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Shang Xinchun (Department of Mathematics and Mechanics,University of Science and Technology Beijing,Beijing 100083,China)Cheng Changjun (Department of Mechanics,Shanghai University,Shanghai 200072,China) (Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 200072,China)  
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 mea- sure.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 nu- merical 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 dis- cussed.The result of the energy comparison shows the cavitated deformation has lower energy than the homo- geneous one,thus the state of cavitated deformation is relatively stable.All investigations illustrate that cavi- tation reflects a local behavior of materials.
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