Subject stiffening

Use the bounding techniques of elasticity to determine upper and lower bounds on the shear modulus, G, of a dispersion-stiffened composite materietl. Express the results In terms of the shear moduli of the constituents (G for the matrix and G for the dispersed particles) and their respective volume fractions (V and V,j). The representative volume element of the composite material should be subjected to a macroscopically uniform shear stress t which results in a macroscopically uniform shear strain y. 

The property possessed by certain colloids of forming a gel-like structure on standing but which revert to a liquid form when subjected to agitation. The term has also been applied to the stiffening effect shown by uncured rubber compounds containing fillers, particularly carbon black. 

Stress-strain characteristics. Linear chain polymers are quite flexible and subject to creep or stretch. Branching or rings in the backbone have a stiffening effect. For example ... 

Another technique—pres sure-shift freezing—also shows promise. In this technique the material is subjected to high pressure (200 MPa) and cooled to -15 C. Under these conditions the water does not freeze. However, when the pressure is released suddenly, many small ice crystals form. This has two results the small ice crystals do not rupture any structures present, but by dehydrating the unfrozen material the remaining stmcture is aggregated and stiffened by the introduction of secondary cross-links. At low concentration of solids there are too few interconnecting chains for there to be a load-bearing continuum, and the material tends to flocculate and settle out. 

These fibers serve a variety of functions in their parent plants. Most commonly, they serve to stiffen the stems and leaves of plants. This allows the plants to weather the storms and high winds to which they are frequently subjected. In some plants, they also provide buoyancy to the seeds. 

Fluoropolymers, as well as other thermoplastics, exhibit a complicated nonlinear response when subjected to loads. The behavior is characterized by initial linear viscoelasticity at small deformations, followed by distributed yielding, viscoplastic flow, and material stiffening at large deformations until ultimate failure occurs. The response is further complicated by a strong dependence on strain rate and temperature, as illustrated in Fig. 11.1. It is clear that higher deformation rates and lower temperatures increase the stiffness of the material. 

However, these equations predict stress softening for a vessel subjected to internal pressurization at fixed lengths, rather than the stress stiffening observed in experimental studies on arteries and veins (see Figure 57.4 and Figure 57.5). 

Liu W, Butler R, Kim HA. Optimization of composite stiffened panels subject to compression and lateral pressure using a bi-level approach. J Struct Multidiscip Optim... 

As chemical production increased, it became possible to export. Exports brought money, helped trade and increased imports. The Trade and Finances Ministries allowed some exports to begin at the end of 1915. These were not generally subject to restrictions if intended for Allied countries, but controls over pharmaceutical exports were stiffened. Such controls were legitimate when the product was scarce any exports of essential drugs, for instance, would deprive the army of them. At the same time, certain exports could not be avoided because they were counterpart to the importation of raw materials. For example, France exported mercury salts to Spain,... 

Figure 1.8 Localized damage in an isogrid stiffened composite subjected to impact energy of 193 J. Source [19] Reproduced with permission from Elsevier...

Ambur, D.R., Jaunky, N., and Hilburger, M.W. (2004) Progressive failure studies of stiffened panels subjected to shear loading. Composite Structures, 65, 129-142. 

P(l) Unstiffened and stiffened webs of members subject to combined bending and shear shall be so dimensioned that ... 

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