multi-laminate rate-dependent modelling of static and dynamic concrete behaviors through damage formulation

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 deformations in 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 different phenomena with different orientations, the multiplane models, like multi-laminate, 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-plane framework accomplished with minimum parameters for calibration, which is appropriate for engineering purposes. damage formulation was done on the basis of two types of essential damage, namely axial damage and shear damage, that could basically happen on each sampling plane and based on this concept, two new axial and shear damage functions were proposed. model verification was performed 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.