A SPECTRAL METHOD FOR NUMERICAL ELASTODYNAMIC FRACTURE-ANALYSIS WITHOUT SPATIAL REPLICATION OF THE RUPTURE EVENT

Authors
Citation
A. Cochard et Jr. Rice, A SPECTRAL METHOD FOR NUMERICAL ELASTODYNAMIC FRACTURE-ANALYSIS WITHOUT SPATIAL REPLICATION OF THE RUPTURE EVENT, Journal of the mechanics and physics of solids, 45(8), 1997, pp. 1393-1418
Citations number
17
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics, Condensed Matter",Mechanics
ISSN journal
0022-5096
Volume
45
Issue
8
Year of publication
1997
Pages
1393 - 1418
Database
ISI
SICI code
0022-5096(1997)45:8<1393:ASMFNE>2.0.ZU;2-5
Abstract
Perrin et al. (1995) and Geubelle and Rice (1995) have introduced a sp ectral method for numerical solution of two- and three-dimensional ela stodynamic 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 an d displacement discontinuity on the rupture plane, are represented as Fourier series in space with time-dependent coefficients. An analytica l solution is found for each Fourier mode, in that each Fourier coeffi cient for stress is expressed by the time convolution of the correspon ding coefficient for displacement with a convolution kernel specific t o the rupture mode. Once the 2D formulation of the method is known, th e method is readily generalizable to 3D problems in that it involves o nly linear combinations of the convolution kernels found for each rupt ure mode in 2D. This conceptual simplicity has, however, a major drawb ack: due to the Fourier series representations of the physical variabl es, the problem solved is in fact an infinite and periodic replication of rupture events on the fracture plane. So, in order to study the ev olution of a single rupture, one has to use a spatial period large eno ugh in order that the waves coming from the replication cracks do not enter the zone of interest during the time duration studied, or provid e negligible stress alteration when they do arrive. We show here how t o rigorously offset this defect while retaining the modal independence . Once expressed in the spatial domain, the method amounts to truncati ng in space the space-time convolution kernels, in a manner that provi des an exact evaluation for all positions within the rupture domain (w here the constitutive law between stress and displacement discontinuit y is to be imposed), but not outside. In order for the method to be id entical in structure to the method of Perrin er al. (1995) and Geubell e and Rice (1995), the period of the Fourier series is requested to be only twice as large as the rupture domain of interest. The only diffe rence, then, to the original spectral method is that the convolution k ernels in the Fourier domain require more elaborate calculations to be established, but this has to be done only once to allow simulations o n a given domain. (C) 1997 Elsevier Science Ltd.