Additive-constitutive models

Viswanadhan, V. N., Ghose, A. K., Singh, U. C., and Wendoloski, J. J. (1999) Prediction of solvation free energies of small organic moleucles additive-constitutive models based on molecular fingerprints and atomic constants.. /. Chem. Inf. Comput. Sci. 39, 405-412. 

Alternatively, the BC(DEF) values can be obtained by - additive-constitutive models based on the contributions of individual fragments and some correction factors to each parameter [Cramer III, 1980b]. A hierarchical additive-constitutive model was derived by multivariate regression between the BC(DEF) values of 112 original compounds (water and methane were excluded from the model) and 35 molecular fragments. Moreover, in the same way a linear additive-constitutive model was also proposed the fragment contributions to BC(DEF) parameters are reported in Table B-2. 

Viswanadhan, V.N., Ghose, A.K., Singh, U.C. and Wendoloski, J.J. (1999). Prediction of Solvation Free Energies of Small Organic Molecules Additive-Constitutive Models Based on Molecular Fingerprints and Atomic Constants. J.Chem.lnf.Comput.Sci., 39,405-412. 

The simplest example of a theory which incorporates both dispersion and dissipation is the so called viscosity-capillarity model (Truskinovsky, 1982, Slemrod, 1983). It combines van der Waals correction to the energy with Kelvin viscoelasticity, which in the present context amounts to the following additional constitutive assumption... 

To model a complete stack, which may be constituted of more than 1000 cells, it is necessary to adopt a different approach. In this chapter a finite difference model is presented. Only energy equation and current conservation are solved. This allows one to examine possible improvements in the stack configuration design that can be achieved by taking advantage of the relation between temperature and elec-tronic/ionic resistivity, heat transfer and chemical reactions, etc. In addition, this model can be used for analyzing the effects of possible anomalies and performance degradation. 

Cramer actually developed two schemes for applying the BC(DEF) values a hierarchical additive-constitutive one and a linear additive-constitutive one. The two schemes are equivalent, but the latter is easier for hand calculations, and thus is the only one presented here. Table 2.6 provides the BC(DEF) fragment constants from the linear model. 

Process-scale models represent the behavior of reaction, separation and mass, heat, and momentum transfer at the process flowsheet level, or for a network of process flowsheets. Whether based on first-principles or empirical relations, the model equations for these systems typically consist of conservation laws (based on mass, heat, and momentum), physical and chemical equilibrium among species and phases, and additional constitutive equations that describe the rates of chemical transformation or transport of mass and energy. These process models are often represented by a collection of individual unit models (the so-called unit operations) that usually correspond to major pieces of process equipment, which, in turn, are captured by device-level models. These unit models are assembled within a process flowsheet that describes the interaction of equipment either for steady state or dynamic behavior. As a result, models can be described by algebraic or differential equations. As illustrated in Figure 3 for a PEFC-base power plant, steady-state process flowsheets are usually described by lumped parameter models described by algebraic equations. Similarly, dynamic process flowsheets are described by lumped parameter models comprising differential-algebraic equations. Models that deal with spatially distributed models are frequently considered at the device... 

The model yields a set of hydrodynamic equations for the solid phase. For equation closure, additional constitutive relations, which can be obtained by using the kinematic argument of the collision and by assuming the Maxwellian velocity distribution of the solids, are needed. Two examples are given to illustrate the applications of this model in this chapter. 

A few rheometers are available for measurement of equi-biaxial and planar extensional properties polymer melts [62,65,66]. The additional experimental challenges associated with these more complicated flows often preclude their use. In practice, these melt rheological properties are often first estimated from decomposing a shear flow curve into a relaxation spectrum and predicting the properties with a constitutive model appropriate for the extensional flow [54-57]. Predictions may be improved at higher strains with damping factors estimated from either a simple shear or uniaxial extensional flow. The limiting tensile strain or stress at the melt break point are not well predicted by this simple approach. 

Of course this list is not exhaustive. (See other models in [1,2].) Also models with internal variables (order parameters) as those of [3] can be put in a similar (though more complicated) framework. In particular, there are additional constitutive equations of differential type for the order parameters [4]. 

In summary, the Eulerian two-fluid model is represented by Eqs. (5.112) and (5.113) in addition to a constitutive model for the fluid stress tensor Tf. As already mentioned, Eq. (5.112) was derived under the assumption that the particle-velocity distribution is very narrow (i.e. small particle Stokes number), and the particles must have the same internal coordinates. If these simplifications do not hold, for example under dense conditions when particle-particle collisions become important, then particle-velocity fluctuations must be taken into account, as discussed at the end of Chapter 4. 

Microarray analysis of the tumors spontaneously induced in ACO-nuU mice showed extensive simUarity with the fiver tumors induced by the PPARa activator ciprofibrate, indicating the mechanism leading to the induction of the tumors was similar (Meyer et al. 2003). Additional mouse models nullizygous for other genes involved in fatty acid oxidation exhibit phenotypes indicative of constitutive PPARa activation (Jia et al. 2003). A mouse model of hepatitis C virus (HCV)-induced... 

Properties relate to measures of molecular size in various ways. Some properties depend heavily on the atom count. Molar volume, heat of atomization, and molar refraction are approximately proportional to atom count contributions can be summed to give an estimate of the total property value. Generally, properties require additional information about the immediate bonding environment of atoms for useful estimation models. Water solubility depends on the branching in the molecular skeleton. Molecular fragments larger than individual atoms are required to estimate most property values. This additive-constitutive nature of properties has been amply demonstrated by many additive property schemes. 

Our programme will thus be completed in the remaining part of Sect. 4.7 by deduction, starting with this postulate, of the additional properties of the discussed constitutive model, namely stability conditions (4.357), (4.358), (4.359) (or (4.360), (4.362)), which assure the stability of the equilibrium state. At the end, reversely, assuming these stability conditions, we try to find the time development of some non-equilibrium states into corresponding equilibrium states, cf. (4.387), (4.400). 

These reciprocity relations are valid if the following additional simple assumptions about our constitutive model is fulfilled... 

Y arin et al. [29, 111] gave a theory of the capillary breakup of thin jets of dilute polymer solutions and formation of the bead-OTi-the-string structure (some additional later results can be foimd in [90]). The basic quasi-one-dimensional equations of capillary jets (1.49) and (1.50) are supplemented with an appropriate viscoelastic model for the longitudinal stress. Yarin et al. [29, 111] used the Hinch rheological constitutive model, which yields the following expression... 

It is noted that while the majority of constitutive modeling focuses on thermally induced dual-shape memory behavior, triple-shape and multishape SMPs have been developed recently and they call for constimtive modeling [1]. In addition, the effect of programming temperature and strain rate on the constimtive behavior also needs modeling [2]. Furthermore, some recent smdies have found that while the shape recovery ratio can be 100%, other mechanical properties such as recovery stress or modulus become smaller and smaller as the thermomechanical cycles increase, which has been explained by the shape memory effect in the microscopic scale [24]. Obviously, these new findings also call for constitutive modeling. 

In summary, there are a number of different constitutive models that can be used to predict different aspects of UHMWPE behavior. The most advanced of the currently available models is the HM, which has been shovm to be able to predict the behavior of both conventional and highly crosslinked UHMWPE used in total joint replacements. The HM is currently limited to isothermal deformation histories, although research is ongoing to enable to arbitrary thermomechanical deformation states. In addition, fatigue, fracture, and wear are targets for current and future studies. 

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