Abstract
This paper is dedicated to achieving the unification of the scattered Lomnitz type creep laws. Thereupon, a novel generalized fractional calculus, that is, Katugampola-like fractional calculus is well-defined and employed as an effective tool, along with some fundamental qualities as by-products. By virtue of the hereditary theory of viscoelasticity and Volterra integral equation method, a compatible stress-strain relation with memory effects and time-varying viscosity established results in a unified Lomnitz creep law. Then, a comparative analysis on the creep function and relaxation function inherited from the unified Lomnitz creep law is exhibited via reasoning and numerical simulation. Besides, physical interpretation of such unified Lomnitz creep law is also provided with the aid of the modified spring-dashpot model of Maxwell type. Results carried out in this paper might provide a full characterization of the creep of igneous rocks to meet some special theoretical and experimental requirements.
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