Nonlinear model of shear flow of thixotropic viscoelastoplastic continua taking into account the evolution of the structure and its analysis. (English. Russian original) Zbl 1515.76013
Mosc. Univ. Mech. Bull. 77, No. 5, 127-135 (2022); translation from Vestn. Mosk. Univ., Ser. I 77, No. 5, 31-39 (2022).
Using continuum mechanics, polymer melts, solutions and gels can be modelled as viscoelastic fluids satisfying a constitutive equation of Maxwell type like (1). Here, the authors continue their studies of viscoelasticity [Mosc. Univ. Mech. Bull. 71, No. 6, 132–136 (2016; Zbl 1464.74027); translation from Vestn. Mosk. Univ., Ser. I 71, No. 6, 36–41 (2016); Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 21, No. 1, 160–179 (2017; Zbl 1413.74026); Mosc. Univ. Mech. Bull. 73, No. 2, 39–42 (2018; Zbl 1471.74013); translation from Vestn. Mosk. Univ., Ser. I 73, No. 2, 59–63 (2018); Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana. Ser. Estestv. Nauki 6, 92–112 (2018; doi:10.18698/1812-3368-2018-6-92-112); Mech. Compos. Mater. 55, 195–210 (2019; doi:10.1007/s11029-019-09809-w); Russ. Metall. (Met.) 2019, 956–963 (2019; doi:10.1134/S0036029519100136)] where they consider a particular multidimensional formulation of Maxwell’s equation.
In the present work, the focus is on coupling the material parameters \(G,\eta\) of Maxwell equation with an evolution equation for the structural parameter \(w\), which is the percentage of polymer intersections that are effectively bonded through the so-called “cross-links”. This evolution equation models the competition between cross-linking \(w\to1\) at a time-scale \(1/k_1\) and the destruction of cross-links \(-g(\tau/\tau_c)w\) as a function of the degree of stress \(\tau/\tau_c\) at a time-scale \(1/k_2\) (\(k_1,k_2>0\) are some material parameters). It is shown that a unique equilibrium point exists, that it is stable, and the coupling makes enough physical sense for applications.
In the present work, the focus is on coupling the material parameters \(G,\eta\) of Maxwell equation with an evolution equation for the structural parameter \(w\), which is the percentage of polymer intersections that are effectively bonded through the so-called “cross-links”. This evolution equation models the competition between cross-linking \(w\to1\) at a time-scale \(1/k_1\) and the destruction of cross-links \(-g(\tau/\tau_c)w\) as a function of the degree of stress \(\tau/\tau_c\) at a time-scale \(1/k_2\) (\(k_1,k_2>0\) are some material parameters). It is shown that a unique equilibrium point exists, that it is stable, and the coupling makes enough physical sense for applications.
Reviewer: Sebastien Boyabal (Chatou)
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