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Multiscale finite element modeling linking shell elements to 3D continuum

. The present paper investigates the response of masonry structural elements with periodic texture adopting an advanced multiscale ﬁnite element model, coupling diﬀerent formulations at the two selected scales of analysis. At the macroscopic structural level, a homogeneous thick shell is considered and its constitutive response is derived by the detailed analysis of the masonry repetitive Unit Cell (UC), analyzed at the microlevel in the framework of the three-dimensional (3D) Cauchy continuum. The UC is formed by the assembly of elastic bricks and nonlinear mortar joints, modeled as zero-thickness interfaces. The Transformation Field Analysis procedure is invoked to address the nonlinear homogenization problem of the regular masonry. The performance of the model in reproducing various masonry textures is explored by referring to an experimentally tested pointed vault under diﬀerent proﬁles of prescribed diﬀerential settlements. The structural behavior of the vault is studied in terms of global load-displacement curves and damaging patterns and the numerical results are compared with those recovered by detailed micromechanical analyses and experimental evidences.