Process continuum mechanics

Abstract A simplified quintuple model for the description of freezing and thawing processes in gas and liquid saturated porous materials is investigated by using a continuum mechanical approach based on the Theory of Porous Media (TPM). The porous solid consists of two phases, namely a granular or structured porous matrix and an ice phase. The liquid phase is divided in bulk water in the macro pores and gel water in the micro pores. In contrast to the bulk water the gel water is substantially affected by the surface of the solid. This phenomenon is already apparent by the fact that this water is frozen by homogeneous nucleation. 

O. C. Zienkiewicz and C. Taylor, Weighted Residual Processes in Finite Elements with Particular Reference to Some Transient and Coupled Problems, in Lectures on Finite Element Methods in Continuum Mechanics, J. T. Oden and E. R. A. Oliveria, Eds., U. A. H. Press, Huntsville, AL, 1973. 

The physical consequences are, of course, well known the cylinder deforms in ways successfully described in almost all respects by the methods of continuum mechanics. But the chemical consequences are less well known. For example, suppose the cylinder contains iron and is surrounded by some second iron-bearing phase suppose further that before the cylinder is compressed axially, the cylinder and its surroundings are in equilibrium. When the axial compression is imposed, how is the equilibrium disturbed and what processes begin to run The purpose of the book is to provide the outline of a comprehensive approach to this question. 

Due to the complexity of the formation of interphases, a completely satisfying microscopic interpretation of these effects cannot be given today, especially since the process of the interphase formation is not yet understood in detail. Therefore, a micromechanical model cannot be devised for calculating the global effective properties of a thin polymer film including the above-mentioned size effects governed by the interphases. On the other hand, a classical continuum-based model is not able to include any kind of size effect. An alternative to the above-mentioned classical continuum or the microscopical model is the formulation of an extended continuum mechanical model which, on the one hand, makes it possible to capture the size effect but, on the other hand, does not need all the complex details of the underlying microstmcture of the polymer network. 

In the last chapter we discussed the relation between stress and strain (or instead rate-of-strain) in one dimension by treating the viscoelastic quantities as scalars. When the applied strain or rate-of-strain is large, the nonlinear response of the polymeric liquid involves more than one dimension. In addition, a rheological process always involves a three-dimensional deformation. In this chapter, we discuss how to express stress and strain in three-dimensional space. This is not only important in the study of polymer rheological properties in terms of continuum mechanics " but is also essential in the polymer viscoelastic theories and simulations studied in the later chapters, into which the chain dynamic models are incorporated. 

The mathematical model, which makes it possible to consider the influence of the hydrodynamic conditions of flow on the processes of mixing and chemical transformations of reacting substances in a liquid phase, assumes that the average flow characteristics of a multicomponent system can be described by the equations of continuum mechanics and will satisfy conservation laws. 

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