Structural Damage Analysis of Masonry Walls using Computational Homogenization

Abstract

This contribution deals with the application of computational homogenization techniques for structural masonry computations, as an alternative to the formulation of complex closed-form macroscopic constitutive laws. The complexity of modeling masonry material stems from the anisotropy evolution and localization induced by mesostructural damage. This phenomenon appears with preferential damage orientations, which are intimately related to the initial periodic structure of the material. The upscaling procedure used here relies on the formulation of mesoscopic constitutive laws at the level of the individual brick and mortar materials. A mesostructural unit cell with its corresponding periodicity requirements is used to deduce the average response of the masonry material through a scale transition. At the macroscopic scale, this averaged material response is used in the frame of an enhanced continuum approach with embedded localization bands, the widths of which are directly deduced from the initial periodicity of the material. The results obtained by the framework are illustrated and discussed by means of a structural computation example, which involves a complex cracking evolution together with fully anisotropic damage development.

A computational library for multiscale modeling of material failure

“…In a nutshell, in these models a crack is injected into Figure 2: Different boundary condition approaches, (a) uniform strain and (b) uniform stress boundary conditions the macroscale model when failure or instability occurs at the RVE. Please refer to the work of Massart et al [76,77] for the masonry cracking, Belytschko et al [21], Belytschko and Song [22] (the MAD method), Allen et al [123,124], Nguyen et al [91,89,90,136] for more details.…”

Computational modelling of crack-induced permeability evolution in granite with dilatant cracks

“…Computational homogenisation was reformulated for allowing nested scale computational schemes in which finite element discretisations are used at both the macroscopic and fine scales simultaneously, which avoids the use of a priori postulated macroscopic laws [53]. This methodology was subsequently adapted to model the failure of quasi-brittle materials [54,55], as well as diffusive phenomena such as thermal conductivity [56,57]. In the recent study [14], these techniques were combined to evaluate damage-induced permeability evolutions in a geomaterial.…”

Numerical homogenization for composite materials analysis. Comparison with other micro mechanical formulations

“…in bending) are passed to the RVE boundaries. To solve problems involving damage and fracture, leading to intense localization, a continuousdiscontinuous homogenization has been developed [29]. It consists in the definition of a localization band at the macro scale, and using the deformation gradient tensor, in this band.…”