A hybrid stress finite element for the efficient nonlinear analysis of masonry walls based on a multi-failure strength domain

A novel 8-node hybrid stress finite element (FE) is proposed for the efficient nonlinear analysis of in-plane loaded masonry walls. To provide a robust, easy-to-characterize mechanically, and computationally efficient practice-oriented numerical framework, masonry is idealized as an elasto-plastic homogeneous continuum. Elasto-plasticity is considered at the FE level by means of a dual-decomposition approach, with plasticity controlled at Gauss–Lobatto points. A state-of-the-art single-surface multi-failure anisotropic strength domain specifically dedicated to masonry is employed. Multiple limit surfaces are considered and condensed into a unique surface through the RealSoftMax function, preserving the distinction between failure modes and the level of activation of each failure thanks to specific weights. The present numerical framework is tested though several structurally meaningful examples with available numerical and experimental reference solutions, comparing the efficiency of the proposed FE with standard displacement-based FEs, as well as other mixed FEs. As a result, the novel 8-node hybrid stress FE shows superior performance with respect to the other FEs, in terms of accuracy and convergence rate. Accordingly, the present numerical framework allows to simulate accurately the nonlinear response of masonry walls and to track realistically the evolution of the considered failure modes even with a few FEs per wall, so being particularly efficient and appealing in engineering common practice.