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The new potential proposed in [1] is used to modify Concrete Damaged Plasticity [2] model. The formulas for plastic multiplier and elastoplastic stiffness tensor are derived and simple numerical test are performed to confirm validity of the change. Predictions of the modified model and the original model are compared. The comparison shows similar character of the resultant curves, although for some cases a distinct quantitative difference between the models is revealed.

A general form of Drucker-Prager type plastic potential suitable for concrete and soil is proposed, allowing to distinguish qualitative difference between stress states with prevailing tension from those with dominant compression. The potential includes six material constants and one arbitrarily chosen function g describing deviatoric section of the potential surface. The influence of the parameters on the shape of the considered yield surface is discussed. The verification of convexity of the proposed potential is carried out in order to impose conditions on the parameters and the unknown function g. The calibration based on results of typical tests for concrete presented in the literature is proposed and the values of the coefficients are given out in relation to the yield limit in uniaxial compression test for common proportions of yield limits for other basic tests.

In order to extend the Concrete Damaged Plasticity model [1], a modification of flow rule is considered. A new plastic potential is proposed. It takes into account the difference in behavior of concrete under compressive and tensile loading. In the present paper the proposed function is examined and compared to the original potential. Influence of parameters of the potential choice on the shape of its surface is analysed. Formulation and preliminary validation of the modified model is shown in the subsequent paper (Part II).

A refined model for elastoplastic damaged material is formulated based on the plastic potential introduced in Part I [1]. Considered model is an extension of Concrete Damaged Plasticity material implemented in Abaqus [2]. In the paper the stiffness tensor for elastoplastic damaged behaviour is derived. In order to validate the model, computations for the uniaxial tests are performed. Response of the model for various cases of parameter’s choice is shown and compared to the response of the CDP model.