Hypoelastic tridimensional model for nonproportional loading of plain concrete

A generalized constitutive model based on hypoelastic theory is proposed to characterize the stress-strain relationship of plain concrete under monotonic and cyclic nonproportional loading. First, the existing hypoelastic incremental models are reviewed and some features of concrete behavior are described. The behavior of concrete is modeled using a normalized scalar damage parameter, the equivalent strain concept, and either the Willam-Warnke five-parameter or the Hsieh-Ting-Chen four-parameter failure surfaces. A new tensile strength criterion and a method for objective modeling of the postpeak compression state are derived. The important features of nonlinear behavior of concrete, such as the volumetric dilatation, the transition state from brittle-softening to ductile-hardening behavior, degradation of the elastic modulus under cyclic loading, and the postcrushing state are all represented by the proposed constitutive model. Comparison of the model predictions with laboratory tests support the validity of the proposed formulation. It is believed that the proposed constitutive relationships provide a good compromise between simplicity and accuracy for modeling plain concrete.