Different Ways to Consider Heterogeneity in Quase-fragile Materials Using a Version of Lattice Model

The simulation of the damage process in quasi-fragile materials may be classified in two large groups, those based on Continuum Mechanics, i.e. the so-called Classical approach and the Statistical Models approach. In the former, plasticity theories are extended to study the damage process, leading to procedures that encounter serious difficulties when dealing with quasi fragile materials, in which scale effects, anisotropic damage and associative behavior among defects are likely to occur. In the present work a version of lattice method is used to simulate the behavior of cubic models submitted to uniaxial tension and compression load. Different levels of ductility were considered in the models using several setting of material properties in their definition. Over the cubic models thus implemented, two source of heterogeneities were considered: Introducing parameters that govern the uniaxial constitutive law of the bars as random fields and introducing imperfection in the coordinates of the lattice mesh. Results in terms on the global strain and stress, energy balance and final configuration are presented.