Exact solution of the stress and velocity fields of a cylinder tube of metallic foams under inner pressure is given in which the Triantafillou and Gibson constitutive law （TG model） for the material is taken as a basis of the calculation. The nonlinear equation is turned linear equation by introducing a kinematics parameter. The differences between the full condensed materials and the effect of the relative density are also discussed.
Weak solution （or generalized solution） for the boundary-value problems of partial differential equations of elasticity of 3D （three-dimensional） quasicrystals is given, in which the matrix expression is used. In terms of Korn inequality and theory of function space, we prove the uniqueness of the weak solution. This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals, and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students.
This study presents the diffusive wave model,relevant dispersion law and the applications to the signal transduction of live cells,phason dynamics of quasicrystals,Brownian movement,electro-magnetic field and fluid dynamics fluctuation,respectively.The common features of these diffusive waves are summarized,which present diffusion as well as wave behaviour,or exactly speaking,they present a duality of diffusion and wave or the duality of wave and diffusion.Furthermore,the general nature of the motion is discussed from the point of view of Landau elementary excitation of condensed matter,this may lead to a concept of generalized elementary excitation（or generalized quasiparticle） corresponding to the diffusive wave.
The fundamental plastic nature of the quasicrystalline materials remains an open problem due to its essential complicacy. By developing the proposed generalized cohesive force model, the plastic deformation of crack in point group 10, 10 decagonal quasicrystals is analysed strictly and systematically. The crack tip opening displacement （CTOD） and the size of the plastic zone around the crack tip are determined exactly. The quantity of the crack tip opening displacement can be used as a parameter of nonlinear fracture mechanics of quasicrystalline material. In addition, the present work may provide a way for the plastic analysis of quasicrystals.
The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the sarne results on nonlinear fracture study of some one-, two- and three-dimensional quasicrystals. This work reveals some inherent connection between the two models, and finds that their common basis is the generalised Eshelby integral based on the generalised Eshelby energy momentum tensor for quasicrystals. Further applications of the theory in solving nonlinear fracture problems of the materials are also discussed.
A model on the coexisting phase of quasicrystal-crystal is proposed, with which we concretely investigate the inter- face effects for coexisting phases of one-dimensional orthorhombic quasicrystal-isotropic crystal and three-dimensional icosahedral quasierystal-cubic crystal. The phason strain fields which play an important role in some processes are determined. Some factors affecting the strain fields, e.g., the material constants of phonon, phason, phonon-phason coupling of the quasicrystal and the elastic modulus and the size of the crystal are also explored.
Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency formula consists of all important parameters of the fluid dynamics. In our observation, the group velocity and phase velocity of the motion of wave propagation are explicitly exhibited as well.
