Continuum-mechanics-based models

Continuum mechanics-based models are used by many researches to investigate properties of CNTs. The basic assumption in these theories is that a CNT can be modeled as a continuum stmcture which has continuous... 

Many computer modeling and simulation methods have been developed to study polymer nanocomposites with different nanofiller geometries. Resulting information on molecular simulation is very useful to understand the level of interaction at the interphase between polymer matrix and nanofiller. Molecular simulations results have been incorporated by several authors into continuum mechanics-based models in order to predict the mechanical behavior of polymer nanocomposites. 

The most common approach in mechanism-based modeling is to model the system as a continuum. The underlying assumption is that the state variables of the system (e.g., species concentrations) vary continuously in time and space and that, therefore,... 

Given the apparent arbitrariness of the assumptions in a purely continuum-mechanics-based theory and the desire to obtain results that apply to at least some real fluids, there has been a historical tendency to either relax the Newtonian fluid assumptions one at a time (for example, to seek a constitutive equation that allows quadratic as well as linear dependence on strain rate, but to retain the other assumptions) or to make assumptions of such generality that they must apply to some real materials (for example, we might suppose that stress is a functional over past times of the strain rate, but without specifying any particular form). The former approach tends to produce very specific and reasonable-appearing constitutive models that, unfortunately, do not appear to correspond to any real fluids. The best-known example is the so-called Stokesian fluid. If it is assumed that the stress is a nonlinear function of the strain rate E, but otherwise satisfies the Newtonian fluid assumptions of isotropy and dependence on E only at the same point and at the same moment in time, it can be shown (see, e.g., Leigh29) that the most general form allowed for the constitutive model is... 

Several authors used the continuum mechanics for modeling conventional polymer composites as well as PNC. Ren and Krishnamoorti [2003] used a K-BKZ integral constitutive model to predict the steady-state shear behavior of a series of intercalated nanocomposites containing an organo-MMT and a disordered styrene-isoprene diblock copolymer. The model predicts the low-y shear stress properties calculated from the experimental linear stress relaxation and the relaxation-based damping behavior. However, as it does not take into account the effect of clay platelet orientation, it is unable to predict the shear stress behavior at intermediate y and the normal stress behavior at all y and clay contents. 

In continuum mechanics, constitutive modeling of materials follows certain steps, including deformation response, stress response, as well as other particular steps based on materials studied, such as structural relaxation for polymers and a plastic flow mle, and a hardening rule for materials with plastic deformation. In the following, we will present the deformation response, structural relaxation, stress response, and flow rule for the thermosetting SMP programmed by cold-compression programming. 

Besides the great deal of experimental work on CNTs and their composites, much effort was made to elucidate the mechanical behavior of CNTs and their composites by theoretical modeUng. Two different approaches have been adopted in theoretical modeling the atomistic or bottom-up approach and the continuum mechanics or top-down approach. In the former, quantum and molecular mechanics-based modeling was used to model the tensile modulus and strength of pure CNTs and interfacial strength between CNTs and certain matrixes (Frankland et al, 2002 Gou et al, 2004 Hernandez et al, 1998 Lu, 1997 Nardelli et al, 1998). In the... 

Peng, X., Cao, J., 2005. A continuum mechanics-based non orthogonal constitutive model for... 

CONTINUUM AND STATISTICAL MECHANICS-BASED MODELS FOR SOLID-ELECTROLYTE INTERPHASES IN LITHIUM-ION BATTERIES... 

In this chapter we provide illustrations of both continuum and statistical mechanics-based models and discuss the insights obtained through comparisons with experimental data related to SEI layer phenomena in lithium-ion batteries. 

As remarked above, a better microscopic understanding of the SEI structural and chemical effects on the open circuit potential (OCP), as well as that of the role of the carbon structure, are needed to complement and provide input to the continuum models used for cell design. Statistical mechanics-based models, usually treated in mean field approximation, provide the nexus between the continuum and the molecular-level models. "... 

Continuum and Statistical Mechanics-Based Models forSEI... 

Ploehn et al. in Chapter 6 use both macroscopic continuum and statistical mechanics-based models to simulate the SEI growth and to predict capacity loss in LIBs. Specifically the former model deals with the effects of electronic conductivity and solvent diffusion on SEI growth, while the latter is a lattice-gas model, which describes the thermodynamics of lithium-ion intercalation in carbons under the presence of a SEI. 

Continuum damage mechanics-based models are now available and implemented in commercial finite element software. Damage may be regarded as the growth of microvoids or microcracks in a material (Lemaitre and Desmorat 2005). Continuum damage mechanics was introduced in the late 1950s (Kachanov 1958) and is able to predict the reduced load-bearing capacity of a material before failure. 

As noted before, thin film lubrication (TFL) is a transition lubrication state between the elastohydrodynamic lubrication (EHL) and the boundary lubrication (BL). It is widely accepted that in addition to piezo-viscous effect and solid elastic deformation, EHL is featured with viscous fluid films and it is based upon a continuum mechanism. Boundary lubrication, however, featured with adsorption films, is either due to physisorption or chemisorption, and it is based on surface physical/chemical properties [14]. It will be of great importance to bridge the gap between EHL and BL regarding the work mechanism and study methods, by considering TFL as a specihc lubrication state. In TFL modeling, the microstructure of the fluids and the surface effects are two major factors to be taken into consideration. 

Finally, it deserves to be mentioned that considerable numbers of models of static friction based on continuum mechanics and asperity contact were proposed in the literature. For instance, the friction at individual asperity was calculated, and the total force of friction was then obtained through a statistical sum-up [35]. In the majority of such models, however, the friction on individual asperity was estimated in terms of a phenomenal shear stress without involving the origin of friction. 

Quantitative evidence regarding chain entanglements comes from three principal sources, each solidly based in continuum mechanics linear viscoelastic properties, the non-linear properties associated with steady shearing flows, and the equilibrium moduli of crosslinked networks. Data on the effects of molecular structure are most extensive in the case of linear viscoelasticity. The phenomena attributed to chain entanglement are very prominent here, and the linear viscoelastic properties lend themselves most readily to molecular modeling since the configuration of the system is displaced for equilibrium only slightly by the measurement. 

The proposed mechanisms of models to explain the drag reduction phenomenon are based on either a molecular approach or fluid dynamical continuum considerations, but these models are mainly empirical or semi-empirical in nature. Models constructed from the equations of motion (or energy) and from the constitutive equations of the dilute polymer solutions are generally not suitable for use in engineering applications due to the difficulty of placing numerical values on all the parameters. In the absence of a more generally accurate model, semi-empirical ones remain the most useful for applications. 

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. 

Abstract An approach based on the theory of mixtures with the concept of molar volume fractions and on the basic principles of continuum mechanics and macroscopic thermodynamics is introduced to model soil freezing of solute saturated soil. 

Abstract In this contribution, the coupled flow of liquids and gases in capillary thermoelastic porous materials is investigated by using a continuum mechanical model based on the Theory of Porous Media. The movement of the phases is influenced by the capillarity forces, the relative permeability, the temperature and the given boundary conditions. In the examined porous body, the capillary effect is caused by the intermolecular forces of cohesion and adhesion of the constituents involved. The treatment of the capillary problem, based on thermomechanical investigations, yields the result that the capillarity force is a volume interaction force. Moreover, the friction interaction forces caused by the motion of the constituents are included in the mechanical model. The relative permeability depends on the saturation of the porous body which is considered in the mechanical model. In order to describe the thermo-elastic behaviour, the balance equation of energy for the mixture must be taken into account. The aim of this investigation is to provide with a numerical simulation of the behavior of liquid and gas phases in a thermo-elastic porous body. 

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