A unified dynamic model for concrete considering viscoplasticity and rate-dependent damage

Precise numerical simulation of structures under dynamic loading is often hampered by the lack of the elaborate rate-dependent nonlinear model of materials. Thus in this article, a unified damage model is proposed to represent the nonlinear behaviors and the rate-dependency of plain concrete in an energy consistent manner. The coupled inviscid plastic damage theory with two damage scalars is first adopted as the multi-dimensional framework of this model. Then based on the strain equivalence hypothesis, the ‘effective stress space plasticity’ is introduced and its rate-dependent extension is proposed by analogy of the Perzyna-type viscoplasticity. To consider the dynamic damage evolution, the rate-dependent damage evolution is introduced according to the simplified Perzyna-type flow rule. Finally, the unified model is developed by introducing both the ‘effective stress space viscoplasticity’ and the rate-dependent damage evolution into the elastoplastic damage framework. Under uniaxial tension, the closed form solution of the dynamic increase factor is analytically derived with two material parameters which have been thoroughly investigated in the literatures. The model results also show well agreements with the experimental data in both material and structural levels.