General Solutions And Green's Functions For Two Orthotropic Poroelastic Materials

Green's functions play an important role in both applied and theoretical studies on the physics of solids.They are not only the foundation for further analysis,but also play a significant role in BEM.Porous materials are composed of solid substrate and pores,which are ubiquitous in nature.In the engineering practice,the pores of the porous material are filled with fluid,and the complex fluid-solid coupling effect may occurs between the solid and the fluid,therefore,the research of fluid-solid coupling field in porous medium is strongly needed for engineering.In addition,for some projects,such as thermal storage,nuclear waste disposal and deep drilling et al,it is also necessary to analyze the impact of temperature on the porous material.Under this engineering background,the orthotropic porous elastic material and the transversely isotropic porous elastic cone are investigated in this paper,and the Green's functions for infinite plane,semi-infinite plane,two-phase infinite plane and three-dimensional cone under different loads are given systematically.The specific research contents are as follows:Firstly,the 2D steady state general solution of orthotropic porous material with solid-liquid coupling state is obtained by differential operator theory.Then,the harmonic function of porous material under line liquid source is assumed.Substituting the above harmonic functions with undetermined coefficients into the general solution,and the values of the undetermined coefficients are determined according to the specific equilibrium conditions,boundary conditions and continuity conditions.Thus,the expressions of the components in the coupled field are obtained.By comparing with the finite element results,the correctness of the Green's functions for poroelastic plane infinite and semi-infinite plane calculated in this paper is verified,and the contours of each component in two-phase infinite plane are plotted.Secondly,for the orthotropic porous elastic material under the temperature and solid-liquid coupling condition,the Green's functions for the two-phase infinite plane under the line liquid source or line heat source are also obtained.However,the temperature variable is added to the constitutive equation of the porous material,so the form of the general solution and the Green function are more complicated.By analyzing the contour,the location of the interface prone to slip and damage can be find,and some conclusions about the interface effect are obtained.Finally,the research extends to three-dimensional problem.For the transversely isotropic poroelastic cone,the 3D steady-state general solutions of the material are introduced,and the boundary condition and the equilibrium condition of the cone body under different loads are analyzed.Then the Green's functions of the porous elastic cone under the action of the point source are obtained by combining the specific conditions,and the contours of each component in the cone are plotted.