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In the non-linear finite element analysis (NFEA) of concrete materials, continuum damage mechanics (CDM) provides a powerful framework for the derivation of constitutive models capable of describing the mechanical behavior of such materials. The internal state variables of CDM can be introduced to the elastic analysis of concrete to form elastic-damage models (no inelastic strains), or to the elastic-plastic analysis in order to form coupled/uncoupled elastic-plastic-damage models. Experimental evidence that is well documented in literature shows that the susceptibility of concrete to damage and failure is distinguished under deviatoric loading from that corresponding to hydrostatic loading. A reduction factor is usually introduced into a CDM model to reduce the susceptibility of concrete to hydrostatic stresses/strains. In this work, the effect of a hydrostatic stress/strain reduction factor on the performances of two NFEA concrete models will be studied. These two (independently published) models did not provide any results showing such effect. One of these two models is an elastic-damage model, whereas the other is an uncoupled elastic-plastic-damage model. Simulations and comparisons are carried out between the performances of the two models under uniaxial tensile and compressive loading conditions. Simulations are also provided for the uncoupled elastic-plastic-damage model under the following additional loading conditions: biaxial tension and biaxial compression, uniaxial cyclic loading, and varying ratios of triaxial compressive loadings. These simulations clearly show the effect of the reduction factor on the numerically depicted behaviors of concrete materials. To have rational comparisons, the hydrostatic stress reduction factor applied to each model is chosen to be a function of the internal state variables common to both models. Therefore, once the two models are calibrated to simulate the experimental behaviors, their corresponding reduction factors are readily available at every increment of the iterative NFEA procedures.

Studying the effect of a hydrostatic stress/strain reduction factor on damage mechanics of concrete materials