Effective elastic and fracture properties of regular and irregular masonry from nonlinear homogenization

Abstract

Prediction of effective elastic and strength parameters of both regular and irregular masonry walls from homogenization is presented. To that end, the widely accepted first order homogenization method is adopted to provide the homogenized elastic stiffnesses or compliances as well as macroscopic parameters of the selected nonlinear constitutive models. These include the tensile and compressive strength and fracture energies of a generally orthotropic material extracted from the computationally derived macroscopic stress strain curves. In this regard, two types of boundary/loading conditions resulting from the strain-based and mix type formulation of the homogenization problem are examined. The response provided by an orthotropic damage model, expected to describe the behavior of the homogenized structure on macroscale, is compared to that derived via a classical isotropic scalar damage model. It reveals that strong constraints of the orthotropic damage model offer results inapplicable for estimating the macroscopic fracture properties thus promoting the application of a simple isotropic damage model when solving the homogenization problem. The results also show that the mixed boundary conditions, allowing us to represent a pure tension/compression loading mode while being capable of tracking the softening branch of the stress–strain curve, deliver the response comparable to that of a purely strain-based formulation.