Homogenization of Unreinforced Old Masonry Wall Comparison of Scalar Isotropic and Orthotropic Damage Models

Abstract

Masonry is a heterogeneous composite material made of bricks bonded by a mortar matrix. Modeling such a material on macroscale typically calls for homogenization adopting a suitable constitutive model capable of capturing its quasi-brittle behavior. The present contribution concentrates on comparison and potential application of classical isotropic and orthotropic damage models in the framework of strain based first order numerical homogenization. As an illustrative example, a representative volume element in terms of a periodic unit cell is constructed to address the response of an unreinforced masonry (URM) structure typical of “Placa” buildings (mixed masonry-reinforced concrete buildings) built in Portugal. The performance of the two models is examined on the basis of macroscopic stress-strain curves constructed for both tensile and compressive loading. The selected geometrical constraints clearly identify the differences in the predictive capabilities of the two models.

Macroscopic response of regular masonry from homogenization: comparison of isotropic and orthotropic damage models

“…It is clear that such a model is not very practical for multi-dimensional stress states and generally anisotropic materials as it reduces all components of to zero even in cases when damage evolves in one direction only. It has been clearly shown in [1] that a suitable method of attack is the application of anisotropic [5] or orthotropic damage models. An equivalent format of Eq.…”

“…3(b). Furthermore, if prescribing the macroscopic strain Δ we arrive at the strain based formulation adopted in [1]. It is perhaps clear that this more general formulation (9) makes it possible to introduce the mixed loading conditions to drive the analysis in the displacement control regime while keeping the onedimensional format of the macroscopic stress-strain law, e.g.…”

“…Similarly to [1], we shall thought the numerical simulations as a substitution for complex laboratory testing. To compare the present results based on Eq.…”

“…To compare the present results based on Eq. (9) with those derived previously on the basis of strain based formulation we adopt the same computational model as well as the same material properties of the mortar and bricks as used in [1]. Thus the periodic unit cell with the brick layout in Fig.…”

“…The initiative study on Placa masonry is presented in [1]. Therein, attention was accorded purely to strain based homogenization with emphases on the performance of various damage models.…”