Elastic constraints

Kubo and Wayman made TEM observations of an aligned (100) spinodal decomposition product in thin foils of long-range ordered /3-brass [20]. (Interestingly, bulk material did not decompose, while thin foils with [001] foil normals did. The difference was attributed to a relaxation of elastic constraint in the thin foil.)... 

These basic properties have been exploited in the experiments described here. Various time scales have been investigated. The static or dynamic nature of the observed local anisotropy has been specified. It has been demonstrated that 2H NMR is sensitive to very low degrees or very small variations in the magnitude of the elastic constraints stored in elastic chains. 

Hie motion of side-chains at low frequencies will be much dependent on the nature of their coimection to the backbone. At higher frequencies, particularly in solution, the damping will be largely characteristic of interaction with the solvent, while bonding to the mmn chain will be approximated by an additional elastic constraint. Something like a Poley absorption has therefore to be sougfrt, and Chantry and co-workers have recently demonstrated its presence in copolymers of ethylene and vinyl acetate, even in the absence of a solvent. 

Zadeh 1975-1978 Development of possibility theory fuzzy sets act as elastic constraints on system parameters... 

The equilibrium swelling theory of Flory and Rehner [64] assumes that the degree of swelling of an uncharged gel results from the effects of just two opposing forces the thermodynamic effects of mixing tending to dilute the polymer component and the elastic constraints imposed by the force required to stretch the polymer chains. At equilibrium, these two forces are equal. 

The deformation and damage mechanisms in creep of ceramics and hard materials are similar to those in metals [150,151]. Under normal loading conditions (in the absence of severe elastic constraint) ceramics fracture at room temperature before any significant plastic flow. Dislocation glide in ionically bonded ceramics is complicated by the presence of both anions and cations, which create electrostatic (Coulombic) barriers to shear. As in metals, three creep regimes have been identified. The initial high strain-rate, observed on applying the load, decreases rapidly... 

Issues related to international operations such as duty drawback and duty relief are also considered. The objective of the problem is to minimize weighted total costs and cumulative production and distribution times. The problem is formulated as a MIP and solved using techniques of elastic constraints (which may be violated at a given linear penalty), and row factorization. It is reported that the results of this study saved DEC over 100 million. 

Inference is viewed as a process of propagation of elastic constraints. 

---