Pressurized Spherical Cavity Expansion In Different Typical Solids

Studies of cavity expansion are of great importance in the fields of geotechnical engineering, mechanical behavior of metal materials, the production process of rubber and cavitation in different structures. They are particularly helpful in constructing models of installation of industrial devices such as driven piles and the modeling of tunnels.Practically, there are many spherical cavities surrounded by different medium in different scales. The existence of the cavities can reduce the property of materials. In the case of metal casting, for example, large scale cavities should be avoided as possibly as we could during the producing process. However, for some newly designed structures and functioning materials, the existence of the cavities can improve the mechanical properties of these materials to some extent. Therefore, it can provide engineering basis for the design and production of materials by investigating expansion problems of spherical cavities.Durban and Fleck introduced and solved the problem of spherical cavity expansion problems in Drucker-Prager solids. Based on the work of Durban and Fleck, the present work contains a solution to expansion problems of spherical cavity subjected to uniform radial loads for different materials, such as Mohr-Coulomb solids and pressure sensitive materials which reflects the pressure sensitivity of soils, with the aid of plastic potential theory and finite strain analysis. Finite strain analysis and relevant incremental theory are of great importance for understanding the mechanical behavior of the cavity expansion problem, especially for the case of soils.By transferring Lagrange configuration to Euler coordinate, the relationship between plastic potential g and equivalent stress e has been deduced in present paper. Then, by introducing the concept of logarithmic strain, geometry equations can be obtained. According to [3],and the self-simulation theory, the governing equation can be obtained and can be simplified to a single first order nonlinear differential equation with the effective stress as the independent variable.Some numerical cases have been discussed in detail such as Drucker-Prager solids, Mohr-Coulomb solids and pressure sensitive materials. The curves are drawn which reflects the effects of material parameters on the expansion of cavities. Stress distribution is also included in relevant graphs. The present can provide referring basis for the further study on cavity expansion.