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Understanding the behavior of concrete at high strain rates loading is a critical issue for theory and applied purposes. The concrete is non-linear, rate-sensitive and pressure-dependent material that will add more difficulties in its modeling at high loading conditions such as impact penetration situations. In the present study, numerical simulation of penetration in a concrete target using an advanced plasticity concrete model is presented using explicit finite element (FE) analysis. A full 3D FE model of impact on unreinforced concrete specimens is carried out. The analysis includes initiation and progressive damage of the composite during impact and penetration Also comparison between some empirical solutions is carried out and their accuracy and precision are checked used experimental solution. Concrete nonlinear behavior was modeled using RHT model which is an advanced plasticity model for concrete at high strain rate loading condition. Two test examples are presented to demonstrate the proposed method. They involve the impact of an ogive-nose projectile on concrete cylinders with variable dimensions. The FEM computational results obtained using RHT plasticity model are very close to the test data, implying that the proposed method will be promising in studies of impact analyses of concrete structures subjected to impact loading. In using RHT model with the default model parameter values, the experimental results cannot be reproduced satisfactorily. Deduced results having good agreement withexperimental ones using suitable calibration of plasticity model parameters value. The RHT plasticity concrete model was developed as an enhancement to the JH concrete model by the introduction of several new features. In this new model, the strain hardening and the third invariant dependence were considered. An independent fracture strength surface was incorporated to allow for a more appropriate modeling of the material softening response. In addition, the concrete hydrostatic tensile strength was made rate dependent. Using a modified parameter setting, the RHT model implemented in AUTODYN hydrocode exhibits a generally excellent behavior. In this paper also, a comprehensive evaluation study of several widely used empirical penetration depth relation is presented. The model formulations are scrutinized and numerical tests are carried out to examine their actual performances subjected to various loading conditions. Comments on the limitations and the appropriate use of these models are given. In addition to penetration depth, damage extension, concrete sapling, scabbing and output velocity of missile and other time dependent structural quantities can captures well. This is in contract with imperial relations that have only penetration depth calculation capability for special conditions. On the other hand investigating of empirical relation shown in addition to their finite application ranges, they haven't good results in majority of cases. Among them, US army corps of engineers'' experimental based relation have better results compared other empirical relations for calculation of penetration depth.

Keywords: Concrete penetration, empirical relation, Numerical solution, Impact, nonlinear solution, RHT plasticity model

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