科研之友
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摘要
In many existing theories for incompressible polymeric liquids the Cauchy stress is decomposed as T = p1 S-v + Se, where p is an arbitrary pressure, S-v = 2 mu D-s a deviatoric viscous stress with ics a viscosity and D the deviatoric stretching tensor, and Se is a deviatoric elastic stress which is introduced to account for stiffening arising from the alignment of long-chain polymer molecules during flow. A constitutive equation for Se needs to be prescribed and there are a large number of different proposals in the literature, with most proposals involving a hypoelastic rate constitutive equation for Se given in terms of a suitable frame-indifferent rate, which is usually taken as the Oldroyd or upper convected rate. As is well-known, a hypoelastic equation for the stress is not thermodynamically consistent, in the sense that the constitutive equation for Se is not derived form a free energy function. The purpose of this paper is to present an alternative thermodynamically -consistent and frame-indifferent continuum theory for incompressible viscoelastic liquids. The theory is based on a Kroner -type multiplicative decomposition of the deformation gradient F of the form F = FeFP. In this theory the elastic stress S5 is derived from a free -energy function which is prescribed in terms of a suitable measure based on the unimodular elastic distortion tensor Fe. This relation is supplemented by an evolution equation for the unimodular plastic distortion tensor FP the plastic flow rule. We study the response of the constitutive theory in steady simple shearing and steady extensional flows. We show: (i) that the theory qualitatively reproduces the experimentally-observed transient shear -thinning and normal stress effects during shearing flows of a polymer melt; and (ii) that it also reproduces the transient extensional response of a polymer melt.
- 出版日期2016-8
