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. 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 expertizes. 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 use a 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. The computations are used to calibrate the model parameters with the help of results from an experimental compaign where two kinds of concretes were studied; one with siliceous aggregates, and one with calcious aggregates. We show the efficiency of the developed numerical tool through a series of examples.