Abstract:
We formulate a nonlinear Maxwell-type constitutive equation for shear deformation of polymers in flow state or polymer viscoelastic melts and solutions which takes into account interaction of deformation process and structure evolution, namely, 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. The constitutive equation is governed by an increasing material function and six positive parameters. We reduce it to the set of two nonlinear autonomous differential equations for two unknown functions (namely, stress and relative cross-links density) and prove existence and uniqueness of its equilibrium point and prove that its coordinates depend monotonically on every material parameter and on shear rate. We derive general equations for model flow curve and viscosity curve and prove that the first one increase and the second one decrease while the shear rate grows. Thus the model describes basic phenomena observed for simple shear flow of shear thinning fluids.
Citation:
A. M. Stolin, A. V. Khokhlov, “Nonlinear model of shear flow of thixotropic viscoelastoplastic continua taking into account the evolution of the structure and its analysis”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2022, no. 5, 31–39; Moscow University Mechanics Bulletin, 77:5 (2022), 127–135
\Bibitem{StoKho22}
\by A.~M.~Stolin, A.~V.~Khokhlov
\paper Nonlinear model of shear flow of thixotropic viscoelastoplastic continua taking into account the evolution of the structure and its analysis
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2022
\issue 5
\pages 31--39
\mathnet{http://mi.mathnet.ru/vmumm4493}
\elib{https://elibrary.ru/item.asp?id=49553377}
\transl
\jour Moscow University Mechanics Bulletin
\yr 2022
\vol 77
\issue 5
\pages 127--135
\crossref{https://doi.org/10.3103/S0027133022050065}
Linking options:
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https://www.mathnet.ru/eng/vmumm/y2022/i5/p31
This publication is cited in the following 13 articles:
Guang-quan Niu, Xue-shi Ma, Liang Wang, Mechanisms and Machine Science, 175, Computational and Experimental Simulations in Engineering, 2025, 571
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
Alexander N. Muranov, Viktor R. Lysenko, Maxim A. Kocharov, “Rheological Behavior Features of Feedstocks with a Two-Component Wax–Polyolefin Binder Compared to Analogs Based on Polyoxymethylene”, J. Compos. Sci., 8:6 (2024), 199
A. V. Khokhlov, “Hybridization of a Linear Viscoelastic Constitutive Equation and a Nonlinear Maxwell-Type Viscoelastoplastic Model, and Analysis of Poisson's Ratio Evolution Scenarios under Creep”, Phys Mesomech, 27:3 (2024), 229
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
A. V. Khokhlov, “Equilibruim point and phase portrait of flow model for thixotropic media with consideration of the structure evolution”, Moscow University Mеchanics Bulletin, 78:4 (2023), 91–101
A. V. Khokhlov, V. V. Gulin, “Analysis of the Properties of a Nonlinear Model for Shear Flow of Thixotropic Media Taking into Account the Mutual Influence of Structural Evolution and Deformation”, Phys Mesomech, 26:6 (2023), 621
A. V. Khokhlov, “Generalization of a Nonlinear Maxwell-Type Viscoelastoplastic Model and Simulation of Creep and Recovery Curves”, Mech Compos Mater, 59:3 (2023), 441
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