Approaches towards computational modeling of masonry structures

Only recently the masonry research community began to show interest in sophisticated numerical tools as an opposition to the prevailing tradition of rules-of-thumb and empirical formulae. The fact that little importance has been attached to numerical aspects is confirmed by the absence of any well established models. The difficulties in adopting existing numerical tools from more advanced research fields, namely the mechanics of concrete, rock and composite materials, are hindered by the particular characteristics of masonry. Masonry is a composite material that consists of units and mortar joints, see Fig. la. A comprehensive analysis of masonry, hereby denoted detailed micro-modeling, must then include a representation of units, mortar and the unit / mortar interface, see Fig. lb. In this case units and mortar in the joints are represented by continuum elements whereas the unit-mortar interface is represented by discontinuous elements. The Young's modulus, Poisson's ratio and, optionally, inelastic properties of both unit and mortar are taken into account. The interface represents a potential crack / slip plane with initial dummy stiffness to avoid inter-penetration of the continuum. This enables the combined action of unit, mortar and interface to be studied under a magnifying glass. Such a representation of masonry leads to large memory and time requirements and a simplified micro-modeling of masonry will be preferably used here, see Fig. Ie. In this case expanded units are represented by continuum elements whereas the behavior of the mortar joints and unit-mortar interface is lumped in discontinuous elements. Each joint, consisting of mortar and the two unit-mortar interfaces, is lumped into an "average" interface while the units are expanded in order to keep the geometry unchanged. Masonry is thus considered as a set of elastic blocks bonded by potential fracture / slip lines at the joints. Accuracy is lost since Poisson's effect of the mortar is not included.
Micro-modeling approaches are suited for small structural elements with particular interest in strongly heterogeneous states of stress and strain. The primary aim of micro-modeling is to closely represent masonry from the knowledge of the properties of each constituent and the interface. The necessary experimental data must be obtained from laboratory tests in the constituents and small masonry samples. Several attempts to use interfaces for the modeling of masonry were carried out in the last decade with reasonably simple models, see e.g. Anthoine (1992) for references. In particular, gradual softening behavior and all failure mechanisms, namely tensile, shear and compressive failure, have not been fully included.

In large and practice-oriented analyses the knowledge of the interaction between units and mortar is, generally, negligible for the global structural behavior. In these cases a different approach can be used, hereby denoted macro-modeling, where a distinction between individual units and joints is not made, see Fig. 1d. Instead the material is regarded as an anisotropic composite and a relation is established between average masonry strains and average masonry stresses. This is clearly a phenomenological approach, meaning that the material parameters must be obtained from masonry tests of sufficient size und8r homogeneous states of stress. A complete macro-model must reproduce an orthotropic material with different tensile and compressive strengths along the material axes as well as different inelastic behavior for each material axis.

 reduced number of orthotropic material models specific for masonry has been proposed, see e.g. Anthoine (1992) and Louren~o (1996) for references. It is not surprising that so few macro-models have been implemented due to the intrinsic complexity of introducing orthotropic behavior. The models proposed in the past have not been widely accepted due to the difficulties of formulat-ing robust numerical algorithms and representing satisfactorily the inelastic behavior. 

It is noted that one modeling strategy cannot be promoted over the other because different appli-cation fields exist for micro-and macro-models. Micro-modeling studies are necessary to give a better understanding about the local behavior of masonry structures. This type of modeling applies notably to structural details, but also to modern building systems like those of concrete or calcium-silicate blocks, where window and door openings often result in piers that are only a few block units in length. These piers are likely to determine the behavior of the entire wall and individual modeling of the blocks and joints is then to be preferred. Macro-models are applicable when the structure is composed of solid walls with sufficiently large dimensions so that the stresses across or along a macro-length will be essentially uniform. Clearly, macro-modeling is more practice ori-ented due to the reduced time and memory exigencies as well as a user-friendly mesh generation. This type of modeling is most valuable when a compromise between accuracy and efficiency is needed. 

Source: https://repository.tudelft.nl/islandora/object/uuid%3Ac39b29ab-3c75-47db-9cb5-bf2b1c678f1f