Document Type : Article

**Authors**

Civil Engineering Faculty, K. N. Toosi University of Technology, No. 1346, ValiAsr Ave., Mirdamad Cross, Tehran, Iran.

**Abstract**

Mathematical simulation of the nonlinear tri-dimensional mechanical behavior of quasi-brittle materials like concrete is one of the biggest challenges in the engineering science. It is vital to have the knowledge of the response of concrete specimens subjected to low and high strain rate deformation for the analysis of concrete structures under the static and dynamic loading cases. The behavior of this material is generally known to be strain rate sensitive. Among phenomena of different orientation, the multi plane models, like multi-laminate models using a constitutive equation in a vectorial form rather than tensorial form by means of capturing interactions, can meet this goal adequately. This paper suggests a robust rate dependent damage based model in the multi-planes framework accomplished with minimum parameters for calibration and appropriate for engineering purposes. This damage formulation has been built on the basis of two types of essential damage, axial damage and shear damage, that basically can happen on each sampling plane and based on this concept two new axial and shear damage functions are proposed. Model verification has been studied under different compressive and tensile loading rates, comparing the results of the proposed model with the experimental data and Mohr-Coulomb failure criterion envelope line.

**Keywords**

**Main Subjects**

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Transactions on Civil Engineering (A)

May and June 2019Pages 1194-1205