On the stability for linear viscoelastic solids
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چکیده
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15 صفحه اولOn Poisson’s Ratio in Linearly Viscoelastic Solids
Poisson’s ratio in viscoelastic solids is in general a time dependent (in the time domain) or a complex frequency dependent quantity (in the frequency domain). We show that the viscoelastic Poisson’s ratio has a different time dependence depending on the test modality chosen; interrelations are developed between Poisson’s ratios in creep and relaxation. The difference, for a moderate degree of ...
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We consider an integro-diierential equation which arises in linear viscoelasticity. By making use of an equivalent inner product, it is shown that the underlying contraction semigroup is exponentially stable. We also show that the nite dimensional semigroups arising from a known approximation scheme are uniformly exponentially stable.
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We study crack propagation in a viscoelastic solid. Using simple arguments, we derive equations for the velocity dependence of the crack-tip radius, a (v) , and for the energy per unit area to propagate the crack, G (v) . For a viscoelastic modulus E (omega) which increases as omega(1-s) (0< s< 1) in the transition region between the rubbery region and the glassy region, we find that a (v) appr...
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Lubrication flows appear in many applications in engineering, biophysics, and in nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubrication fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loa...
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 1997
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/1486541