A rotating smeared crack approach in Sequentially Linear Analysis using the Elastic-brittle fraction model

Sequentially Linear Analysis (SLA), an event-by-event solution strategy in which a sequence of scaled linear analyses with decreasing secant stiffness is performed, representing local damage increments; is a robust alternative to nonlinear finite element analysis of quasi-brittle structures. Since it is based on a fixed smeared crack constitutive model, severe spurious stresses and inaccuracies may develop due to misalignment of the crack with the principal stress directions. To this end, the elastic-brittle fraction model was conceived. The model separates the continuum into several parallel fractions or layers, each with different properties, chosen in order to represent the overall constitutive softening behaviour as accurately as possible. The main idea is to mimick a rotating crack by a superposition of fractions, each with a fixed crack direction. In this article, the model is presented for both the 2-dimensional and 3-dimensional frameworks, with a general transition from any saw-tooth law to fraction material properties. The fraction models are then validated and compared against the fixed crack model with SLA: using single element and structural case studies. It is shown that the fraction model is able to mimick the rotating crack model, that it leads to lesser spurious cracks and narrower localisation bands, and in turn results in a more flexible post-peak response over all case studies compared to the fixed crack model.