Boundary element method for the strain-softening response of quasi-brittle materials in compression

In the present paper, the mechanical compressive behavior of quasi-brittle materials is analyzed by means of an ad hoc boundary element algorithm. The analysis is carried out by taking into account the initial crack distribution, which cannot be neglected if the experimental reality (developing over three scales of observation, micro-, meso- and macro-scale) is to be modeled. The algorithm permits us to follow the evolution of the crack geometry during the loading process, which is characterized, at each step, by the propagation of the most critical meso- or macro-crack. Moreover, in order to take into account the micro-crack effect causing the progressive decay of the material, a decreasing variation of the elastic modulus is assumed, depending on the strain energy density absorbed during the loading process. Different geometries, with different slenderness and size scale, are analyzed by the proposed model, with and without friction between specimen and loading platens. The numerical simulations represent the experimental results consistently.