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Dynamics in prestressed media with moving phase boundaries: a continuum theory of failure in solids

Archambeau, C. B. and Minster, J. B. (1978) Dynamics in prestressed media with moving phase boundaries: a continuum theory of failure in solids. Geophysical Journal of the Royal Astronomical Society, 52 (1). pp. 65-95. ISSN 0016-8009. doi:10.1111/j.1365-246X.1978.tb04222.x.

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Spontaneous failure in a solid medium is described as a localized transition of the material from one physical state to another, characterized in part by contrasting rheological properties and density. Such a process is viewed as a local disordering of the relatively ordered structure of the solid due to any variety of causes, such as massive microfracturing or shear melting, and can be confined to a very thin zone, but nevertheless of finite volume such that a volumetric transition energy can be defined. This leads to the description of failure as a generalized phase transition in a prestressed continuum, with instability and transition zone growth being driven by the energy contributions from the relaxation of stress in the surrounding medium. Direct application of mass, momentum and energy conservation to such a generalized phase transition leads to ‘jump’ conditions specified on the growing boundary surface of the transition zone, that relate the rupture growth to discontinuous changes in the dynamic field variables across the failure zone boundary. These field discontinuities are, in turn, related to the localized changes in physical properties induced by failure. Dynamical conditions for rapid spontaneous failure growth in a stressed medium are investigated in some detail, and we find that the failure boundary growth can be simply expressed in terms of energy ‘failure condition’ and a dynamic growth condition specifying the rupture velocity. These results imply that the integral energy change associated with earthquakes is in the range 10^4−10^6 erg/g. Further the failure growth rate is shown to be expressible in terms of the rheological properties of the material before and after failure. For shear melting resulting in a low viscosity fluid, for example, the rupture velocity will be near the shear velocity of the original material. A general Green's function solution for the radiation due to stress relaxation in the medium surrounding the growing failure zone is given and provides the basis for detailed computations of the strain or displacement field changes due to spontaneous failure processes. In particular, it is shown that the jump conditions for the growing transition zone boundary appear naturally as surface integral terms over the boundary. Since these boundary conditions contain the failure rate explicitly, then these terms include effects that have not been represented in previous integral representations of the radiation field resulting from failure. Further, we show that the formal Green's integral representation for the dynamical wave field can be used with known, simple Green's functions to generate approximate solutions for complex failure processes occurring in media with inhomogeneous material properties and prestress.

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Additional Information:Copyright © 1978 The Royal Astronomical Society. Received 1977 June 20; in original form 1976 April 19. This research has been supported under Advanced Research Projects Agency, Department of Defense, Contracts F 44620-72-C-0078 and F 44620-72-C-0083 monitored by the Air Force Office of Scientific Research and the Air Force Cambridge Research Laboratory monitored contract No. F 19628-76-C-0061. A part of this work was also supported by the National Science Foundation under grants GI-44212 and DES 75-20137.
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Advanced Research Projects Agency (ARPA)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)F 44620-72-C-0078
Air Force Office of Scientific Research (AFOSR)F 44620-72-C-0083
Air Force Cambridge Research LaboratoriesF 19628-76-C-0061
NSFDES 75-20137
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Record Number:CaltechAUTHORS:20141111-164554679
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Official Citation:C. B. Archambeau and J. B. Minster Dynamics in prestressed media with moving phase boundaries: a continuum theory of failure in solids Geophys. J. Int. (1978) 52 (1): 65-95 doi:10.1111/j.1365-246X.1978.tb04222.x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51619
Deposited By: George Porter
Deposited On:12 Nov 2014 15:50
Last Modified:10 Nov 2021 19:13

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