A spectral method for three-dimensional elastodynamic fracture problems

Geubelle, Philippe H.

doi:10.1016/0022-5096(95)00043-i

Cited by 202 publications

(212 citation statements)

References 35 publications

Supporting

Mentioning

211

Contrasting

Order By: Relevance

“…Stress perturbations can be obtained by solving the elastodynamic plane strain equations forû x (x; y; t) andû y (x; y; t), and calculating the associated stresses. The results can be taken from Geubelle and Rice (1995), and show that the perturbation of shear stress is…”

Section: Response To In-plane Perturbationsmentioning

confidence: 99%

See 1 more Smart Citation

Rate and state dependent friction and the stability of sliding between elastically deformable solids

Rice

Lapusta

Ranjith

2001

Journal of the Mechanics and Physics of Solids

574

622

View full text Add to dashboard Cite

We study the stability of steady sliding between elastically deformable continua using rate and state dependent friction laws. That is done for both elastically identical and elastically dissimilar solids. The focus is on linearized response to perturbations of steady-state sliding, and on studying how the positive direct e ect (instantaneous increase or decrease of shear strength in response to a respective instantaneous increase or decrease of slip rate) of those laws allows the existence of a quasi-static range of response to perturbations at su ciently low slip rate. We discuss the physical basis of rate and state laws, including the likely basis for the direct e ect in thermally activated processes allowing creep slippage at asperity contacts, and estimate activation parameters for quartzite and granite. Also, a class of rate and state laws suitable for variable normal stress is presented. As part of the work, we show that compromises from the rate and state framework for describing velocity-weakening friction lead to paradoxical results, like supersonic propagation of slip perturbations, or to ill-posedness, when applied to sliding between elastically deformable solids. The case of sliding between elastically dissimilar solids has the inherently destabilizing feature that spatially inhomogeneous slip leads to an alteration of normal stress, hence of frictional resistance. We show that the rate and state friction laws nevertheless lead to stability of response to su ciently short wavelength perturbations, at very slow slip rates. Further, for slow sliding between dissimilar solids, we show that there is a critical amplitude of velocity-strengthening above which there is stability to perturbations of all wavelengths. ?

show abstract

Section: Response To In-plane Perturbationsmentioning

confidence: 99%

“…The explicit form of the transfer functions M ij involves rather complicated expressions, that can be developed from Geubelle and Rice (1995) and are given in Ranjith and Rice (2001). …”

Section: Quasistatic Analysis Of Stability Of Slow Frictional Slidingmentioning

confidence: 99%

Rate and state dependent friction and the stability of sliding between elastically deformable solids

Rice

Lapusta

Ranjith

2001

Journal of the Mechanics and Physics of Solids

574

622

View full text Add to dashboard Cite

show abstract

“…Once j-(x, t) is thus known, the velocity S,,(x, t) at that time can be computed by simultaneously solving (1) together with some constitutive relation between z and 6, and possibly 6,,. For example, Geubelle and Rice (1995) modeled mode I cracking with a simple cohesive model with linear displacement-weakening from peak to zero strength. More complex constitutive laws have been used to characterize shear rupture surfaces, such as rate-and state-dependent friction laws (Perrin et al, 1995) which relate the strength to both the slip velocity and a state variable whose value depends on previous slip history.…”

Section: F(t) = -F(f)'['a C(i$+(t-b))d(h)dbmentioning

confidence: 99%

“…

ABSTRACT Perrin et al (1995) and Geubelle and Rice (1995) have introduced a spectral method for numerical solution of two-and three-dimensional elastodynamic fracture problems. The method applies for ruptures confined to a plane separating homogeneous elastic half spaces.

…”

mentioning

confidence: 99%

See 1 more Smart Citation

A spectral method for numerical elastodynamic fracture analysis without spatial replication of the rupture event

Cochard¹,

Rice²

1997

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

Perrin et al. (1995) and Geubelle and Rice (1995) have introduced a spectral method for numerical solution of two-and three-dimensional elastodynamic fracture problems. The method applies for ruptures confined to a plane separating homogeneous elastic half spaces. In this method, the physical variables, such as the traction components of stress and displacement discontinuity on the rupture plane, are represented as Fourier series in space with time-dependent coefficients. An analytical solution is found for each Fourier mode, in that each Fourier coefficient for stress is expressed by the time convolution of the corresponding coefficient for displacement with a convolution kernel specific to the rupture mode. Once the 2D formulation of the method is known, the method is readily generalizable to 3D problems in that it involves only linear combinations of the convolution kernels found for each rupture mode in 2D. This conceptual simplicity has, however, a major drawback : due to the Fourier series representations of the physical variables, the problem solved is in fact an infinite and periodic replication of rupture events on the fracture plane. So, in order to study the evolution of a single rupture, one has to use a spatial period large enough in order that the waves coming from the replication cracks do not enter the zone of interest during the time duration studied, or provide negligible stress alteration when they do arrive. We show here how to rigorously offset this defect while retaining the modal independence.Once expressed in the spatial domain, the method amounts to truncating in space the space-time convolution kernels, in a manner that provides an exact evaluation for all positions within the rupture domain (where the constitutive law between stress and displacement discontinuity is to be imposed), but not outside. In order for the method to be identical in structure to the method of Perrin et al. (1995) and Geubelle and Rice (1995). the oeriod of the Fourier series is requested to be only twice as large as the rupture domain of interest. The only difference, then, to the original spectral method is that the convolution kernels in the Fourier domain require more elaborate calculations to be established, but this has to be done only once to allow simulations on a given domain. '$3 1997

show abstract

A Numerical Scheme for Mode Iii Dynamic Fracture Problems

Morrissey

Geubelle

1997

Int. J. Numer. Meth. Engng.

View full text Add to dashboard Cite

SUMMARYThis paper summarizes the formulation and numerical implementation of a spectral scheme specially designed for dynamic anti-plane shear (mode III) fracture problems. The scheme allows for a wide variety of simulations ranging from the dynamic loading of stationary cracks to the spontaneous propagation of faults. The method is based on a spectral form of the elastodynamic relation between the shearing tractions acting on the fracture surface and the resulting slip velocity response for a planar two-dimensional crack in an infinite linearly elastic medium. The formulation is expressed in the Fourier domain and involves a convolution over the past slip or slip rate history. Conversion between spectral and real domains is performed through the fast Fourier transform algorithm. The time-integration scheme is explicit and a variety of constitutive laws can be used to express the strength of the material on the fault plane. The stability and accuracy of the numerical scheme are discussed through comparison with existing analytical solutions involving non-propagating and propagating cracks. The extraction of the dynamic stress intensity factor from the computed slip history is described.1997 by John Wiley & Sons, Ltd.

show abstract

A spectral method for three-dimensional elastodynamic fracture problems

Cited by 202 publications

References 35 publications

Rate and state dependent friction and the stability of sliding between elastically deformable solids

Rate and state dependent friction and the stability of sliding between elastically deformable solids

A spectral method for numerical elastodynamic fracture analysis without spatial replication of the rupture event

A Numerical Scheme for Mode Iii Dynamic Fracture Problems

Contact Info

Product

Resources

About