The present work concentrates on the model of concrete under dynamic loading. The stochastic damage constitutive model for concrete under static loading developed by the authors’ research group is firstly reviewed in this paper. The strain rate effect is considered as viscous effect so that the dynamic generalization of the static model could be developed by analogy with viscous-plastic theory. Combined with static damage expressions, the frame work of dynamic stochastic damage constitutive relationship for concrete is established. The analytical expression of dynamic increase factor (DIF) of peak stresses under tension and compression are derived according to the present dynamic damage model. Several simulation results of concrete under static as well as dynamic loading are provided to demonstrate its capacity of reproducing the salient features experimentally observed.
A micro-cell size dependent damage law is proposed by the multi-scale damage representation to remedy the mesh sensitivities involving in the numerical simulations. The homogenization based multi-scale damage representation is firstly introduced in obtaining the macro-damage evolution from micro-cell analysis. Then, the micro-cells with different sizes are generated and the corresponding simulations are given. Based on the simulation results, we define the micro-cell size dependent damage law. Finally, the accuracy and efficiency of the proposed damage law are verified by the notched beam simulation results.
The heterogeneous lattice model is presented to simulate the behaviors of concrete, in which the concrete is regarded as random medium and the stochastic damage constitutive model is proposed. The parameters of the stochastic damage constitutive is identified compared with the experiment results of concrete under uniaxial tension and uniaxial compression.
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