Application of a penalty function to void growth in non-linear incompressible material

Initial growth of an isolated void in an infinite block of incompressible, linear and non-linear viscous material under remote axisymmetric stress is studied. This problem was first considered by Budiansky et al. [in Mechanics of Solids, The Rodney Hill 60th Anniversary Volume (Edited by H.G. Hopkins and M.J. Sewell), pp. 13-45]. In that investigation, an unintuitive deformation pattern was produced for the non-linear material; that is, for certain ranges of the relevant parameters, the largest deformation of the void occurred in the direction of the smallest stress. To re-examine this behavior, the initial change of void shape and size are determined by means of another method: the finite element method. The incompressibility condition is imposed by means of the 'penalty function' procedure. An important feature of this investigation is the explicit inversion of the non-linear creep law. As shown by Budiansky et al., under high triaxiality conditions the behavior of the void in non-linear viscous material is qualitatively different from that in linear viscous material.