The description of the mechanical behaviour of brick/block masonry through equivalent continua is presented here as a paradigmatic example of the problem of gross modelling of discontinuous and heterogeneous materials as continua with microstructure. The approaches reported in the literature differ for the way identification of the continuum is carried out or the nature of the continuum itself. In this paper, continuous models equivalent to rigid particle systems with free or constrained rotations are derived within the general framework of the principle of virtual work. In particular, an integral equivalence procedure is used to derive micropolar, second gradient and classical models. The non-classical models have in the field equations non-standard kinematic and static descriptors accounting for the presence of the material internal structure. The differences in the material responses of the various continua are identified referring to their internal work formulas. For the reference material, it is shown that, unlike the Cauchy continuum, both micropolar and second gradient models are effective in the presence of load and geometrical singularities, which involve significant scale effects on the material response. On the other hand, the second gradient model, as well as the classical model, disregards the role of relative rotation between the local rigid rotation (macrorotation) and the microrotation, which is related to the presence of non-symmetric strains. This circumstance, significant in strongly anisotropic systems, allow us to point out the advantages of the micropolar modelling especially for orthotropic masonry assemblies made of elements of any size. These statements are discussed by means of selected numerical examples of masonry panels differing in size, shape and arrangement, under shear loading conditions. © 2013 Springer-Verlag Wien
A description of brick/block masonry by continua equivalent to discrete systems made of blocks of different geometry and texture is proposed in this paper. Here, the reasons for the selection of a micropolar continuum with respect to the classical continuum are discussed. As recent research in various micromorphic multifield formulations shows, the problem of the choice of the most appropriate continuum to model masonry mechanical behavior is still open, and the advantages of non-classical continuum modeling are not yet completely ascertained. Earlier analyses performed on masonry panels in the presence of load and geometrical singularities pointed out the significant role of the additional degree of freedom of the micropolar continuum (microrotation) and of its gradient. The present study aims to expand the investigation into the consequences of changes in blocks' shape, size and arrangement on the response of block masonry panels under shear forces. This analysis points out the greater effectiveness of micropolar models in capturing the gross structural response of masonry, with respect to the classical modeling. The cases analyzed herein show that apart from the very peculiar case of orthotetragonal symmetry, not only the gradient of microrotation but also the relative rotation between the local rigid rotation and the microrotation, to which relevant non-symmetric strains correspond, are predominant in the majority of the performed numerical tests. Models lacking in these strain measures are therefore inappropriate. The results obtained, ascertained by analyses performed on discrete block assemblies, point out that the micropolar continuum provides a proper description of the masonry behavior. Moreover, the differences between micropolar and classical models remain when the internal lengths vanish.
The dynamics of a parabolic arch is studied in its undamaged and damaged states. The damage consists of a notch that reduces the height of the cross section at a given abscissa. A damage identification technique, based on the minimization of an objective function measuring the differences between numerical and experimental variations of natural frequencies for undamaged and damaged states, is used. The uniqueness of the solution in different damage configurations is investigated using pseudo-experimental data and the reliability of the identification procedure is assessed. The identification procedure is then applied to an experimental case, where frequencies are obtained by impulsive tests on a prototype arch. The minimum number of experimental data needed to identify damage parameters is defined and the sensitivity of the identification algorithm to different possible choices of sets of data is analyzed
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