Koeller RC (1984) Applications of fractional calculus to the theory of viscoelasticity. Kang HP (2014) Support technologies for deep and complex roadways in underground coal mines: a review. Jiao Z, Chen YQ, Podlubny I (2012) Distributed-order dynamic systems: stability, simulation, Applications and Perspectives. Ingman D, Suzdalnitsky J, Zeifman M (2000) Constitutive dynamic-order model for nonlinear contact phenomena. Ingman D, Suzdalnitsky J (2005) Application of differential operator with servo-order function in model of viscoelastic deformation process. Heymans N, Bauwens JC (1994) Fractal rheological models and fractional differential equations for viscoelastic behavior. In: Fractals and fractional calculus in continuum mechanics. Gorenflo R, Mainardi F (1997) Fractional calculus: integral and differential equations of fractional order. Ann Phys 12(11–12):692–703įjar E, Holt RM, Raaen AM, Risnes R, Horsrud P (2008) Petroleum related rock mechanics. Science Press, ChinaĬoimbra CF (2003) Mechanic with variable-order differential operators. Appl Math Model 55(3):551–568Ĭhen W, Sun HG, Li XC (2010) Fractional derivative modeling in mechanics and engineering. Finally, the variations and influence of elastic modulus and relaxation time on creep response based on proposed Caputo variable-order fractional damage creep model are discussed and expounded deeply.īouras Y, Zorica D, Atanacković TM, Vrcelj Z (2018) A non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete. ![]() And then, a comparative study with constant-order fractional damage creep model was performed to present the advantages of proposed Caputo variable-order fractional damage creep model, which gives further references for application of Caputo variable-order fractional derivative in rheological model. Next, for verifying the applicability of proposed damage creep model, a series of uniaxial creep experiments were conducted on sandstone under step by step loading, the creep data predicted by proposed damage creep model are well agreement with experimental creep data. Meanwhile, considering the importance of relaxation time in rheology, a modified damage factor is also presented and introduced in proposed model. The significance of relaxation time is firstly highlighted to reveal the evolution mechanism of viscoelasticity of creep and relaxation response by constructing equivalence between rheological responses of constant-order fractional Maxwell model and that of time-varying viscosity Maxwell model. ![]() In this study, based on the Caputo variable-order fractional derivative, a Caputo variable-order fractional creep model is proposed, whose physical interpretation is clearly stated by setting a varying-order function related to relaxation time. Establishing a fractional creep model with few parameters and explicit physical interpretation is of significant meaning for predicting rheological deformation of rock.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |