A new generalized Drucker–Prager flow rule for concrete under compression

In this paper, a new generalized Drucker–Prager flow rule for concrete under compression with infinitesimal deformation is proposed, where the plastic volumetric strain is taken as the hardening parameter. The flow rule is proposed based on two fundamental phenomenological deformation properties of concrete, and on the fact that the deviatoric part of the plastic strain has no contribution to plastic volumetric strain. There is only one material parameter needing calibration for each grade of concrete in the flow rule. This parameter has a clear physical meaning to reflect the brittleness of concrete, and is defined as the brittleness index of concrete. The flow rule has a concise and simple form similar to the traditional Drucker–Prager flow rule, and for the case of uniaxial compression, the proposed flow rule is identical to the traditional Drucker–Prager flow rule. The effect of confinement stress is well considered by multiplying the hydrostatic part of the flow rule with a simple piecewise function, which differentiates the proposed flow rule from the traditional Drucker–Prager flow rule. An iterative method is proposed to determine the incremental stress–strain relationship when determining the flow rule. The correctness and reliability of the suggested flow rule are is validated using uniaxial, biaxial, and triaxial experimental results.