Anisotrope und isotrope fliessbedingung für polymere

Abstract

This paper uses as a starting point the plastic potential for pressure-dependent anisotropic solids. It is proposed that the yielding of an anisotropic material is governed by the “distortion” tensor of rank 4 and the “translation” tensor of rank 2. The translation tensor introduced corresponding to residual stress describes both the initial strength differential effect and the Bauschinger phenomenon. The proposed potential leads to an orthotropic yield criterion which seems more fundamental than the Hill condition, even if further modified to account for the pressure dependence of yielding. If the solid is isotropic the anisotropic coefficients can be taken as a linear combination of the isotropic tensor of order 2. The corresponding isotropic potential leads to the non-linear and the linear pressure-dependent von Mises criteria. The yield locus studies of both orthotropic and isotropic polymers support the proposed plastic potential in its prediction of the macroscopic yielding of pressure-dependent solids.