning

confidence: 99%

“…These are commonly referred to as "super-shear" ruptures. Super-shear cracks have long been considered in the fracture literature [3,199,200], but until they were observed in the beautiful experiments by Rosakis and coworkers [151], they were often considered to be of purely theoretical value. Since this first observation in weakly bonded homogeneous blocks that were ballistically loaded, mode II super-shear ruptures have been observed numerically [201][202][203] as well as in a variety of other scenarios that include frictional interfaces and quasi-static loading [141,146,149,152].…”

Section: Fig 12mentioning

confidence: 99%

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Recent developments in dynamic fracture: some perspectives

Fineberg

Bouchbinder

2015

Int J Fract

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We briefly review a number of important recent experimental and theoretical developments in the field of dynamic fracture. Topics include experimental validation of the equations of motion for straight tensile cracks (in both infinite media and strip geometries), validation of a new theoretical description of the near-tip fields of dynamic cracks incorporating weak elastic nonlinearities, a new understanding of dynamic instabilities of tensile cracks in both 2D and 3D, crack front dynamics, and the relation between frictional motion and dynamic shear cracks. Related future research directions are briefly discussed.

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Section: Fig 12mentioning

confidence: 99%

Section: Fig 12mentioning

confidence: 99%

Recent developments in dynamic fracture: some perspectives

Fineberg

Bouchbinder

2015

Int J Fract

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“…In spite of the impressive progress in the field, formation of cracks under energy-minimal deformations, to our knowledge, is not fully resolved. In this domain the best reference is the book by K. B. Broberg [12].…”

Section: Introductionmentioning

confidence: 99%

Mappings of Least Dirichlet Energy and their Hopf Differentials

Iwaniec

Onninen

2013

Arch Rational Mech Anal

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Abstract. The paper is concerned with mappings h : X onto − − → Y between planar domains having least Dirichlet energy. The existence and uniqueness (up to a conformal change of variables in X ) of the energyminimal mappings is established within the class H 2(X, Y) of strong limits of homeomorphisms in the Sobolev space W 1,2 (X, Y) , a result of considerable interest in the mathematical models of Nonlinear Elasticity. The inner variation (of the independent variable in X) leads to the Hopf differential hzhz dz ⊗ dz and its trajectories. For a pair of doubly connected domains, in which X has finite conformal modulus, we establish the following principle:A mapping h ∈ H 2(X, Y) is energy-minimal if and only if its Hopf-differential is analytic in X and real along ∂X. In general, the energy-minimal mappings may not be injective, in which case one observes the occurrence of cracks in X . Nevertheless, cracks are triggered only by the points in ∂Y where Y fails to be convex. The general law of formation of cracks reads as follows:Cracks propagate along vertical trajectories of the Hopf differential from ∂X toward the interior of X where they eventually terminate before making a crosscut.

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“…that elasticity theory is entirely sufficient to describe the crack front dynamics. Since elasticity theory predicts the divergence of stress at the crack front [4], realistic materials will almost surely yield plastically or develop additional local damage. Such a change in material properties, precisely where the dynamics is taking place, may very well change the nature of the long-range interactions of the bulk degrees of freedom.…”

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confidence: 99%

“…The RHS of Eq. (1) is the difference between the local driving force (below referred to as G, related physically to the energy release rate driving the crack [4]), and Γ(x, h) which is a random quenched noise (representing the random material fracture energy [4]). G (0) is the control parameter that represents the energy release rate of a straight front.…”

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confidence: 99%

Self-affine roughness of a crack front in heterogeneous media

2007

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The long-ranged elastic model, which is believed to describe the evolution of a self-affine rough crack-front, is analyzed to linear and non-linear orders. It is shown that the nonlinear terms, while important in changing the front dynamics, are not changing the scaling exponent which characterizes the roughness of the front. The scaling exponent thus predicted by the model is much smaller than the one observed experimentally. The inevitable conclusion is that the gap between the results of experiments and the model that is supposed to describe them is too large, and some new physics has to be invoked for another model.The self-affine roughness of a crack-front propagating under a tensile load in a randomly heterogeneous system is a well studied issue, both experimentally and theoretically. Experimentally one measures the position h(x, t) of the crack front, where h is the position of the front as a function of the span-wise coordinate x at time t, and finds that this is a self-affine function whose roughness is characterized by a scaling exponent ζ (defined below in Eq. (4)) in the range of 0.5-0.65 [1,2]. Theoretically there appears to be a consensus that the appropriate model for such dynamical roughening is a long-ranged elastic string close to its depinning threshold. This model is defined by the equation of motion for a front h(x, t), which is allowed to move only forward due to the irreversibility of the fracture process [3] ∂h(x, t) ∂tHere and bellow the integral is meant in the Cauchy Principal Value sense. The RHS of Eq. (1) is the difference between the local driving force (below referred to as G, related physically to the energy release rate driving the crack [4]), and Γ(x, h) which is a random quenched noise (representing the random material fracture energy [4]). G (0) is the control parameter that represents the energy release rate of a straight front. The integral term stands for the long ranged restoring forces stemming from bulk elastic degrees of freedom. The correspondence between the theoretical model and the experimental findings remained however unclear, since the best numerical studies of the resulting self-affine graph h(x) of this model came up with a roughness exponent ζ = 0.388 ± 0.002 [5], clearly outside the range of error of the experimental measurements. This apparent difficulty led to a number of interesting studies, insisting that the model is basically right, and that the result concerning the scaling exponent is not final. Thus, for example, in [6] the authors analyzed Eq.(1) using a functional renormalization group. They have calculated the scaling exponent ζ to one-and two-loop orders in ǫ, where ǫ = 2 − d. To one-loop order the result is ζ = ǫ/3, predicting ζ = 1/3 at d = 1, deviating considerably from the best numerical estimate.To two-loop order the prediction increases to about 0.466, leading to a statement that the model probably describes properly the experimental findings. Unfortunately, it is well known that the ǫ expansion is often an asymptotic series [7], sometime ...

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Elastostatic Cracks

Cited by 56 publications

References 0 publications

Recent developments in dynamic fracture: some perspectives

Recent developments in dynamic fracture: some perspectives

Mappings of Least Dirichlet Energy and their Hopf Differentials

Self-affine roughness of a crack front in heterogeneous media

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