ABSTRACT
With the rapid advancements in experimental techniques and the growth in the amount of available data, especially when using digital image correlation and tomography, modelling is facing the challenge of transforming this enormous amount of knowledge into analytical equations that govern the material response. Classical constitutive equations may struggle to capture complex material responses, which is among the reasons why data driven approaches emerged. In this study, we apply a data-driven scheme to the modelling of failure of a quasi-brittle material such as concrete and discuss the difficulties induced when modelling localized failure. For the sake of simplicity, we consider a one-dimensional problem. Synthetic data sets are generated from a bi-linear damage model and exhibit strain softening. As expected, the one-dimensional example of a bar subjected to tension demonstrates that the obtained solutions are sensitive to the finite element discretization. A localization limiter is needed and the implementation of a non-local (integral) model circumvents the difficulty. There is, however, a notable observation in this case: optimal sets of strain, stress, and non-local history variable lie consistently outside the data set and do not converge within the data set upon mesh refinement. Several possibilities for solving this problem are considered, from the enlargement of the data set with non-local effects to the introduction of an additional constraint e.g., following the Lip-field approach. The latter method preserves locality of the constitutive response and it is found to be very easy to implement.
