Cavitation in hookean elastic membranes

An exact solution to cavitation is found in tension of a class of Cauchy elastic membranes. The constitutive relationship of materials is based on Hookean elastic law and finite logarithmic strain measure. A variable transformation is used in solving the two-point boundary-value problem of nonlinear ordinary differential equation. A simple formula to calculate the critical stretch for cavitation is derived. As the numerical results, the bifurcation curves describing void nucleation and suddenly rapidly growth of the cavity are obtained. The boundary layers of displacements and stresses near the cavity wall are observed. The cata-strophic transition from homogeneous to cavitated deformation and the jumping of stress distribution are discussed. The result of the energy comparison shows the cavitated deformation has lower energy than the homogeneous one, thus the state of cavitated deformation is relatively stable. All investigations illustrate that cavitation reflects a local behavior of materials. Project supported by the National Natural Science Foundation of China (No. 19802012) the Scientific Research Foundation for Returned Overseas Chinese Scholars, and the Scientific Research Foundation for Key Teachers in Chinese Universities.