Ergodicity in Mesh Refinement for Modeling Concrete Fracture Using VEM and IE

Abstract

This paper proposes a procedure for modeling brittle failure behavior based on the combination of virtual elements (VEs) and nonlinear interface elements (IEs) from a stochastic approach. It is essentially based on the ergodic behavior of the refinement of randomly generated polyhedral meshes used to model the tortuous crack propagation of concrete subjected to mode II or shear fracture. In particular, two typical cases in the literature, the Three-Point Beam test and the Hassanzadeth test, are analyzed. The results show that the average obtained by a group of randomly generated coarse meshes are more accurate in terms of maximum load than the result obtained by a single fine mesh. Finally, the magnitude of the dispersion obtained based on these results is discussed, compared to those generated by the randomness of other variables such as the arrangement of aggregates in cases such as concrete.