Deformation and elasticity

In this review, we have given our attention to Gaussian network theories by which chain deformation and elastic forces can be related to macroscopic deformation directly. The results depend on crosslink junction fluctuations. In these models, chain deformation is greatest when crosslinks do not move and least in the phantom network model where junction fluctuations are largest. Much of the experimental data is consistent with these theories, but in some cases, (19,20) chain deformation is less than any of the above predictions. The recognition that a rearrangement of network junctions can take place in which chain extension is less than calculated from an affine model provides an explanation for some of these experiments, but leaves many questions unanswered. 

The indentation process is driven by the applied load, and resisted by two principal factors the resistance of the specimen to plastic deformation (and elastic deformation) plus the frictional resistance at the indenter/specimen interface. The ratio of these resistances changes with the size of the indentation because the plastic resistance is proportional to the volume of the indentation, while the frictional resistance is proportional to the surface area of the indentation. Therefore, the ratio varies as the reciprocal indentation size. This interpretation has been tested and found to be valid by Bystrzycki and Varin (1993). 

The significant differences in the moduli of latexes and the cement hydrates (elastic moduli 0.001-10 GPa and 10-30 GPa respectively) causes most LMMs and LMCs to have a higher deformability and elasticity than ordinary cement mortar and concrete. Depending on the polymer type and polymer-cement ratio, the deformability and elastic modulus tends to initially increase with an increase in the polymer-cement ratio and subsequently decrease at higher ratios. Poisson s ratio however is only marginally affected [87, 94, 98]. 

At low temperatures (A zone) the polymer is found in the vitreous state. In this state the polymer behave as a rigid solid with low capacity of motions and then the strain is very low. To produce a small strain it is necessary a great stress. Therefore in this zone only specific and local motions take place and the polymer can be considered as undeformable. As the temperature increases (B zone) the glass transition temperature, Tg, is reached and the motions of the different parts of the polymers increases but is not enough to produce important strain. Under this conditions the polymers behave as a rubber. If the temperature remain increasing (C zone) the polymer behave as deformable and elastic rubber but the modulus is small. In this zone the motions of the side chains and also of the main chain increases due to the application of the strain. 

Thus the 3D model allows us to characterize the tableting process completely and to distinguish time-dependent information from pressure-dependent deformation and elasticity in one step of the analysis. 

One of the key challenges in the area of organometallic polymers has been the development of truly high molecular weight materials. The main reasons for the widespread use of polymers are their excellent mechanical properties such as strength, deformability, and elasticity. Typically, chains must be 100 chain atoms for such connections to be possible. For a monomer of molecular weight 100, this corresponds to = ca. 10,000, where = number-average... 

The surrounding medium would be of permanent deformation and elastic deformation with explosion underground. The seismic wave would be rippled outwards from the explosion center and reflected when it contacts with some heterogeneous medium interfaces. The information of reflection and refraction could be achieved and recorded by specialized instmmentation to be used for the analysis of geological structure and mineral distribution [29]. 

Fig. 2. Compaction, curve of a commercial spray-dried alumina sample. Regions 1, 2 and 3 correspond to rearrangement, deformation and elastic behavior. The apparent yield stress ((Tayp) is the transition between regions t and 2. The join point (Ojom) is the transition between regions 2 and 3 it is related to the granule envelope density (penv) where inter-granule porosity (eict) is substantially eliminated and intra-granular porosity (eua) remains, (Note points a, b, and c correspond to the photo-micrographs shown in Fig. 3,]...

Several types of spontaneous periodic director pattern yield information about elastic coefficients. Static stripe textures, as described by Lonberg and Meyer [45], appear in polymer nematics if the twist/splay ratio below the critical value of 0.303. Calculations of director fields and the influence of elastic constants and external fields on the appearance of these periodic patterns have been performed by several authors (e.g. [49-51]). In nematic cells with different anchoring conditions at the upper and lower cell plates (hybrid cells), other types of striped texture appear these are similar in nature, but involve different director deformations and elastic coefficients. For a description of various types of static periodic texture and their relationship to elastic coefficients see, for example, Lavren-tovich and Pergamenshchik [52]. In thin hybrid aligned films, a critical thickness is observed below which the director align-... 

Joyce, J.A., Hackett, E.M., Roe, C. Effect of Cyclic Loading on the Deformation and Elastic-Plastic Fracture Behavior of a Cast Stainless Steel. David Taylor research Center, DTRC/ SME-91-11 (1991)... 

---