During a 3D concrete printing process, the mechanical charactesitics of the material at hand are continuously evolving due to hydration. From the theoretical point of view, the constitutive relations must be defined in rate form. We think that this restriction is mandatory and must be taken into account. On another hand, to predict eventual instabilities, the finite strain range is a priori assumed within the formulation where the kinematics must be adapted in adequacy. Here use is made of a multiplicative decomposition of the actual deformation gradient into its known intermediate part at an earlier time and the relative deformation gradient with respect to the configuration at that time. The incremental constitutive relations and evolution equations can then be ideally defined on the above intermediate configuration prior to be transported back to the reference configuration within a Lagrangian formulation. The early age creep is here introduced through an internal variable approach that is motivated by the generalized Maxwell model. A set of finite element simulations is performed to illustrate the efficiency of the proposed framework. In particular, a slump-test-like example is given where a method can be highlighted to help identifying, in future works, the material parameters relative to the early-age creep.