Continuum Model for In-Plane Anisotropic Inelastic Behavior of Masonry

The paper addresses the problem of describing the anisotropic damage process and the dissipative behavior of masonry structures under static incremental and dynamic loads. A homogenized continuum model, based on simplified micromechanical hypotheses, is presented. The plane stress is considered. The finite-element method is adopted as a framework for numerical implementation. Masonry is considered as a composite material made up of blocks, mortar bed joints, and mortar head joints. Mortar bed joints are schematized as interfaces characterized by cohesion, tensile strength and friction, whereas mortar head joints are considered as geometrical discontinuities. Internal symmetries of the material leads to distinguishing two couples of emisymmetric bed joints, characterized by equal state variables. The computation of the displacement jumps in these two couples of joints is sufficient to evaluate the displacement jumps of all the joints contained in the assumed unit cell. Constitutive equations consider the nonlinear stress–strain relation in terms of mean stresses and mean strains. The latter are produced by an elastic strain contribution and by different inelastic strain contributions depending on the damage in mortar joints and in blocks. The damage processes are described by means of an energetic approach. The hysteretic behavior is described by considering a Coulomb-type friction law on the mortar bed joints. The model is implemented in a general purpose finite-element code (ANSYS). A simple example of a cyclic load history is presented in order to demonstrate the effectiveness of the model.