Delayed Ettringite Formation (DEF) in concrete is likely to develop in massive civil engineering structures such as bridges, nuclear plants, and dams with major security issues. In many cases, DEF pathology can lead to swelling and cracking which may significantly impact mass transfer and mechanical properties. It is then of major importance to build predictive tools for engineering conceptions and expertises. In this contribution, the chemical swelling evolution is integrated within the overall constitutive law of concrete that, besides, can experience other phenomena such like damage, plasticity, and long term creep, not all considered here. On another hand, as DEF is activated by environmental humidity above a certain threshold, we introduce the notion of effective time that takes into account the cumulative exposition above this threshold. Hence, a special care is taken with regards to the chemical irreversibility, together with the humidity-drying cycles. Computations are used to calibrate various sets of model parameters with the help of results from the literature, on the one hand, and from an experimental campaign where a calcareous aggregates-based concrete is studied, on the other hand. We show the efficiency of the developed numerical tool through a series of numerical examples.