Viscoplastic modelling

S.A. Silling, Stability and Accuracy of Differencing Schemes for Viscoplastic Models in Wavecodes, SAND91-0141, Sandia National Laboratories, Albuquerque, NM, 1991. 

It is instructive to describe elastic-plastic responses in terms of idealized behaviors. Generally, elastic-deformation models describe the solid as either linearly or nonlinearly elastic. The plastic deformation material models describe rate-independent behaviors in terms of either ideal plasticity, strainhardening plasticity, strain-softening plasticity, or as stress-history dependent, e.g. the Bauschinger effect [64J01, 91S01]. Rate-dependent descriptions are more physically realistic and are the basis for viscoplastic models. The degree of flexibility afforded elastic-plastic model development has typically led to descriptions of materials response that contain more adjustable parameters than can be independently verified. 

A B also present arguments that indicate that inhomogeneities in the solid, unless they are as large as 0.1mm, do not affect the heating mechanism. They also argue that Kholevo s original viscoplastic model (Ref 6) is unrealistic and that their model of a brittle body is closer to reality... 

Petrie and Ito (84) used numerical methods to analyze the dynamic deformation of axisymmetric cylindrical HDPE parisons and estimate final thickness. One of the early and important contributions to parison inflation simulation came from DeLorenzi et al. (85-89), who studied thermoforming and isothermal and nonisothermal parison inflation with both two- and three-dimensional formulation, using FEM with a hyperelastic, solidlike constitutive model. Hyperelastic constitutive models (i.e., models that account for the strains that go beyond the linear elastic into the nonlinear elastic region) were also used, among others, by Charrier (90) and by Marckmann et al. (91), who developed a three-dimensional dynamic FEM procedure using a nonlinear hyperelastic Mooney-Rivlin membrane, and who also used a viscoelastic model (92). However, as was pointed out by Laroche et al. (93), hyperelastic constitutive equations do not allow for time dependence and strain-rate dependence. Thus, their assumption of quasi-static equilibrium during parison inflation, and overpredicts stresses because they cannot account for stress relaxation furthermore, the solutions are prone to numerical instabilities. Hyperelastic models like viscoplastic models do allow for strain hardening, however, which is a very important element of the actual inflation process. 

Flow models have been used also to derive expressions for velocity profiles and volumetric flow rates in tube and channel flows, and in the analysis of heat transfer phenomenon. Numerous flow models can be encountered in the rheology literature and some from the food rheology literature are listed in Table 2-1. Also, here those models that have found extensive use in the analysis of the flow behavior of fluid foods are discussed. Models that account for yield stress are known as viscoplastic models (Bird et al., 1982). For convenience, the flow models can be divided in to those for time-independent and for time-dependent flow behavior. 

For T < Tg, the viscoplastic model used here accounts for intrinsic softening upon yielding followed by progressive orientational hardening. Rate dependent flow is taken to be governed by Argon s formulation [5] of the equivalent plastic strain rate... 

Fig. 17. Hydrodynamic and viscoplastic models for pore collapse, (a) Hydrodynamic collapse is much faster. Heat is generated when the upstream surface impacts the downstream surface. A pressure spike is generated by hydrodynamic focusing, (b) Viscoplastic collapse occurs more slowly, behind shock front. Heat is generated by viscoplastic work. Both collapse processes break up and attenuate the shock front, and generate time-delayed shocklets. Reproduced from ref. [120].

In the viscoplastic model of Carroll and Holt [49], later extended by Khasainov et al., [52] Butler et al., [158] and Frey [164] (Fig. 17b), pores in a viscous material collapse slowly behind the shock front via ID (radial) plastic deformation. Heating results from viscoplastic work. In the small Reynolds number limit (see below), the viscous time constant Xyis is independent of pore diameter [52] ... 

Dumais, J., Shaw, S.L., Steele, C.R., Long, S.R., Ray, P.M. (2006). An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth. International Jourtml of Developmental Biology, Vol.50, pp. 209-222. 

With increasing interparticle collisions the probability of formation of floes from dispersed (nonflocculated) particles increases. Thus the horizontal axis can also be interpreted to mean a change from weakly flocculated particles on the left to increasingly flocculated particles toward the right. An outcome is that, irrespective of the degree of interparticle interaction, at low values of cp the viscosity rises slowly, but tends to increase rapidly when particle packing becomes dense.For randomly packed spheres this change occurs at about 95 = 0.60. A simple viscoplastic model is the Herschel-Bulkley equation... 

Although the choice of the rheological model varies quite significantly with tp and Pe, some broad albeit approximate trends are also evident in Fig. 27.10. Most importantly, it appears that the poroelastic response is bracketed between Pe = 0.4 and 2. At higher values of Pe one of the viscoplastic models (including purely viscous) applies depending on the value of p. At lower values of Pe bed friction and percolation are the two important dissipation mechanisms. 

Viscoplastic Model, ASME Journal of Electronic Packaging, 2005,127(3), pp. 290-298. 

Models involving non-linear rate-dependent plastic elements such as the Eyring process -so-called viscoplastic models - have also been implemented in finite element schemes. Some of these will be discussed in Chapter 12. 

Lui, M.C.M. and Krempl, E. (1979) A uniaxial viscoplastic model based on total strain and overstres. J. Mech. Phys. Solids, 27,377. 

As law of mechanical behavior we use the viscoplastic model with internal variables of Chaboche [Chaboche, 1977 Lemaitre and Chaboche, 1988]. The strain is partitioned into an elastic and plastic part ... 

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