Elasto-Plastic Analysis On The Spherical Cavity Expansion Problem In The Pressure Sensitive Medium

The pressure-sensitive dilatant materials, such as rock, soil, foam metal, polymeric material, rubber and so on, are the most widely applied materials in nature. As these materials contain micro-structures (such as micro-voids, defects, inclusions and cracks), the deformation and failure mechanism are complicated. Thus, in-depth study on the deformation and failure mechanism of the pressure-sensitive dilatant material is an important research subject in solid mechanics at present.During the study on the deformation and failure mechanism of the pressure-sensitive dilatant material, researchers paid great attention to spherical cavity inflation model for its symmetry, simplicity, and convenience to get the stress and strain field solutions by theoretical deduction and reveal the deformation law. So investigation on spherical cavity inflation through elastoplastic analysis was devoted much attention by researchers from no matter solid mechanics, materials science, solid state physics, explosion mechanics etc.In this paper, based on expatiation of the finite deformation elastic-plastic theory, for the hypoelastoplastic problem, the key to solve it is how to choose the yield functions, so three kinds of two-independent-parameters yield functions were discussed. Then the elliptic-equation yield function was chosen to make elastoplastic analysis on spherical cavity inflation problem in pressure-sensitive dilatant materials, owing to it can maintain the continuity from the elastic deformation to the plastic deformation. In this paper, the main jobs are as follows:1. The constitutive model of the pressure-sensitive dilatant materials was established based on the frame of the hypoelastoplastic finite deformation theory. The expressions of the constitutive equations and the equilibrium equations were deduced in spherical coordinate system. Then the geometry equations, the compatibility equations and the boundary conditions were obtained by the use of the logarithmic strain. Accordingly, through the numerical calculation, the stress distribution and the strain distribution of the spherical cavity were given in the pressure-sensitive dilatant materials under internal pressure. The influence of the pressure sensitive coefficient on the stress field and the strain field were also discussed.2. The problems on the spherical cavity inflation with finite elastoplastic deformation in the elastic-perfectly plastic materials were studied. It is the statically indeterminate problem for the stress fields in the Euler coordinate system, which can be solved by using the yield functions and the equilibrium equations. Via the transforming rules from the Lagrange coordinate system to the Euler coordinate system pre-and post-deformation, the logarithmic strain and the numerical calculation, the stress distribution and the strain distribution of the spherical cavity are given in the elastic-perfectly plastic pressure-sensitive dilatant materials under internal pressure. The influence of the pressure sensitive coefficient on the stress field and the strain field are also discussed.3. The problem on the spherical cavity dynamic expansion was studied, through the use of the elliptic-equation yield function, the self-similarity hypothesis and the three region model. Then the stress distribution and the continuous conditions in the intersection of plastic and elastic areas were deduced in the elastic region; the nonlinear differential equations on∑r and∑θare also given in the plastic region. The numerical calculation results on the basic physical quantities (∑θ,∑r,V,ρ/ρ0) are obtained, at last, the effects of the material parameters on the stress and strain fields are discussed.4. The problem on the spherical cavity dynamic expansion was studied in the perfectly pressure-sensitive dilatant materials.Drawing out the theoretical model from the practical problems in engineering to investigate the general deformation law for the experiment design and the numerical calculation model, combining the theoretical research, numerical calculation with the experiment closely and permeating each other to understand the physical essence of the engineering problem deeply and find the general law for guiding practice, all of these things above are inevitable trends in the development of mechanics. With the emergence of the new materials as well as the development of science and technology, there are many complex problems to solve in aviation, navigation, national defense, textile industry, which demand profound comprehension on the mechanical behavior of the materials and structure at microcosmic, microscopic and macroscopic level respectively. Therefore, further study on the spherical cavity inflation by elasto-plastic analysis in the pressure-sensitive dilatant materials has theoretical significance and practical value.