CAVITATION IN HOOKEAN ELASTIC MEMBRANES
摘要
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 ordinarydifferential 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 cavityare 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.