AbstractA framework of the plastic-damage model with double scalar variables is established in nominal stress space under the small deformation assumption. In the damaged part, a damage tensor composed of double scalar variables is presented to comprehensively characterize the isotropic damage behavior in three-dimensional (3D) conditions. The damage laws of Young’s modulus and shear modulus are proposed to capture their different damage characteristic observed in the test. For one-dimensional (1D) and 3D conditions, the applicability of single scalar and double scalar damage variables is discussed. The macroscopic damage difference between these two damage variables when describing damage under 3D conditions is analyzed. In the plastic part, the plastic strain increment is determined by two parts of magnitude and direction. The magnitude is obtained by the consistency condition, and the flow direction is defined by the nonorthogonal flow rule that can satisfactorily reproduce the dilatancy behavior of concrete. The proposed model is implemented by the explicit Runge–Kutta (RK) method with the fifth-order accuracy and the Pegasus method. The performance of the model is assessed by the comparison results between the model and the cyclic loading and unloading test data under different stress paths.

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