Abstract:
We continue the systematic analytical study of a nonlinear Maxwell-type constitutive equation for shear flow of thixotropic viscoelastic media accounting for interaction of deformation process and structure evolution, namely, the influence of the kinetics formation and breakage of chain cross-links, agglomerations of molecules and crystallites on viscosity and shear modulus and deformation influence on the kinetics. We formulated it in the previous article and reduced it to the set of two nonlinear autonomous differential equations for two unknown functions (namely, the stress and relative cross-links density). We examine the phase portrait of the system for arbitrary (increasing) material function and six (positive) material parameters governing the model and prove that the (unique) equilibrium point is stable and the only three cases are realized: the equilibrium point is a stable node or a degenerated stable node or a stable spiral point. We found criteria for every case in the form of explicit restrictions on the material function and parameters and shear rate.
Key words:
thixotropy, viscoelasticity, rheological model, polymeric systems, equilibrium point, phase portrait, stable spiral point, flow curve, viscosity anomaly.
Citation:
A. V. Khokhlov, “Equilibruim point and phase portrait of flow model for thixotropic media with consideration of the structure evolution”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 4, 30–39; Moscow University Mеchanics Bulletin, 78:4 (2023), 91–101
\Bibitem{Kho23}
\by A.~V.~Khokhlov
\paper Equilibruim point and phase portrait of flow model for thixotropic media with consideration of the structure evolution
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2023
\issue 4
\pages 30--39
\mathnet{http://mi.mathnet.ru/vmumm4551}
\crossref{https://doi.org/10.55959/MSU0579-9368-1-64-4-5}
\elib{https://elibrary.ru/item.asp?id=54354437}
\transl
\jour Moscow University Mеchanics Bulletin
\yr 2023
\vol 78
\issue 4
\pages 91--101
\crossref{https://doi.org/10.3103/S0027133023040039}
Linking options:
https://www.mathnet.ru/eng/vmumm4551
https://www.mathnet.ru/eng/vmumm/y2023/i4/p30
This publication is cited in the following 7 articles:
A. V. Khokhlov, V. V. Gulin, “Influence of Structural Evolution and Load Level on the Properties of Creep and Recovery Curves Generated by a Nonlinear Model for Thixotropic Viscoelastoplastic Media”, Phys Mesomech, 28:1 (2025), 66
A. V. Khokhlov, V. V. Gulin, “Families of Stress-Strain, Relaxation, and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 1. The model, Its Basic Properties, Integral Curves, and Phase Portraits”, Mech Compos Mater, 60:1 (2024), 49
A. V. Khokhlov, V. V. Gulin, “Families of Stress–Strain, Relaxation and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 2. Relaxation and Stress-Strain Curves”, Mech Compos Mater, 60:2 (2024), 259
A. V. Khokhlov, V. V. Gulin, “Families of Stress-Strain, Relaxation, and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 3. Creep Curves”, Mech Compos Mater, 60:3 (2024), 473
A. V. Khokhlov, “Creep curves generated by a nonlinear flow model of tixotropic viscoelastoplastic media taking into account structure evolution”, Moscow University Mеchanics Bulletin, 79:4 (2024), 119–129
A.V. KHOKHLOV, V.V. GULIN, “INFLUENCE OF STRUCTURE EVOLUTION AND LOAD LEVEL ON THE PROPERTIES OF CREEP AND RECOVERY CURVES PRODUCED BY A NONLINEAR MODEL FOR THIXOTROPIC VISCOELASTOPLASTIC MEDIA”, FM, 27:5 (2024)
A. V. Khokhlov, “Osobennosti povedeniya vyazkouprugoplasticheskikh materialov, modeli i sistema programm kvazistaticheskikh ispytanii polimerov i kompozitov dlya kompleksnogo izucheniya ikh svoistv i vybora i identifikatsii opredelyayuschikh sootnoshenii”, Vysokomolekulârnye soedineniâ. Seriâ C, 66:2 (2024), 157
Citation in format AMSBIB
Contact us: