Research on constructing a new method in the composite model of rock rheology and a new principle for solving constitutive relation

Abstract

Rheological model plays an important role in revealing rheological characteristics of rocks. Due to the model’s construction and solution without considering the size-dependent effect of the elements, its physical mechanism and mathematical description decouples, as well as the loss in physical interpretability. To address these deficiencies, scale effects must be need to be considered when constructing and solving rheological models. Firstly, the new method of the one-dimensional(1D) rheological composite models, in consideration of the size relationship between the elements and the composite model, is proposed according to the physical mechanism and the mechanical principles. Secondly, the new principle consisted of 1D constitutive relations in the composite model is constructed through the composite relationship between the force and the deformation of each element. Thirdly, based on the new method, the Maxwell model, Kelvin model, and ideal viscoelastic model are improved and reconstructed. Meanwhile, the constitutive relations, creep and stress relaxation of the composite model are solved based on the new principle. The research results are prospected to provide a sound theoretical basis for the construction and solution of 1D rheological models of rocks.