Continuum Mechanics Aspects of Geodynamics and Rock Fracture by K. E. Bullen (auth.), P. Thoft-Christensen (eds.)

By K. E. Bullen (auth.), P. Thoft-Christensen (eds.)

During a NATO complicated research Institute in Izmir, Tur­ key, July 1973 on sleek advancements in Engineering Seis­ mology and Earthquake Engineering it emerged debate on Continuum Mechanics points of Geodynamics and Rock Fracture Mechanics will be very welcome. consequently, it used to be made up our minds to hunt NATO sponsorship for a sophisticated research In­ stitute in this topic. the aim of the hot complex examine Institute was once to supply a hyperlink among mechanics of continuum media and geo­ dynamic s. by way of bringing jointly a bunch of best scientists from the above fields and members actively engaged in examine and functions within the similar fields, it was once believed that fruitful discussions may emerge to facilitate an trade of information, event and newly-conceived rules. The Institute aimed essentially on the answer of such difficulties as hooked up with the learn of tension and pressure con­ ditions within the Earth, frequent factors of earthquakes, strength unlock and focal mechanism and seismic wave propagation in­ troducing glossy equipment of continuum and rock fracture mechanics. Secondly to motivate scientists operating in continuum mechanics to open new avenues of analysis attached with the above difficulties, and seismologists to evolve smooth, complicated equipment of continuum and rock fracture mechanics to their work.

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Additional info for Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics: Proceedings of the NATO Advanced Study Institute held in Reykjavik, Iceland, 11—20 August, 1974

Sample text

In trying to explain the discrepancy between the theoretical (ideal) strength and the practical (bulk) strength of a solid undergoing brittle fracture and subjected to uniaxial tension, one assumes that the solid contains randomly distributed (penny-shaped) cracks. Usually it is then stated that the tensile strength aT is related to (say) kIC through (1) where a o is the radius of the (largest) penny-shaped crack and k IC is a material constant which is determined from standard plane strain fracture tests.

Astr. , 4, 295, 1961. R. A. W. Haddon and K. E. Bullen, Phys~ Earth Planet. ' 35, 1969. A. M. Dzievwnski and F. Gilbert, Geo,ehxs. , R. Astr. , ~, 401, 1973. ~ J. Asbel, V. I. Keilis-Borok and T. B. Yanovskaya, Geophys. , R. Astr. , ~, 25, 1966. F. Press, J. Geo,ehx~ Res. ~, 5223, 1968. L. B. Slichter, Proc. R. So~ Lond. A, 224, 43, 1954. G. Backus and F. Gilbert, Geophys. , ~Astr. , 16, 169, 1968. E. 7:, == CONSTRUCTION OF EARTH MODELS 19. 20. 21 H. Takeuchi and K. Sudo, J. Geophys. Res. 73, 3801, 1968.

The externally added (dU) and internally released energy (dVJ per unit crack front may then be expressed as follows: dU = 0 dV = - a+da Ja 2 a+da '" - aJ 21 cr yy (x)v(x-da)dx kl 2kl l2(x-a) E1. h (a+da-x) dx = - 2 7Tk l El da , Noting that for unit crack front dA = 2da, the fracture criterion becomes d -(U-V) da = (2l) Since U-V is a "potential" and a is a "distance", the deri vati ve in (21) has the dimension of "force". Consequently 2 d 7Tk l G = -(U-V) = da El (22) is also known as the "crack extension force" (after Irwin).

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