Elastic matrix

Both sohd-solution hardening and precipitation hardening can be accounted for by internal strains generated by inserting either solute atoms or particles in an elastic matrix (11). The degree of elastic misfit, 5, produced by the difference, Ai , between the lattice parameter, of the pure matrix and a, the lattice parameter of the solute atom is given by... 

Analysis of the relationships between the moduli and bond strength between particles [222] has shown that for Vf = 0.1 — 0.15 the concentration dependence of the modulus corresponds to the lower curve in the Hashin-Shtrikman equation [223] (hard inclusion in elastic matrix), and for Vf — 0.34 to the upper boundary (elastic inclusion in a hard matrix). The 0.1 to 0.34 range is the phase inversion region. 

In recent years PETN sheet explosive, consisting of PETN in a rubber-like elastic matrix, has found considerable use in metal-forming, metalcladding and metal-hardening. Physical expl characteristics of rubber-bonded sheet expl are described by W. Kegler R. Schall (Ref 45, p 496), by Kegler (Ref 59), and in Refs 30c,... 

Similar effect of relatively stable cycling on the level of discharge capacity of 500 mA-h/g can be achieved, for example, using tin-based alloys with different metals (please, see the detailed investigation of such alloys in this book [5]). These metals perform probably the functions of elastic matrix in such alloys and gave possibility to compensate for the volumetric changes of Sn. 

Cox (1952) first considered a shear-lag model where an elastic fiber is embedded in an elastic matrix which is subjected to uniaxial tension. Perfect bonding is assumed... 

Banbaji, J. (1988). On a more generalised theory of the pull-out test from an elastic matrix. Part 1-theoretical considerations. Composites Sci. Technol. 32, 183-193. 

Gray, R..1. (1984). Analysis of the effect of embedded fiber length on the fiber debonding and pull-out from an elastic matrix. J. Mater. Sci. 19, 861-870. 

In the case of a high dissolution rate of excipient and/or high matrix loading, strong initial swelling, rapid depletion of matrix excipient and consequently depletion of the elastic matrix pores occur. This should lead to curved release plots. It is noteworthy that swelling maxima have no influence on release profiles obviously, therefore, excipient is released from zones of the matrix already drug depleted. 

Elastomeric syntactic foams have recently attracted attention. They use an elastic matrix and either elastic or rigid microspheres 114 12S 128). 

Thermal shrinkage stresses must be superposed on the stress of Equation 3. Assuming an elastic sphere embedded in an infinite elastic matrix, the complete analytical solution for thermal stress is obtained ... 

Surimi is fish paste from deboned fish used to make simulated crab legs and other seafood. For preservation the paste is blended with cryoprotectants, such as sucrose, sorbitol and phosphates, and frozen. To make the final product, the frozen paste is thawed, blended with starch and extruded as a film onto a belt. The belt takes the film into an oven that heat-denatures the fish protein and cooks the starch. The film is then rolled to form striations, shaped, colored and cut. Depending on the required distribution, the product is frozen or refrigerated. Potato and tapioca starch were used in surimi products 400 years ago, since they provided a cohesive, elastic matrix consistent with seafood. Frozen distribution has made the use of highly-stabilized, moderately crosslinked tapioca starch popular, alone or with native tapioca starch. Modified waxy maize products are used, as is unmodified com starch, for increased cuttability. Kim188 reported that the gel strengthening ability of starch correlates with starch paste viscosity. 

For materials with a strong bond between the matrix and the fiber, models for steady transverse creep are available. The case of a linear matrix is represented exactly by the effect of rigid fibers in an incompressible linear elastic matrix and is covered in texts on elastic materials.7,11,12 For example, the transverse shear modulus, and therefore the shear viscosity, of a material containing up to about 60% rigid fibers in a square array is approximated well... 

Opp is the longitudinal to longitudinal or p to p-wave" scattering cross section of an isolated scatterer. At low frequencies it is primarily associated with the monopole scattering mode. Ops is the mode conversion or longitudinal to shear wave or p to s-wave cross section. It is primarily associated with the dipole mode at low frequencies, oa is the absorption cross section which describes energy dissipation inside viscoelastic inclusions (embedded in an otherwise elastic matrix material). It is active in all modes of excitation. Combining Equation 29 and 30 yields... 

With respect to energy dissipation by solid inclusions in rigid elastic matrix materials, the situation according to Equation 29 is that in the dipole mode, is relatively small compared to ops regardless of the magnitude of the loss factor of the inclusion material. Hence, its contribution to attenuation is relatively weak. This is true regardless of whether or not the real parts of the characteristic impedances of the matrix and inclusion materials are matched. 

In the quasi-static case, effective frequency dependent moduli and loss factors may be calculated from Equation 8. With respect to Equation 29, a lossy matrix material implies that k is now a complex number. The new expressions for c and a differ from Equations 31 and 32, but follow straightforwardly. Equation 30 is usually cited only for elastic matrix materials, but, of course, it need not be used to interpret a. The potential problem (also with viscoelastic inclusions) is that the derivation of Equation 30 is based on homogeneous stress waves, whereas in viscoelastic materials one should, strictly speaking, consider inhomogeneous waves. The results obtained from Equation 29 are reasonable in the sense of yielding the expected superposition of scattering and dissipation effects. 

It is seen in the figures that the magnetoelast shows ideal mechanical behavior in the studied deformation range. Similar ideal mechanical behavior was observed for other magneto elasts characterized by different cross-linking densities and different amount of fillers dispersed randomly in the elastic matrix. It has to be mentioned that within the experimental accuracy (5%) no hysteresis has been found. 

The physical dimension of a template defines the boundary of regeneration. Thus, the size of the collagen template should match the tissue defect to be repaired. A properly sized meniscal substitute has been found to function better than a substitute which mismatches the physical dimension of the host meniscus [Rodkey et al., 1998 Sommerlath et al., 1991]. For a porous, elastic matrix such as the one designed from collagen for meniscal tissue repair, the shape of the meniscus is further defined in vivo by the space available between the femoral condyles and tibial plateau within the synovial joint. 

---