Rigorous Estimates for Effective Creep-coefficients of Microcracked Masonry Accounting for Cracks Interactions

Based on the association of finite elements homogenization method and a rigorous homogenization scheme accounting for crack interactions, this paper provides rigorous predictions for the local and effective properties of microcracked viscoelastic masonry with or without creep of bricks. For the sake of simplicity, viscoelastic brick and mortar are assumed to follow the Generalized Maxwell rheological model and to be respectively safe and microcracked. In the mortar, the distribution of microcracks orientations is assumed to be random. Two steps are followed. The first one is based on the identification at the short and long terms of an approximate analytical creep function for the mortar. This step relies on the coupling between the Griffith’s brittle fracture theory and a rigorous homogenization scheme - the Ponte Castañeda & Willis model - accounting for crack interaction instead of the dilute scheme adopted previously in Rekik et al. Two cases are considered: open and closed cracks. The first step allows to avoid recourse to 'heavy' numerical inversion of the Laplace-Carson transform. The second one provides overall creep coefficients of masonry by means of periodic homogenization carried out by finite elements method. For open cracks state, time-dependent crack density is investigated. The proposed model is validated by comparison with an analytical one available for a compressed masonry wall with "standard" viscoelastic mortar joints. Effect induced by microcracks is also highlighted by comparison with uncracked masonry. At last, results provided by the proposed model can be considered to be rigorous solution improving on dilute estimates for the creep behavior of microcracked mortar and demonstrating the interest to not neglect both cracks interactions and creep of bricks units.