TY - JOUR
T1 - Fractional-order derivative and time-dependent viscoelastic behaviour of rocks and minerals
AU - Kawada, Yusuke
AU - Yajima, Takahiro
AU - Nagahama, Hiroyuki
N1 - Funding Information:
Acknowledgements. The authors would like to thank T. Ohuchi, H. Hara, T. Yamashita, and K. Yamasaki for their encouragements and valuable and fruitful comments for this study. The authors also appreciated helpful comments from two anonymous reviewers. YK and TY were financially supported by a research fellowship from Japan Society for the Promotion of Science.
Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013/12
Y1 - 2013/12
N2 - A general constitutive equation for viscoelastic behaviour of rocks and minerals with fractional-order derivative is investigated. This constitutive law is derived based on differential geometry and thermodynamics of rheology, and the fractional order of derivative represents the degree of time delay. Analyzing some laboratory experimental data of high temperature deformation of rocks and minerals such as halite, marble and orthopyroxene, we propose how to determine the orders of fractional derivative for viscoelastic behaviours of rocks and minerals. The order is related to the exponents for the temporal scaling in the relaxation modulus and the stress power-law of strain rate, i.e., the non-Newtonian flow law, and considered as an indicator representing the macroscopic behaviour and microscopic dynamics of rocks.
AB - A general constitutive equation for viscoelastic behaviour of rocks and minerals with fractional-order derivative is investigated. This constitutive law is derived based on differential geometry and thermodynamics of rheology, and the fractional order of derivative represents the degree of time delay. Analyzing some laboratory experimental data of high temperature deformation of rocks and minerals such as halite, marble and orthopyroxene, we propose how to determine the orders of fractional derivative for viscoelastic behaviours of rocks and minerals. The order is related to the exponents for the temporal scaling in the relaxation modulus and the stress power-law of strain rate, i.e., the non-Newtonian flow law, and considered as an indicator representing the macroscopic behaviour and microscopic dynamics of rocks.
KW - differential geometry
KW - fractional-order derivative
KW - memory effect
KW - rock rheology
KW - viscoelasticity
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U2 - 10.2478/s11600-013-0153-x
DO - 10.2478/s11600-013-0153-x
M3 - Article
AN - SCOPUS:84884819092
SN - 1895-6572
VL - 61
SP - 1690
EP - 1702
JO - Acta Geophysica
JF - Acta Geophysica
IS - 6
ER -