Chapter 11 - Symmetrization of the effective stress tensor

Abstract

The aim of this chapter is to provide a solid mathematical basis for symmetrization methods of the effective stress tensor, and justification for their use and validity. The effective stress tensor is examined within the framework of continuum damage mechanics. For a general state of deformation and damage, it is seen that the effective stress tensor is usually not symmetric. Therefore, its symmetrization is necessary for a continuum theory to be valid. There are three types of symmetrization methods: explicit symmetrization, square root symmetrization, and implicit symmetrization. These three symmetrization methods are compared, and certain recommendations are made regarding their suitability. This chapter concludes that the explicit method produces higher damage effect values, thus resulting in higher effective stresses than the other two methods. The implicit method produces the lowest symmetrized stress values. All three symmetrization methods display qualitatively the same variation of the damage effect tensor. Only the explicit and implicit symmetrization methods depict more accurately the physics of the material damage behavior.