Cavitation in elastomeric solids: Ⅱ-Onset-of-cavitation surfaces for Neo-Hookean materials

摘要

In Part I of this work we derived a fairly general theory of cavitation in elastomeric solids based on the sudden growth of pre-existing defects. In this article, the theory is used to determine onset-of-cavitation surfaces for Neo-Hookean solids where the defects are isotropically distributed and vacuous. These surfaces correspond to the set of all critical Cauchy stress states at which cavitation ensues; general three-dimensional loadings are considered. Their computation requires the numerical solution of a nonlinear first-order partial differential equation in two variables. The theoretical results indicate that cavitation occurs only for stress states where the three principal Cauchy stresses are tensile, and that the required hydrostatic tensile component increases with increasing shear components. These results are confronted to finite-element simulations for the growth of a small spherical cavity in a Neo-Hookean block under multi-axial loading. Good agreement is found for a wide range of loading conditions. Comparisons with earlier results available in the literature are also provided and discussed. We conclude this work by devising a closed-form approximation to the theoretical surface, which is of remarkable accuracy and mathematical simplicity.