Magnetic susceptibility and plastic strain of rocks by the differential geometric theory of the physical interaction field

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Abstract

From the differential geometric theory of the physical interaction field between the deformational field and the magnetic field and thermodynamics principles, we can derive a new non-linear equation on the piezomagnetic effects of plastically deformed rocks without using special knowledge of material properties. Moreover, from von Mises' yield condition (plastic potential), Onsager's theorem (non-linear phenomenological equation) and a new flow rule of the plasticity theory generalized by the theory of the physical interaction field, we lead to a new theoretical relationship between the magnetic susceptibility tensor χmnPl on the plastic deformation and the plastic strain tensor εijPl of plastically deformed rocks given by χmnPl = 2/3ESω̃mnijεij Pl where ω̃mnij is the fourth-rank asymmetric tensor with a non-linear property on the physical interaction coefficient and ES is the secant modulus referred to plastic strain. Let χ̌mn be an initial magnetic susceptibility tensor, then the second-rank asymmetric tensor (3/2ES)χ̌mnω̃ij mn is equivalent to Borradaile-Alford's empirical matrix Mij relating strain to susceptibility change. We are developing this relation to infer the strain of plastically deformed rocks from magnetic susceptibility changes.

Original languageEnglish
Pages (from-to)167-173
Number of pages7
JournalPhysics and Chemistry of the Earth
Volume22
Issue number1-2 SPEC. ISS.
DOIs
Publication statusPublished - 1997

ASJC Scopus subject areas

  • Earth and Planetary Sciences(all)

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