The Mullins effect in equibiaxial deformation

Common experience teaches that the pressure required to inflate a balloon is noticeably reduced by prestretching it several times prior to its primary inflation. This preconditioning phenomenon is known as stress-softening and often is called the Mullins effect. A theory of stress-softening in incompressible isotropic materials is applied to study this effect in an equibiaxial extension for which some general results are presented. It is shown, for example, that effects of stress-softening in a simple uniaxial compression can be adduced from those demonstrated for equibiaxial extension under plane stress. The general equibiaxial results are applied to study the Mullins effect in the inflation of a spherical membrane. The stress-softening phenomenon in cyclic inflation and deflation of the balloon is investigated for Mooney-Rivlin and biotissue parent material models. It is shown analytically that the effect of preconditioning in uniaxial extension is to significantly reduce the pressure required to first inflate a balloon to an equivalent strain intensity. This result characterizes the familiar softening phenomenon associated with balloon inflation.