An anisotropic multi-plane elastic-damage model with axial and shear damage and its application to concrete behavior

The prediction of material response is necessary for the analysis of structure under static or dynamic loading. Mathematical modeling of the nonlinear tri-dimensional mechanical behavior of quasi-brittle materials, like concrete, caused by damaging and plasticity effects is one of the most serious classical challenges we face in the engineering science. Among phenomena of different orientations, the micro-plane models, like multiplanes models, which use a constitutive equation in a vectorial form rather than tensorial form by means of capturing interactions, can serve this goal adequately. This paper presents a simple realistic and robust damage based model in the multi-plane framework accomplished with a few parameters for calibration and suitable for engineering purposes without volumetric-deviatoric split of strain tensor and its problems. This damage formulation has been built on the basis of two types of fundamental damage, namely, axial damage and shear damage, that can essentially occur on each micro-plane and, based on this concept, two new axial and shear damage functions are presented. By comparing the results of the proposed model and experimental data, model verification has been done under different loading/unloading/reloading stress/strain paths.