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Continuum modeling for masonry-like material accounting for bricks or blocks texture is discussed. The constitutive functions for the contact actions - expressed in terms of size, shape and arrangement of the block assembly - are derived within the framework of the linear elastic Cosserat and Cauchy theories. By varying some important geometrical parameters: the scale factor between the wall and the blocks size, the shape of the bricks and their arrangement, micropolar materials with particular internal constraints are obtained. In a few situations the constrained continuum behaves as a Cauchy continuum. In general, the Cauchy continuum does not provide a proper description of the brick masonry behaviour while the structured continuum model, accounting for the mutual blocks rotation, gives satisfactory results

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A structured continuum model is formulated to describe the behaviour of block masonry modelled as distinct rigid body systems with elastic interfaces. A correspondence between the two motions is obtained by postulating a relationship between the displacement fields of the continuum and the discrete models. The constitutive functions for the dynamic actions of the continuum are derived by equating the power of the two models

A multiscale approach to model the mechanical behaviour of blocky materials that exhibit microscale features is proposed. From the description of these materials at microscopic level, as systems of interacting rigid elements, a formula for the stored energy is given in order to derive the macroscopic constitutive equations of a linear elastic equivalent multifield continuum. This continuum results. to be a micropolar continuum suitable to describe the mechanical behaviour of brick/block masonry, as well as jointed rocks or matrix/particle composites, accounting for the size, the orientation and the arrangement of the elements. This multiscale approach proves to be effective also in the non-linear framework. The material non-linear behaviour is represented through internal constraints derived from delimitations imposed to the interactions of the block system. Some numerical examples show the correspondence between discrete and continuum modelling, both in the linear and in the non-linear frame. (c) 2005 Elsevier Ltd. All rights reserved

Mechanical behaviour of particle composite materials is growing of interest to engineering applications. A computational homogenization procedure in conjunction with a statistical approach have been successfully adopted for the definition of the Representative Volume Element (RVE) size, that in random media is an unknown of the problem, and of the related equivalent elastic moduli. Drawback of such a statistical approach to homogenization is the high computational cost, which prevents the possibility to perform series of parametric analyses. In this work, we 2 M. Pingaro et al.propose a so-called Fast Statistical Homogenization Procedure (FSHP) developed within an integrated framework that automates all the steps to perform. Furthermore within the FSHP, we adopt the numerical framework of the Virtual Element Method (VEM) for numerical simulations to reduce the computational burden. The computational strategies and the discretization adopted allow us to efficiently solve the series (hundreds) of simulations and to rapidly converge to the RVE size detection.

Several composite materials used in engineering – such as ceramic/metal matrix composites, concrete, masonry-like/geo–materials and innovative meta–materials – have internal micro-structures characterized by a random distribution of inclusions (particles) embedded in a matrix. Their structural response is highly influenced not only by the mechanical properties of components, but also by the shape, size and position of the inclusions. In this work, we adopt a statistically-based micropolar homogenization procedure, to obtain the overall elastic properties of homogeneous micropolar continua able to naturally account for scale and skew–symmetric shear effects. Attention is paid to the sensitivity to material contrast, defined as the mismatch between classical and micropolar constitutive properties of matrix and inclusions. A statistical specifically conceived convergence criterion is adopted which allow us to identify the REV (Representative Volume Element) for any value of material contrast