Model micromechanical

As with any constitutive theory, the particular forms of the constitutive functions must be constructed, and their parameters (material properties) must be evaluated for the particular materials whose response is to be predicted. In principle, they are to be evaluated from experimental data. Even when experimental data are available, it is often difficult to determine the functional forms of the constitutive functions, because data may be sparse or unavailable in important portions of the parameter space of interest. Micromechanical models of material deformation may be helpful in suggesting functional forms. Internal state variables are particularly useful in this regard, since they may often be connected directly to averages of micromechanical quantities. Often, forms of the constitutive functions are chosen for their mathematical or computational simplicity. When deformations are large, extrapolation of functions borrowed from small deformation theories can produce surprising and sometimes unfortunate results, due to the strong nonlinearities inherent in the kinematics of large deformations. The construction of adequate constitutive functions and their evaluation for particular... 

Much of what we currently understand about the micromechanics of shock-induced plastic flow comes from macroscale measurement of wave profiles (sometimes) combined with pre- and post-shock microscopic investigation. This combination obviously results in nonuniqueness of interpretation. By this we mean that more than one micromechanical model can be consistent with all observations. In spite of these shortcomings, wave profile measurements can tell us much about the underlying micromechanics, and we describe here the relationship between the mesoscale and macroscale. 

The aim of this chapter is to describe the micro-mechanical processes that occur close to an interface during adhesive or cohesive failure of polymers. Emphasis will be placed on both the nature of the processes that occur and the micromechanical models that have been proposed to describe these processes. The main concern will be processes that occur at size scales ranging from nanometres (molecular dimensions) to a few micrometres. Failure is most commonly controlled by mechanical process that occur within this size range as it is these small scale processes that apply stress on the chain and cause the chain scission or pull-out that is often the basic process of fracture. The situation for elastomeric adhesives on substrates such as skin, glassy polymers or steel is different and will not be considered here but is described in a chapter on tack . Multiphase materials, such as rubber-toughened or semi-crystalline polymers, will not be considered much here as they show a whole range of different micro-mechanical processes initiated by the modulus mismatch between the phases. 

The developed micromechanical model of reinforcement by active fillers allows for a better control of material properties and a more fundamental engineering praxis in mbber industry. In particular. 

The experimental determination of RBA, however, is difficult but some attempts have been made and these include direct observation, measurements of electrical conductivity, shrinkage energy, gas adsorption and light scattering. The linear elastic response of paper has been explained in terms of various micromechanical models which take into account both fibre and network properties, including RBA. An example of one which predicts the sheet modulus, Es is given below ... 

One of the major differences between the results obtained from the micromechanics and FE analyses is the relative magnitude of the stress concentrations. In particular, the maximum IFSS values at the loaded and embedded fiber ends tend to be higher for the micromechanics analysis than for the FEA for a large Vf. This gives a slightly lower critical Vf required for the transition of debond initiation in the micromechanics model than in the FE model of single fiber composites. All these... 

In order to understand the effects of filler loading and filler-filler interaction strength on the viscoelastic behavior, Chabert et al. [25] proposed two micromechanical models (a self-consistent scheme and a discrete model) to account for the short-range interactions between fillers, which led to a good agreement with the experimental results. The effect of the filler-filler interactions on the viscoelasticity... 

On the epoxy side of the interface, high fracture toughness and low residual stresses 72,73) are a requirement for optimum transverse strength in graphite and glass-epoxy 1A) composites. Since the adsorption of epoxy components has been shown to be probable, the local structure of the epoxy at the interphase will most likely not be the same as in the bulk. This local anisotropy caused by the interphase is a limitation in the predictive capability of micromechanical models which do not include the interphase as a component. 

Fig. 6 Micromechanical model of a section of a semi-crystalline polymer with lamellae oriented perpendicular to the principal stress direction showing the long period L and the thicknesses of crystalline (Lc) and amorphous layers (La) the latter are composed of loose segments, entangled chains and more or less extended tie molecules. Large forces can be transferred at those points (o) where highly extended tie molecules (eTM) enter crystalline lamellae...

J. Aboudi The generalized method of cells and high-fidelity generalized method of cells micromechanical models A review. J Mech. Adv. Matls. Struct. 11, 329-366 (2004)... 

Kliippel M, Schramm J (1999) An advanced micromechanical model of hyperelasticity and stress softening of reinforced rubbers. In Dorfmann A, Muhr A (eds) Constitutive models for rubber. A.A. Balkema, Rotterdam... 

Micromechanical modeling and available experimental evidence indicates that the composite toughness, KIc (composite), can be described as the sum of the matrix toughness, KIc (matrix), and a contribution due to whisker toughening, AKIc (whisker reinforcement).1,23 In other words,... 

Micromechanical models that incorporate oxidation phenomena and allow quantitative prediction of effects of oxidation on interface properties. 

MICROMECHANICAL MODELLING OF RATE AND TEMPERATURE DEPENDENT FRACTURE OF GLASSY POLYMERS... 

Micromechanical Modelling of Rate and Temperature Dependent Fracture of Glossy Polymers 157... 

Micromechanical Modelling oj Rate and Temperature Deperuient Fracture of Glossy Polymers 15 9... 

The fracture toughness measurements, combined with the post-mortem surface analysis of the fracture surfaces, allow us to develop some simple micromechanical models to account for these three situations. 

Li, V.C., Wang, Y., and Backer, S. (1991) A statistical-micromechanical model of tension-softening behavior of short fiber reinforced brittle matrix composites , Journal of Mechanics and Physics of Solids, Vol. 39, No. 5, 1991, 607-625. 

Hounslow MJ, Mumtaz HS, Collier AP, Barrick JP, Bramley AS. A micromechanical model for the rate of aggregation during precipitation from solutions. Chem Eng Sci 2001 56 2543-2552. 

A complete series of mechanical testing of these joints shall be made after the whole array of the data will be obtained. In order to disclose the general peculiarities of FG-joints, the calculations of their basic properties were made by a micromechanical model [2,4]. 

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