TY - JOUR

T1 - Magnetic susceptibility and plastic strain of rocks by the differential geometric theory of the physical interaction field

AU - Nakamura, Norihiro

AU - Nagahama, H.

N1 - Funding Information:
Acknowledgments. We wish to thank B. Henry and G. 1. Borradaile for valuahle and useful suggestions on the earlier version of this rnanuscript. We also thank K. Yamasaki for valuable discussions. This work was supported by a Grant-in-Aid from the Tohoku Developing Memorial Foundation.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

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U2 - 10.1016/s0079-1946(97)00097-9

DO - 10.1016/s0079-1946(97)00097-9

M3 - Article

AN - SCOPUS:0031419939

VL - 22

SP - 167

EP - 173

JO - Physics and Chemistry of the Earth

JF - Physics and Chemistry of the Earth

SN - 1474-7065

IS - 1-2 SPEC. ISS.

ER -