Continuous and discrete models for masonry like material: A critical comparative study

The aim of this paper is to present a critical comparative review of different models that may be adopted for modelling the mechanical behaviour of masonry, with particular attention to microstructured models. Several continuous and discrete models are discussed. Such models are based on the following assumptions: i) the structure is composed of rigid blocks; ii) the mortar is modelled as an elastic material or an elastic interface. The rigid block hypothesis is particularly suitable for historical masonry, in which stone blocks may be assumed as rigid bodies. For this type of masonry, mortar thickness is negligible if compared with block size, hence it can be modelled as an interface. Masonry-like materials may be modelled taking into account their heterogeneity by adopting a heterogeneous Finite Element Model (FEM) or a Discrete Element Model (DEM). The former seems to be more representative of masonry, but it is computationally onerous and results interpretation may be difficult; the latter is limited to rigid block assumption and mortar joints modelled as interfaces. For this reason, continuous equivalent models may be suitable to investigate masonry behaviour. Continuum equivalent models provide, in an analytical form, constitutive functions, but Cauchy model may be not suitable to describe masonry behaviour due to not negligible size of heterogeneity (block size) with respect to masonry panel size. For this reason, micropolar equivalent continuum may be adopted. By reference to the existing literature, a simple and effective DEM is adopted, in which masonry is modelled as a 'skeleton' having a behaviour depending on forces and moments transferred between blocks through the interfaces (mortar joints). Moreover for the micropolar equivalent continuum, an ad hoc enriched homogenised FEM is formulated by means of triangular elements. The proposed numerical models represent two possible simple approaches for solving heterogeneous problems. Such models are developed both by means of fast numerical routines and do not require specific computer codes, whereas the heterogeneous FEM may be studied by adopting a traditional FE code. DEM and heterogeneous FEM are adopted to verify reliability and application field of Cauchy and micropolar continua. Moreover, sensitivity of micropolar model to the Representative Elementary Volume (REV) chosen is discussed. For these purposes, ad hoc FE models are adopted, with constitutive functions obtained from an identification procedure (both for Cauchy and micropolar continua). An extensive comparison between DEM, heterogeneous FEM and equivalent homogenous FEM is presented in some meaningful cases, taking into account also the effect of heterogeneity size on models behaviour.