Expansion of a cylindrical cavity in a compressible elastic-plastic medium

This paper presents a new problem formulation related to the cylindrical cavity expansion in a compressible elastic-plastic medium. Nonlinear compressibility, finite strains and Mises-Schleicher criterion are taken into account in the problem formulation The feature of the formulation (nonlinear compressibility) allows us to investigate different porous materials and analyze the effect of porosity on problem parameters. We have presented the derivation of the analytical relations that determine the cavity expansion resistance and size of the plastic zone for two classes of materials, such as metals and porous media (soils). These analytical relations are used to obtain qualitative results about the nature and size of strains in the medium. For example, the flowing medium is characterized by an anomalously large zone of plastic strain. We have considered a set of metals, alloys and soft soils within the numerical analysis. On the basis of the numerical analysis, we have obtained the estimated range of values of the most important parameters. For metals, this parameter is the dimensionless bulk modulus. By using the bulk modulus, we have approximated the expansion resistivity, the sizes of the cavity and compaction zone. Since soft soil is the material with nonlinear properties, the dependence of parameters has a more complicated form, namely, the additional effect of the material porosity on the expansion resistance and size of strains. By using the results of numerical calculations we have made a comparative analysis of the porosity effect on the size of the compaction zone in the neighborhood of the cavity for sandy and clay soils. These estimations of the expansion medium resistance of the cylindrical cavity are useful to pose and refine the applied relations with regard to the theory of the dynamic penetration of slender (sharp) impactors.