Stability analysis of quasi-brittle materials - creep under multiaxial loading

The aim of this paper is to develop a simple time-dependent Continuum Damage Mechanics model applied to quasi-brittle materials such as rock or concrete. The three-dimensional constitutive visco-damage model describes phenomena like relaxation, creep and rate-dependent loading using a unified framework. A material stability analysis devoted to creep tests highlights a general creep stress stability domain. This convex domain is connected to the property of the associated time-independent Continuum Damage Mechanics model. More particularly, the boundary of this domain in the creep stress space coincides with the invertibility condition of the constitutive matrix considering infinitely slow loading. Phenomenon as creep failure under high-sustained load is explained quite simply within stability theory. Creep failure appears as the manifestation of a saddle-node bifurcation phenomenon.