A mixed membrane finite element for masonry structures

A mixed membrane eight-node quadrilateral finite element for the analysis of 2D masonry structures is presented, to be used in conjunction with a phenomenological and/or macromechanical masonry material model. Resorting to mixed finite elements to overcome well- known limitations of displacement-based formulations, the element derivation is based on a Hu–Washizu variational statement, involving displacement, strain and stress fields as independent variables. Peculiar feature of the formulation is a discontinuous, piecewise-constant interpo- lation of the strain field at element level. That is motivated by the typical behavior of masonry structures, characterized by strain localization phe- nomena and highly nonlinear strain spatial distributions. Some computa- tional aspects related to strain softening behavior are discussed. Specif- ically, for the implementation in standard strain-driven finite element computer programs, Newton’s method of solution is adopted for the ele- ment state determination problem. Moreover, typical regularization tech- niques for guaranteeing mesh-objectivity are integrated in the present approach. By the comparison with competing serendipity displacement- based formulation, numerical simulations prove high performances of the proposed finite element, especially when coarse meshes are adopted.