Fracture modeling using a micro-structural mechanics approach––I. Theory and formulation

Stress–strain relationships used for modeling the mechanical behavior of materials have been traditionally derived following a phenomenological approach, without explicit considerations of the micro-structures of material. Here, we adopt a micro-structural mechanics approach to model the development of fracture in concrete. The continuum is assumed to have an underlying micro-structure of lattice type, which has been demonstrated as a useful description for concrete fracture. A finite element formulation is also described that incorporates the developed stress–strain relationship. In an accompanying paper, we will show the results of finite element analyses, discuss its characteristics with respect to mesh size independency, and evaluate the applicability of this method.