Of interest in this paper is a modelling framework when constitutive relations are given in incremental form. This is particularly true for aging concretes due to hydration. Furthermore, having in mind applications to 3D concrete printing, geometrical nonlinearities must be accounted for due to the soft nature of the fresh material. The kinematics must then be adapted adequately for a theoretically sound formulation. For this, the multiplicative split is chosen here for the deformation gradient into its known part at an earlier time and the relative deformation gradient. From the geometric point of view, this gives rise to an intermediate configuration on which incremental constitutive relations can be ideally defined prior to be transported back to the reference configuration for a Lagrangian formulation. Model examples are given for the purpose of demonstration and a set of simulations illustrate the effectiveness of the proposed framework.