A 3D Model for Non-linear 'Microscopic' FE Analysis of Masonry Structures

A non-linear 3D finite element model for the ‘microscopic’ analysis of masonry structures, subjected to static and seismic loads, is presented in this study. The model presented considers masonry as a two-phase material, treating bricks and mortar joints separately, thus allowing for non-linear deformation characteristics and progressive local failure of both bricks and mortar joints. The influence of the mortar joints is taken into account by using ‘interface’ elements to simulate the timedependent sliding and separation along the interfaces. Analytical and experimental solutions available in the literature have been employed to verify the results obtained from the present finite element model, showing that it is capable of a high degree of accuracy. NOTATION [B] = Matrix of shape functions of interface element [H] = A transformation matrix [J] = The Jacobian matrix [K] = Element stiffness matrix in global coordinates [K / ] = Element stiffness matrix in local coordinates [M] = Mass matrix hi = Interpolation (or shape) function [k] = Element material property matrix ksx, ksy = Unit shear stiffness along the x and y directions knz = Unit normal stiffness along the z direction {qi} = Vector of nodal displacements {ui} = Vector of displacement components u, v, w = Displacement components parallel to x, y, z axes wi, wj = Weighting coefficients for Gaussian integration η, ξ = Natural coordinates of the interface element τ = Shear stress