STABILITY CONSIDERATIONS FOR ELASTIC-PLASTIC PROCESSES WITH DAMAGE

Abstract

Classical theory of plasticity is fairly complete with flow rules, convexity of yield surfaces, extremum principles, and the uniqueness theorem. For the strain-hardening plasticity, Drucker’s postulates are established and proven based on the plastic-work and energy principles. Plasticity models have been further applied to heterogeneous and cementitious materials with certain degrees of success. In this paper, the stability statements of strain-hardening and strain-softening processes in concrete are examined by utilizing thermodynamic potential functions in the stress space and by applying Euler’s theorem of homogenous functions. It is shown that by specifying a strain-hardening parameter to account for the plastic strains and a damage parameter to represent the effect of microcracking, the dissipation inequality can be used to establish the Drucker’s stability postulate for the plastic flow within the framework of the internal variable theory of thermodynamics. Using the same approach and assuming uncoupling between plastic flow and microcracking, the formation leads to a softening stability statement for damage processes in concrete.