Expansion of spherical cavity of strain-softening materials with different elastic moduli of tension and compression

An expansion theory of spherical cavities in strain-softening materials with different moduli of tension and com-pression was presented. For geomaterials,two controlling parameters were introduced to take into account the different moduli and strain-softening properties. By means of elastic theory with different moduli and stress-softening models,general solutions cal-culating Tresca and Mohr-Coulomb materials' stress and displacement fields of expansion of spherical cavity were derived. The effects caused by different elastic moduli in tensile and compression and strain-softening rates on stress and displacement fields and development of plastic zone of expansion of cavity were analyzed. The results show that the ultimate expansion pressure,stress and displacement fields and development of plastic zone vary with the different elastic moduli and strain-softening prop-erties. If classical elastic theory is adopted and strain-softening properties are neglected,rather large errors may be the result.

Non-spherical multi-oscillations of a bubble in a compressible liquid

Bubble dynamics are associated with wide and important applications in cavitation erosion in many industrial systems, medical ultrasonics and underwater explosions. Two recent developments to this classical problem are reviewed in this paper. Firstly, computational studies on the problem have commonly been based on an incompressible fluid model. However, a bubble usually undergoes significantly damped oscillation due to the compressible effects. We model this phenomenon using weakly compressible theory and a modified boundary integral method. This model considers the energy loss due to shock waves emitted at minimum bubble volumes. Secondly, the computational studies so far have largely been concerned with the first-cycle of oscillation. However, a bubble usually oscillates for a few cycles before it breaks into much smaller ones. We model both the first- and second-cycles of oscillationand predict damped oscillations. Our computations correlate well with the experimental data.

Catalan Number and Enumeration of Maximal Outerplanar Graphs

Catalan number is an important class of combinatorial numbers. The maximal outerplanar graphs are important in graph theory. In this paper some formulas to enumerate the numbers of maximal outerplanar graphs by means of the compressing graph and group theory method are given first. Then the relationships between Catalan numbers and the numbers of labeled and unlabeled maximal outerplanar graphs are presented. The computed results verified these formulas.

Effect of formulation of alginate beads on their mechanical behavior and stiffness

The aim of this work was to determine the effect of formulation of alginate beads on their mechanical behavior and stiffness when compressed at high speed. The alginate beads were formulated using different types and concentrations of alginate and gelling cations and were produced using an extrusiondripping method, Single wet beads were compressed at a speed of 40 mm/min, and their elastic limits were investigated, and the corresponding force versus displacement data were obtained. The Young＇s moduli of the beads were determined from the force versus displacement data using the Hertz＇s contact mechanics theory. The alginate beads were found to exhibit plastic behavior when they were compressed beyond 50% with the exception of copper-alginate beads for which yield occured at lower deformation, Alginate beads made of higher guluronic acid contents and gelling cations of higher chemical affinity were found to have greater stiffness. Increasing the concentration of alginate and gelling ions also generated a similar effect. At such a compression speed, the values of Young＇s modulus of the beads were found to be in the range between 250 and 900 kPa depending on the bead formulation.

Effects of Cooling Rate and Component on the Microstructure and Mechanical Properties of Mg–Zn–Y Alloys

The microstructure and mechanical properties of Mg–6Zn–1Y and Mg–6Zn–3Y（wt%） alloys under different cooling rates were investigated. The results show that the second dendrite arm spacing（SDAS） of Mg–6Zn–1Y and Mg–6Zn–3Y is reduced by 32 and 30% with increasing cooling rates（Rc） from 10.2 to 23 K/s, which can be predicted using a empirical model of SDAS=68 R 0：45：45cand SDAS=73 R 0c, respectively. The compressive strength of both alloys increases with increasing the cooling rate, which is attributed to the increase of volume fraction（Vf） of secondary phases under high cooling rate. The interaction of the cooling rate and component with SDAS has been theoretically analyzed using interdependence theory.