Dynamic mode III fracture in viscoelastic media

Geubelle, Philippe H.; Danyluk, Michael; Hilton, Harry H.

doi:10.1016/s0020-7683(97)00084-x

Cited by 10 publications

(2 citation statements)

References 26 publications

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“…This is also what happens in the viscoelastic case, even for the formulation with replication, as shown by Geubelle et al (1997).…”

Section: The Spectral Methods Without Replication Two-dimensional Prosupporting

confidence: 53%

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

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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

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“…This is also what happens in the viscoelastic case, even for the formulation with replication, as shown by Geubelle et al (1997).…”

Section: The Spectral Methods Without Replication Two-dimensional Prosupporting

confidence: 53%

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

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“…The original formulation (Perrin, Rice, and Zheng, 1994;Geubelle and Rice, 1995;Morrissey and Geubelle, 1997) dealt with the homogeneous linearly elastic problem. Special forms have since then been introduced to tackle dynamic crack propagation in bimaterial (Geubelle and Breitenfeld, 1997;Breitenfeld and Geubelle, 1998) and viscoelastic (Geubelle, Danyluk, and Hilton, 1997;Danyluk, Geubelle, and Hilton, 1998) media. Although these various formulations present some important differences, for example, in the expression of the convolution kernels, all share the same basic structure.…”

Section: -D Dynamic Fracture Events 27mentioning

confidence: 99%

Parallel Implementation of a Spectral Scheme for Simulations of 3-D Dynamic Fracture Events

Breitenfeld

Geubelle

2000

The International Journal of High Performance Computing Applica

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The spectral scheme, whose parallel implementation is described in this paper, is currently one of the most efficient computational approaches available to solve a class of fundamental 3-D dynamic fracture problems. The scheme uses a special form of the boundary integral elastodynamic formulation and allows for the solution of the spontaneous motion (initiation, propagation, and arrest) of arbitrary shape planar cracks embedded in a homogeneous or bimaterial medium and subjected to arbitrary loading conditions. The parallel implementation described hereafter allows for the efficient solution of very large dynamic fracture problems, typically one to two orders of magnitudes larger than those available to date. It is based on a stacking scheme that distributes the spectral modes across the processors to achieve balance in memory and CPU time requirements. Although developed for dynamic fracture simulations, the spectral scheme and its parallel implementation are applicable to other problems in computational physics characterized by a convolution operation involving a decaying kernel.

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The role played by viscoelasticity in the bulk material during the propagation of a dynamic crack in elastomers

2021

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Investigation of dynamic fracture of elastomers can still be considered to be a relatively open area. When a sheet of elastomer is stretched in a tensile machine and a crack is introduced, the crack propagates at a speed that depends on the initial stretch level. There are instances where this speed is noted to exceed the shear wave speed based on the elastic modulus under high imposed stretches. Such cracks are called transonic cracks. It was usually hypothesized that either the hyperelastic or viscoelastic stiffening of the bulk material raises the wave speeds resulting in crack speeds entering the transonic regime. This article revisits the experiments performed on Polyurethane elastomers in Corre et al. (Int J Fract 224(1):83-100, 2020) to study the implications of both these hypotheses. Crack propagation has not been explicitly modeled, but the crack speeds are implicitly imposed on the geometry using the boundary conditions extracted from the experimental data. It has been determined that the viscoelasticity in the bulk is needed to describe and understand the transonic cracks in polyurethane elastomer. The inclu-

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Dynamic mode III fracture in viscoelastic media

Cited by 10 publications

References 26 publications

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

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

Parallel Implementation of a Spectral Scheme for Simulations of 3-D Dynamic Fracture Events

The role played by viscoelasticity in the bulk material during the propagation of a dynamic crack in elastomers

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