Evolutionary analysis of the fracturing process in masonry arches: application of the cohesive crack model.

In the present contribution, the cohesive crack model was applied to the masonry arches. The model used is an elasto-plastic model able to coherently describe the behaviour of materials as it uses a couple of constitutive laws: •??A tension - strain relationship, which describes the elastic and hardening behaviour of the integral material up to the ultimate tension u; •??A tension - opening of the slot relationship, which describes the "softening" behaviour of the cracked material, up to the critical opening wc, in addition to which the interaction between the slit faces is annulated. In the '80s an algorithm of calculation was developed, it was called "Frana", allowing it to apply the model of the cohesive crack to beam segments, simply supported, subject to simple bending moment. In the present work, the above mentioned algorithm has been translated into Matlab’s language, after which it has been passed to adapt this model to the case of masonry arches. They may be considered as structures subject to off-centered compression. To do this I used the theory of prestressing structures. In fact, the first part of the constitutive law which describes the "softening" behaviour of the cracked material, has been translated in such a way that the tensile stresses due to the flexion were applied to a structure subjected to simple compression. The compression tension was considered equal to the compression tension produced in each section for the "arch’s effect". The disordered and fragile materials such as concrete, rocks, ceramics and masonry contain a large number of defects and micro-cracks. By subjecting them to high tensile stresses, an interaction occurs between the growth processes of the micro-cracks which causes the localization of the deformation in a very narrow band, where the dissipation of energy occurs, while the material, outside this band, involves elastic and linear. According to the concepts of the continuous mechanics, it can be said that in this band (called the process zone), a reduction in load-bearing capacity occurs as a consequence of an increase in inelastic strain. This phenomenon is called a negative incrimination. The classical theory of plasticity is not applicable because the stability postulate of Drucker is violated. The consequences of this violation, even in the absence of geometrically unstable effects, are: •??possibility to have loss of stability in the crack opening control (snap-back); •??possibility to have loss of stability in displacement control (snap-through); The algorithm developed identifies the section of the arch most stressed, in terms of tensile stress, that is, it identifies the section in which the crack will be created. At this point identify the load necessary for the crack to be born. In the following phases it identifies the load necessary for the increase to the crack. The iteration ends when the height of the crack has reached to 90 percent of the total height of the section. At the same time, the algorithm performs a crushing check, that is, it evaluates, in the same section, if the maximum compression tension reaches to resistance of the material.