Development of a Macroscopic Yield Function for Polymeric Foams

A macroscopic yield function is proposed here to characterize a polymeric foam under a full range of loading conditions. The principal stresses of a stress tensor and the second invariant of the deviatoric stress tensor are the main parameters in the yield function. The yield function is expressed in terms of a linear combination of non-quadratic functions of the relative principal stresses and the second invariant of the deviatoric stress tensor. The non-quadratic yield function can be used to describe the yield behavior of a polymeric foam in Deshpande and Fleck [1] under a full range of loading conditions. A comparison of different macroscopic yield functions to describe the yield behavior of the foam is also presented.