A multiscale model for reinforced concrete with macroscopic variation of reinforcement slip

A single-scale model for reinforced concrete, comprising the plain concrete continuum, reinforcement bars and the bond between them, is used as a basis for deriving a two-scale model. The large-scale problem, representing the “effective” reinforced concrete solid, is enriched by an effective reinforcement slip variable. The subscale problem on a Representative Volume Element (RVE) is defined by Dirichlet boundary conditions. The response of the RVEs of different sizes was investigated by means of pull-out tests. The resulting two-scale formulation was used in an FE2 analysis of a deep beam. Load–deflection relations, crack widths, and strain fields were compared to those obtained from a single-scale analysis. Incorporating the independent macroscopic reinforcement slip variable resulted in a more pronounced localisation of the effective strain field. This produced a more accurate estimation of the crack widths than the two-scale formulation neglecting the effective reinforcement slip variable