Softening hyperelasticity for modeling material failure: Analysis of cavitation in hydrostatic tension

Material failure analysis based on the constitutive model of isotropic softening hyperelasticity is presented. In addition to the bulk and shear moduli the model includes only one material constant of volumetric failure work. The latter is in contrast to the traditional damage theories, which include internal variables that are difficult to calibrate experimentally. The softening hyperelasticity model is used to analyze the critical hydrostatic tension corresponding to the onset of instability of spherical and cylindrical voids. It is shown that the critical tension predicted by the softening hyperelasticity model does not depend on the void size in agreement with the linear elasticity solution showing that the stress/strain state at the edge of the void does not depend on its size. This prediction stays in contrast to the prediction based on the Griffith energy method where the critical tension depends on the size of the void and tends to infinity when the void radius approaches zero. It is argued that the controversial results of the Griffith method are a consequence of a separation of stress analysis and criticality conditions. It is concluded, based on the considered examples, that a description of material failure should be an inseparable part of constitutive models of materials.