A homogeneous constitutive model for masonry

Masonry has been a broadly used material since the beginning of human life. Despite its popularity, the analysis of masonry structures is a complex task due to the heterogeneity and the non-linear material behaviour. The need for reliable analysis procedures capable of predicting damage evolution and failure in historical structures in order to design e$cient repair and maintenance has motivated the work of many structural analysts in this "eld. Here the "nite element method has emerged as one of the most powerful procedures for linear and non-linear analysis of masonry structures. The main problem pending is the development of accurate and e$cient constitutive models capable of predicting the behaviour of masonry in the non-linear range and this has been the motivation of this work. The constitutive model presented is based on the homogenized anisotropic elastoplasticity previously developed by the authors. The e!ect of anisotropy is introduced by means of "ctitious isotropic stress and strain spaces. The material properties in the "ctitious isotropic spaces are mapped into the actual anisotropic space by means of a consistent fourth-order tensor. The advantage of the model is that the classical theory of plasticity can be used to model the non-linear behaviour in the isotropic spaces. Details of the model for masonry structures and its implementation in a general non-linear "nite element code are given. Examples of application to the analysis of some masonry structures are presented, showing the e$ciency of the model