An implicit/explicit integration scheme for non-linear constitutive models is presented. It aims at providing additional computability to those solid mechanics problems were robustness is an important issue, i.e. material failure models equipped with strain softening, soft materials, contact-friction models, etc., although it can also provide important advantages, in terms of computational cost, with respect to purely implicit integration schemes. The proposed scheme is presented based on general families of constitutive models (continuum damage and elasto-plasticity) and its properties, in terms of robustness and accuracy, are analytically derived and computationally assessed by means of numerical simulations. An adaptive time stepping algorithm, based on a priori control of the committed error and the application of the proposed scheme to contact/friction interfaces are also presented.