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Breitenfeld, Michael; Geubelle, Philippe H.

doi:10.1023/a:1007535703095

Cited by 53 publications

(33 citation statements)

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“…The right-hand-side of Eq. (13) represents the infinite half-space linear elastodynamic Green's function [75][76][77], corresponding to the momentum balance equation ρü = ∇·σ (where ρ is the mass density and the stress tensor σ is related to displacement gradients ∇u through Hooke's law), and contains two contributions. The contribution µ∂ t δ(x, t)/2c s is 'instantaneous', i.e.…”

Section: Bulk Elasticity In Frictional Systemsmentioning

confidence: 99%

“…Mathematically handling the infinitely long-range interaction in the H → ∞ limit generally raises significant difficulties and in many case a variety of numerical methods are invoked, e.g. spectral techniques [75][76][77]. The spatiotemporal range of interaction encapsulated in F τ [∂ x δ(x, t), ∂ t δ(x, t)] diminishes as the system height H is reduced.…”

Section: Bulk Elasticity In Frictional Systemsmentioning

confidence: 99%

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Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity

et al. 2019

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Frictional interfaces are abundant in natural and engineering systems, and predicting their behavior still poses challenges of prime scientific and technological importance. At the heart of these challenges lies the inherent coupling between the interfacial constitutive relation -the macroscopic friction law -and the bulk elasticity of the bodies that form the frictional interface. In this feature paper, we discuss the generic properties of the macroscopic friction law and the many ways in which its coupling to bulk elasticity gives rise to rich spatiotemporal frictional dynamics. We first present the widely used rate-and-state friction constitutive framework, discuss its power and limitations, and propose extensions that are supported by experimental data. We then discuss how bulk elasticity couples different parts of the interface, and how the range and nature of this interaction are affected by the system's geometry. Finally, in light of the coupling between interfacial and bulk physics, we discuss basic phenomena in spatially-extended frictional systems, including the stability of homogeneous sliding, the onset of sliding motion and a wide variety of propagating frictional modes (e.g. rupture fronts, healing fronts and slip pulses). Overall, the results presented and discussed in this feature paper highlight the inseparable roles played by interfacial and bulk physics in spatially-extended frictional systems. * eran.bouchbinder@weizmann.ac.il arXiv:1908.02820v1 [cond-mat.soft]

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Section: Bulk Elasticity In Frictional Systemsmentioning

confidence: 99%

Section: Bulk Elasticity In Frictional Systemsmentioning

confidence: 99%

Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity

et al. 2019

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“…Discussion.-Taking advantage of the fine discretization allowed by the boundary integral formulation [20], we investigate numerically the interplay of a dynamic crack front with heterogeneities. A planar straight crack under plane strain conditions interplays with an idealized microstructure made of equispaced stripes of weaker and stronger areas.…”

Section: 144101 (2017) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

“…The rupture is assumed to propagate along a weak interface under mode-II plane strain conditions. This heterogeneous fracture problem is solved using a boundary integral formulation of the elastodynamics equation proposed by Breitenfeld and Geubelle [20]. This approach, initially developed by Geubelle and Rice [21], allows an extremely fine discretization of the fracture plane associated with a prescribed cohesive model, particularly suited to describe phenomena occurring in the immediate vicinity of dynamic crack tips [22].…”

mentioning

confidence: 99%

“…Problem description: Numerical scheme.-The dynamic fracture problem is solved with the aid of the spectral scheme [20,21], a spectral form of the elastodynamic boundary integral relations between the displacements u AE along the fracture plane and the corresponding traction stress τðx; tÞ. The numerical method allows for a detailed description of the evolution of the displacements, velocities, and traction stresses along the interface, especially in the failure zone captured with the aid of a cohesive failure model relating the displacement jump in the slip direction, δ x , and the interface strength…”

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confidence: 99%

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Interplay between Process Zone and Material Heterogeneities for Dynamic Cracks

2017

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Using an elastodynamic boundary integral formulation coupled with a cohesive model, we study the problem of a dynamic rupture front propagating along an heterogeneous plane. We show that small-scale heterogeneities facilitate the supershear transition of a mode-II crack. The elastic pulses radiated during front accelerations explain how microscopic variations of fracture toughness change the macroscopic rupture dynamics. Perturbations of dynamic fronts are then systematically studied with different microstructures and loading conditions. The process zone size is the intrinsic length scale controlling heterogeneous dynamic rupture. The ratio of this length scale to asperity size is proposed as an indicator to transition from quasihomogeneous to heterogeneous fracture. Moreover, we discuss how the shortening of the process zone size with increasing crack speed brings the front to interact with smaller details of the microstructure. This study shines new light on recent experiments reporting perturbations of dynamic rupture fronts, which intensify with crack propagation speed. DOI: 10.1103/PhysRevLett.119.144101 Introduction.-Our modern understanding of fracture arose from Griffith [1] and Irwin [2] which viewed crack propagation as a thermodynamic process where, at equilibrium, the energetic cost of creating new surfaces in the material is balanced by the release of strain energy subsequent to crack advance. This theoretical framework known as linear elastic fracture mechanics (LEFM) has been successfully used over the last 50 years to predict the stability of flaws in engineering materials. Consequently LEFM was extended to cracked bodies far from equilibrium, i.e., to dynamic fracture mechanics [3,4]. Experiments on brittle solids showed that this dynamic theory of fracture gives good prediction for slow crack propagation but is unsuitable to describe fast rupture events where the crack front speed is a significant fraction of material shear wave speed c s . In particular, linear elastic theory overestimates the propagation speed and significantly underestimates the dissipated energy. For a review of dynamic fracture experiments, the reader is referred to [5][6][7][8][9]. A three-stage transition is universally observed within brittle materials, usually referred to as "mirror," "mist," and "hackle" in reference to the postmortem appearance of fracture surface. At low rupture velocity, fracture surfaces are planar and smooth (mirror) and crack dynamics is thereby well predicted by LEFM theory. As crack speed increases, the rupture remains in plane but fracture surface roughens (mist), followed by a stage characterized by the formation of out-of-plane microbranches (hackle), and finally the onset of macroscopic branching. This transition observed in various brittle materials [7,10] and at different scales [11,12] explains how linear elasticity fails at describing fast rupture events where the front starts to interplay with the microstructure and/or dynamic instabilities

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A hybrid finite element‐spectral boundary integral approach: Applications to dynamic rupture modeling in unbounded domains

Hajarolasvadi

Albertini

et al. 2018

Num Anal Meth Geomechanics

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Summary The finite element method (FEM) and the spectral boundary integral method (SBI) have both been widely used in the study of dynamic rupture simulations along a weak interface. In this paper, we present a hybrid method that combines FEM and SBI through the consistent exchange of displacement and traction boundary conditions, thereby benefiting from the flexibility of FEM in handling problems with nonlinearities or small‐scale heterogeneities and from the superior performance and accuracy of SBI. We validate the hybrid method using a benchmark problem from the Southern California Earthquake Center's dynamic rupture simulation validation exercises.We further demonstrate the capability and computational efficiency of the hybrid scheme for resolving off‐fault heterogeneities by studying a 2D in‐plane shear crack in two different settings: one where the crack is embedded in a high‐velocity zone and another where it is embedded in a low‐velocity zone. Finally, we discuss the potential of the hybrid method for addressing a wide range of problems in geophysics and engineering.

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Cited by 53 publications

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Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity

Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity

Interplay between Process Zone and Material Heterogeneities for Dynamic Cracks

A hybrid finite element‐spectral boundary integral approach: Applications to dynamic rupture modeling in unbounded domains

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