kinematic enriched formulation for the analysis of the in-plane behavior of regular masonry walls is proposed in order to overcome the limits of the typical plane stress and plane strain assumptions. The boundary value problem for the masonry RVE subjected to periodic boundary conditions is formulated for the enriched plane state. In particular, the displacement field is represented assuming that the components can be written using the separation of variables; in fact, they are obtained as product of inplane and transversal functions. The in-plane displacement components are expressed as the superposition of a known field, depending on the macroscopic deformations applied to the RVE, and a periodic perturbation described as an even function of the transversal coordinate. The bending effects is avoided representing the out-of-plane displacement field in terms of odd functions of the transversal coordinate. A 2D finite element is formulated and used for performing micro-mechanical and homogenization analyses. Numerical results are compared with analytical ones in order to assess the accuracy of the numerical procedure. Results obtained by employing the proposed model are compared with the ones evaluated on the basis of the classical plane stress, plane strain, generalized plane strain assumptions and with the three-dimensional solution. Finally, the proposed kinematically enriched model is used to derive the elastic domain of the masonry material.

### A kinematic enriched plane state formulation for the analysis of masonry panels

#### Abstract

kinematic enriched formulation for the analysis of the in-plane behavior of regular masonry walls is proposed in order to overcome the limits of the typical plane stress and plane strain assumptions. The boundary value problem for the masonry RVE subjected to periodic boundary conditions is formulated for the enriched plane state. In particular, the displacement field is represented assuming that the components can be written using the separation of variables; in fact, they are obtained as product of inplane and transversal functions. The in-plane displacement components are expressed as the superposition of a known field, depending on the macroscopic deformations applied to the RVE, and a periodic perturbation described as an even function of the transversal coordinate. The bending effects is avoided representing the out-of-plane displacement field in terms of odd functions of the transversal coordinate. A 2D finite element is formulated and used for performing micro-mechanical and homogenization analyses. Numerical results are compared with analytical ones in order to assess the accuracy of the numerical procedure. Results obtained by employing the proposed model are compared with the ones evaluated on the basis of the classical plane stress, plane strain, generalized plane strain assumptions and with the three-dimensional solution. Finally, the proposed kinematically enriched model is used to derive the elastic domain of the masonry material.
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2014
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11580/28472`
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