Role of Covariance in Continuum Damage Mechanics

The subject of objective rates in continuum damage mechanics is under consideration. It is shown that by changing the definition of the objective rate in constitutive theory, one obtains different material behavior and different final fracture modes as causes of intrinsic microdamage evolution. Theoretical considerations and a numerical example include the comparison of two special cases of objective rates for which the symmetric part of the spatial velocity gradient defines a true rate of the assumed strain rates, namely Lie and Logarithmic. The problem is described in the framework of the recently proposed Perzyna-type viscoplasticity, including an anisotropic damage description; nevertheless, final conclusions are general.