A standard linear solid model of a rubber-toughened polymer has relaxed (long-time)…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Condensed Matter, Materials & Soft Matter · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Non-Newtonian and viscoelastic fluids

Problem

A standard linear solid model of a rubber-toughened polymer has relaxed (long-time) modulus G∞=1.0 MPaG_\infty = 1.0\,\mathrm{MPa}, arm spring modulus G1=4.0 MPaG_1 = 4.0\,\mathrm{MPa}, and arm viscosity η=2.0×105 Pa s\eta = 2.0\times10^5\,\mathrm{Pa\,s}. ((a)) Find the arm's relaxation time τM=η/G1\tau_M = \eta/G_1. ((b)) Find the retardation time τR=τM(1+G1/G∞)\tau_R = \tau_M(1 + G_1/G_\infty). ((c)) Find the angular frequency at which G′′G'' peaks (ωτM=1\omega\tau_M = 1) and the angular frequency at which the loss factor G′′/G′G''/G' peaks (ωτMτR=1\omega\sqrt{\tau_M\tau_R} = 1).

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