A non-quadratic yield function for polymeric foams

The yield behavior of a closed cell polymeric foam is investigated under multiaxial loadings. A phenomenological yield function is developed to characterize the initial yield behavior of the closed cell polymeric foam under a full range of loading conditions. The principal stresses of a relative stress tensor and the second invariant of the deviatoric stress tensor are the main parameters in the yield function. The yield function is a linear combination of non-quadratic functions of the relative principal stresses and the second invariant of the deviatoric stress tensor. The convexity of the yield surface based on the non-quadratic yield function is proved. The non-quadratic yield function is shown to well characterize the yield behavior of a closed cell polymeric foam in [Deshpande, V.S., Fleck, N.A., 2001. Multi-axial yield behavior of polymer foams. Acta Materialia 49, 1859–1866] under a full range of loading conditions. Finally, a comparison of different phenomenological yield functions to characterize the yield behavior of the foam is presented.