A new constitutive equation that models extensional flow strain hardening based on evolving natural configurations: stability analysis |
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Authors: | Liviu-Iulian Palade Jay R Walton |
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Affiliation: | a Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA b Department of Mathematics, Texas A&M University, College Station, TX 77843, USA c Universita’ degli Studi di Firenze, Dipartimento di Matematica “U. Dini”, Viale Morgagni 67/a, 50134 Firenze, Italy |
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Abstract: | Polymer melt viscoelastic fluids often exhibit in elongational flows a significant increase in the elongational viscosity known as strain hardening. This phenomenon could be related to polydispersity, e.g. the presence of a small fraction of very high molecular weight chains whose time frame relaxation spectrum is different from the small chains one. In the present work, we present a fully objective constitutive equation (CE) to primarily model extensional strain hardening based on the new concept of multiple configuration materials. Next, we analyze the CE stability properties with respect to small perturbations about the rest state. |
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Keywords: | Extensional flows Viscoelastic constitutive equation Hadamard stability |
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