Monotonic and Cyclic Constitutive Law for Concrete

A simple time‐independent, mathematical model is proposed for the monotonic and cyclic behavior of concrete under multiaxial stress conditions. An essential feature of the model is a bounding surface in stress space, which is a function of ${\epsilon }_{\max }=$ the maximum strain experienced by the material to the present time. The “yield” surface degenerates into the current stress point. Strain increments $d{\epsilon }_{\mathrm{ij}}$ are considered completely plastic and are computed by superposition of: (1) An isotropic component, proportional to the hydrostatic stress increment; and (2) deviatoric and isotropic components, proportional to the octahedral shear stress increment. The plastic modulus for calculation of the latter strain components is a function of: (1) The distance of the stress point from the bounding surface, measured along the direction of the stress increment $d{\epsilon }_{\mathrm{ij}};$ and (2) ${\epsilon }_{\max }\text{.}$ This functional dependence of the plastic modulus and the fact that the bounding surface shrinks as emax increases allow realistic modeling of the nonlinear unloading and reloading behavior of concrete.