Spring network

We present the major results established in the description of crazing and the recent developments in this field. Crazing has been investigated within continuum or discrete approaches (e.g., spring networks or molecular dynamics calculations to model the craze fibrils), which have provided phenomenological or physically based descriptions. Both are included in the presentation of the crazing process, since they will provide the basis for the recent cohesive surface model used to represent crazing in a finite element analysis [20-22],... 

As the craze microstructure is intrinsically discrete rather than continuous, the connection between the variables in the cohesive surface model and molecular characteristics, such as molecular weight, entanglement density or, in more general terms, molecular mobility, is expected to emerge from discrete analyses like the spring network model in [52,53] or from molecular dynamics as in [49,50]. Such a connection is currently under development between the critical craze thickness and the characteristics of the fibril structure, and similar developments are expected for the description of the craze kinetics on the basis of molecular dynamics calculations. 

Fig. 3.11. Molecular dynamic simulation results for the average fracture stress CTf for various disorder concenrations on triangular lattices, (a) For site dilute Lennard-Jones system (Chakrabarti et al 1986), and (b) for bond dilute spring network (Beale and Srolovitz 1988).

J.E. Bolander, Spring network model of fiber-reinforced cement composites , in H.W. Reinhardt and A.E. Naaman (eds) High Performance Fiber Reinforced Cement Composites (HPFRCC 3), RILEM Proceedings PRO 6, RILEM Publications, Bagneux,1999, pp. 341-350. 

The Maxwell and Voigt models of the last two sections have been investigated in all sorts of combinations. For our purposes, it is sufficient that they provide us with a way of thinking about relaxation and creep experiments. Probably one of the reasons that the various combinations of springs and dash-pots have been so popular as a way of representing viscoelastic phenomena is the fact that simple and direct comparison is possible between mechanical and electrical networks, as shown in Table 3.3. In this parallel, the compliance of a spring is equivalent to the capacitance of a condenser and the viscosity of a dashpot is equivalent to the resistance of a resistor. The analogy is complete... 

Molecula.rMecha.nics. Molecular mechanics (MM), or empirical force field methods (EFF), ate so called because they are a model based on equations from Newtonian mechanics. This model assumes that atoms are hard spheres attached by networks of springs, with discrete force constants. 

J. C. Hoskins, K. M. Kahyur, and D. M. Himmelblau, "The AppHcation of Artificial Neural Networks to Fault Diagnosis in Chemical Processing," paper presented tAIChE Spring Meetings Houston, Tex., 1988. 

For a consideration of filler-network breakdown at increasing strain, the failure properties of filler-filler bonds and filler clusters have to be evaluated in dependence of cluster size. This allows for a micromechanical description of tender but fragile filler clusters in the stress field of a strained mbber matrix. A schematic view of the mechanical equivalence between a CCA-filler cluster and a series of soft and hard springs is presented in Figure 22.9. The two springs with force constants... 

Cytoscape http //www.cytoscape.org/ Network building software Spring embedded layout, hierarchical layout, circular layout 104... 

See also Smart polymers applications of, 22 355 biodegradable networks of, 22 364 cyclic and thermomechanical characterization of, 22 358—362 defined, 22 355-356 examples of, 22 362-364 molecular mechanism underlying, 22 356-358, 359t Shape-memory rings, 22 351 Shape-memory springs, in virtual two-way SMA devices, 22 346-347 Shape-memory stents, 22 352 Shape, of fiber polymers, 77 174-175. 

Equation (2.53) is stating that the network modulus is the product of the thermal energy and the number of springs trapped by the entanglements. This is the result that is predicted for covalently crosslinked elastomers from the theory of rubber elasticity that will be discussed in a little more detail below. However, what we should focus on here is that there is a range of frequencies over which a polymer melt behaves as a crosslinked three-dimensional mesh. At low frequencies entanglements... 

If Ni = 1, when chains are linked together a network will not be formed but just longer chains. When there are two or more, each site can lead to a network spring if more than two hydrophobes can cluster to form a node. (Note that this is different from the situation of a chemically crosslinked network where only two chains would be joined by the formation of the link. In this latter case a value of N > 2 is required for a network.) The potential number of network springs is... 

The above examples show that we can describe the network modulus of polymer gels by using the concept of entropic springs making up the network. In some cases corrections to the network are required to... 

According to the model, a perturbation at one site is transmitted to all the other sites, but the key point is that the propagation occurs via all the other molecules as a collective process as if all the molecules were connected by a network of springs. It can be seen that the model stresses the concept, already discussed above, that chemical processes at high pressure cannot be simply considered mono- or bimolecular processes. The response function X representing the collective excitations of molecules in the lattice may be viewed as an effective mechanical susceptibility of a reaction cavity subjected to the mechanical perturbation produced by a chemical reaction. It can be related to measurable properties such as elastic constants, phonon frequencies, and Debye-Waller factors and therefore can in principle be obtained from the knowledge of the crystal structure of the system of interest. A perturbation of chemical nature introduced at one site in the crystal (product molecules of a reactive process, ionized or excited host molecules, etc.) acts on all the surrounding molecules with a distribution of forces in the reaction cavity that can be described as a chemical pressure. 

Symptoms The roots, corms, tubers, and stems of many plants are attacked, most severely in spring and fall, but damage can occur through the year. Potatoes show small entry holes and when cut open a network of tunnels runs through the tuber. Later these holes may be enlarged by slugs or millipedes. 

The transfer of autoclave pressure to the resin in the laminate does not occur hydrostatically because the resin is not enclosed in a constant-volume system. Flow can occur initially both vertically (thickness direction) and horizontally. Furthermore, the network of fibers can also eventually act as a network of springs to which the vacuum bag and bleeder assembly transfer the stress from the autoclave pressure. This stress can then be transferred... 

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