Multi-level modeling of viscoelastic microcracked masonry

Abstract

• We propose a multi-level model to predict the orthotropic behavior of cracked masonry • This model relies on the coupling between Griffith’s theory and homogenization methods • Overall estimates of Cecchi & Taliercio model are softer than the Cecchi & Tralli’s ones • The Modified Maxwell model is relevant for the mortar’s creep at short and long terms • Both short and long terms, constant and time-dependent crack densities were investigated This paper provides multi-level modeling of microcracked viscoelastic masonries generally present in historical masonries or refractory linings. It is an extension of the Cecchi and Tralli (2012) or Cecchi & Barbieri (2008) and Cecchi & Taliercio (2013) works for the typical Burgers and Modified Maxwell models followed by both undamaged and microcracked masonries. For the sake of simplicity and in order to provide rigorous analytical global estimates, only the mortar is assumed to be viscoelastic and microcracked. Bricks are assumed to be undamaged, elastic or quasi-rigid. The distribution of microcracks is assumed to be isotropic. The effective behavior of the viscoelastic microcracked masonry is provided by two steps. The first one relies on the coupling between the Griffith’s brittle fracture theory and linear mean-field homogenization scheme in order to account for the effect of microcracks on the macroscopic deformation of the mortar and establishes a linear relation between apparent macroscopic stress and strain. This step allows to easily and fast determine the effective creep function of the microcracked mortar without recourse to ’complex’ or heavy numerical inversion of the Laplace–Carson transform. The second step is based on the coupling between asymptotic analysis and homogenization theory applied for a periodic masonry. The proposed models provide analytical solutions - explicit functions of the crack density parameter - for the effective orthotropic behavior of a microcracked viscoelastic periodic masonry cell. This study proves that the Cecchi & Tralli’s and Cecchi & Taliercio’s extension estimates are close and that the later are softer. Such overall properties are used to perform finite element computations on a compressed masonry panel as a first application. These models allow then the prediction of mostly stressed and deformed areas in microcracked masonry structures. This study demonstrates that modeling a mortar (at its undamaged or microcracked state) with this Burgers formulation is only suitable for a masonry with too high values of the Maxwell’s relaxation time otherwise it yields to vanishing effective properties with the increase of time and crack density leading thus to a premature collapse of the masonry. On the other hand, the Modified Maxwell model permits the masonry to preserve a certain resistance for every range value of Maxwell’s relaxation time. These conclusions are valid for masonry either with elastic or quasi-rigid undamaged bricks.