The Homogenization of a Masonry Unit Cell Using a Lattice Approach: Uniaxial Tension Case

Abstract

This study provides an explanation on how a lattice model is employed in homogenizing a heterogeneous anisotropic masonry unit cell made of brick, mortar and their interface using energy equivalence concepts. The direct tension test was only considered in this study. Other loading scenarios like shear and compression may also be included using the same approach. The purpose is to obtain a post-peak scalar damage parameter of a homogenized isotropic finite element from the fracture energy results of a lattice masonry unit cell. A 2-D plane strain lattice formulation was implemented to evaluate energy release rate values of the masonry unit cell. Different strength failure criteria were assigned to brick, mortar, and interface strength material properties that were mapped on top of the mechanical model of the lattice according to their geometric locations. An energy method was subsequently employed to obtain the energy release rate of the lattice mesh as the crack propagates which was obtained by the change in the global stiffness matrix of the lattice approach before and after of strut removal. It was assumed that the total strain energy released in the lattice masonry unit cell in direct tension as the crack propagates equals the total strain energy dissipated in the equivalent homogenized isotropic continuum finite element under the same loading. Since these dissipated energy values correspond to the crack propagation and the damage incurred in the masonry unit cell, a scalar damage parameter can be defined based on the dissipated strain energy and energy release rate values during the analysis. The homogenization technique may be regarded as a bridge between the micro-scale lattice analysis and macro-scale masonry wall.