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.
ASJC Scopus subject areas
- Earth and Planetary Sciences(all)