A cyclic multiaxial model for concrete

Abstract

A rate-independent plasticity constitutive model is proposed, for the stress-strain and strength behavior of plain concrete, under complex multiaxial stress-paths, including stress reversals. The only material parameters required by the model are the uniaxial cylinder strength f _cand the strain at the peak of the monotonic stress-strain curve, ε₀ . The model is based on a bounding surface in stress space, which is the outermost surface that can be reached by the stress point. When the size of the bounding surface decreases with increasing maximum compressive principal strain ε_max on the material, strength degradation during cyclic loading as well as the falling “post-failure” branch of the stress-strain curves, can be modeled. The distance from the current stress point to the bounding surface, determines the values of the main parameters of the inelastic stress-strain relations, i.e. of the plastic shear modulus H ^P, and the shear-compaction/dilatancy factor β Strains are almost completely inelastic from the beginning of deformation. The inelastic portion of the incremental strain is computed by superposition of 1) the deviatoric strain increment, which occurs in the direction of the deviatoric stress and is proportional to the octahedral shear stress increment and inversely proportional to the plastic shear modulus 2) the volumetric strain increment, which consists of a portion which is proportional to the hydrostatic stress increment, and another which equals the product of the octahedral shear strain increment and the shear compaction/dilatancy factor β Stress reversals are defined separately for the hydrostatic and the deviatoric component of the stress tensor, and the parameters of the inelastic stress-strain relations are given as different functions of the stress and strain history, for virgin loading, unloading, reloading, or for the “post-failure” falling branch.

The incremental stress-strain law is set in the form of incremental compliance and rigidity matrices, and implemented into a nonlinear dynamic finite element code.