Nonequilibrium thermodynamics and rheology of viscoelastic polymer media

Leonov, A. I.

doi:10.1007/bf01517499

Cited by 514 publications

(238 citation statements)

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“…For this model, the total deformation rate is a sum of elastic deformation rate and inelastic deformation rate, which is represented by the following evolution equation (see Eckart [1948]; Leonov [1976]; Rubin [1987Rubin [ , 1994; Rubin and Yarin [1993] for three-dimensional models of this type),…”

Section: A Simple One-dimensional Modelmentioning

confidence: 99%

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Brittleness of fracture in flowing magma

Ichihara

Rubin

2010

J. Geophys. Res.

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[1] Understanding the transition to brittle fracture of flowing magma is essential for estimating the explosiveness of a volcanic eruption. In order to quantify brittleness of flowing magma, a new parameter b is introduced, which is a function of the ratio of the rate of change of the strain energy due to elastic distortional deformation to the mechanical power due to total distortional deformation rate. From the perspective of b, dependence of brittle fracture of magma on stress, decompression rate, strain rate, and shear-thinning effects are reviewed. The experimental data of Kameda et al. (2008) for rapid decompression of simulants of bubbly magma have also been reexamined. The results show that b exhibits a strong transition that correlates well with the observed transition between ductile expansion to brittle fragmentation. Moreover, b is useful in considering the effects of shear-thinning and steady-creep conditions on brittle fracture. Statements in the literature that suggest that materials behave in a brittle manner at sufficiently high strain rate are correct. However, these statements do not precisely quantify the notion of high strain rate so they are easy to misinterpret when considering the effect of shear thinning. Although shear thinning tends to increase the absolute magnitude of the total strain rate, it does not necessarily increase brittleness. Also, in principle, it is unlikely for brittle fracture to occur at steady creep. Cracking observed in steady-creep experiments of magma (Lavallee et al., 2007 may be attributed to small fluctuations with sufficiently high frequencies to satisfy the conditions for brittle fracture.

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Section: A Simple One-dimensional Modelmentioning

confidence: 99%

“…[60] Constitutive equations for elastic-viscoplastic response of a Maxwell-type material have been developed [Eckart, 1948;Leonov, 1976;Rubin, 1987Rubin, , 1994Rubin and Yarin, 1993]. In particular, the equations presented in Rubin [1987Rubin [ , 1994 exhibit a continuity of solid and fluid states.…”

Section: A2 Constitutive Equationsmentioning

confidence: 99%

Brittleness of fracture in flowing magma

Ichihara

Rubin

2010

J. Geophys. Res.

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“…(8) as the Leonov equation after its original proposer (Leonov, 1976 (8) may be integrated to obtain the evolution of stress for a given deformation history.…”

Section: Approach Based On Additive Decomposition Of the Velocity Gramentioning

confidence: 99%

“…One group have employed models based on additive split of the rate of deformation tensor (Nemat-Nasser, 1979 together with the assumption of zero viscous spin (Leonov, 1976). Another group assumed multiplicative decomposition of the deformation gradient (Kröner, 1960;Lee, 1969), together with a particular, convected, interpretation of the viscous velocity gradient and the assumption of zero viscous spin (Boyce et al 2000;Drozdov et al 2008).…”

Section: Introductionmentioning

confidence: 99%

On the modelling of highly elastic flows of amorphous thermoplastics

Figiel

Buckley

2009

International Journal of Non-Linear Mechanics

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International audienceTwo approaches to the kinematic structuring of constitutive models for highly elastic flows of polymer melts have been examined systematically, assuming either: (1) additivity of elastic and viscous velocity gradients, or (2) multiplicability of elastic and viscous deformation gradients. A series of constitutive models was compared, with differing kinematic structure but the same linear responses in elastic and viscous limits. They were solved numerically and their predictions compared, and they were also compared to those of the Giesekus model. Several variants, previously proposed as separate models, are shown to be equivalent and qualitatively in agreement with experiment, and therefore a sound basis for construction of models. But the assignment of viscous spin is critical: if it is assumed equal to the total spin with approach (1), or equal to zero with approach (2), then unphysical viscoelastic behaviour is predicted

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“…They compared flow-induced stresses, calculated in a fully coupled way, with results obtained by the decoupled method. The constitutive equation used was the compressible version of the Leonov model (see Leonov;59 Baaijens;' Flaman26). Results of both calculations compared satisfactorily.…”

Section: Introductionmentioning

confidence: 99%

The computation of properties of injection-moulded products

Douven

Baaijens

Meijer

1995

Progress in Polymer Science

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-Injection moulding is a flexible production technique for the manufacture of complex shaped, thin walled polymer products that require minimal finishing. During processing, the polymer experiences a complex deformation and temperature history that affects the final properties of the product.In a growing number of applications, injection-moulded products must meet high demands concerning their properties and dimensional stability. As a consequence, the ultimate aim of numerical simulations of the injection-moulding process is not only to analyse the processing stage but also to calculate the mechanical (and optical) properties of the product, starting from the material properties and the processing conditions. This also requires measurement techniques that can determine molecular orientation, residual stresses and density distributions.In all recent models of the injection-moulding process, the so-called 2iD approach is employed, referring to limitations of the mould geometry to narrow, weakly curved channels. Thus the ratio of the cavity thickness h and a characteristic length 1 in the mid-plane of the cavity must be much less than unity. In this paper an attempt is made to model all the stages of the production process, using this 2iD approach. The analysis is restricted to amorphous thermoplastics.Residual stresses in injection-moulded products stem from two main sources: first, the frozen-in flow-induced stresses, caused by viscoelastic flow of the polymer during the filling and post-filling stage of the injection-moulding process. These stresses correspond with the orientation of macromolecules; second, the thermally-and pressure-induced stresses, which are caused by differential shrinkage. In absolute value, the thermally-induced stresses are usually substantially larger than the frozen-in flowinduced stresses. However, the molecular orientation, as reflected in the frozen-in flow-induced stresses, determines the anisotropy of mechanical, thermal and optical properties and influences the long-term dimensional stability of an injection-moulded product.A decoupled method is proposed to calculate flow-induced stresses. Firstly, the kinematics of the flow field are determined, employing a viscous, generalized Newtonian constitutive law for the Cauchy stress tensor in combination with the balance laws. This is realized for all stages of the process: injection, packing, holding and cooling. The flow kinematics are subsequently substituted in a viscoelastic constitutive equation to calculate the transient stresses. Two constitutive models are used: a compressible version of the Leonov model (differential formulation) and a compressible version of the Wagner model (integral formulation). In the decoupled method, the flow kinematics are, consequently, supposed not to be influenced by the viscoelastic character of the flowing polymer melt. This decoupled method has a number of advantages compared to a coupled viscoelastic computation: the computation time is reduced considerably, an arbitrary viscoelastic c...

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Nonequilibrium thermodynamics and rheology of viscoelastic polymer media

Cited by 514 publications

References 3 publications

Brittleness of fracture in flowing magma

Brittleness of fracture in flowing magma

On the modelling of highly elastic flows of amorphous thermoplastics

The computation of properties of injection-moulded products

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