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Within a 3D concrete printing process, the fresh concrete is aging due to hydration. One of the consequences from the purely mechanical point of view is that its constitutive relation must be defined in rate form. This restriction is taken into account in this contribution and, besides on the incremental elasticity, we moreover introduce the relaxation of the internal stresses in order to describe the creep at early age. On another hand, due to the soft nature of the material, the finite strain range is herein a priori assumed. Eventual structural instabilities during the printing process can therefore be predicted as well. On another hand, with regards to the incremental formulation of the boundary value problem, the kinematics must be adapted as well. We use for this the multiplicative decomposition of the actual deformation gradient into its known part at an earlier time and the relative deformation gradient with respect to the configuration at that time. Within a Lagrangian formulation, the incremental constitutive relations and evolution equations can then be ideally defined on the above mentioned intermediate configuration prior to be transported back to the reference configuration. In particular, the early age creep is here described through an internal variable approach the evolution of which is motivated by the generalized Maxwell model. In this work, this latter is adapted for incremental viscoelasticity. Model examples are proposed and the numerical efficiency of the proposed framework is illustrated through a set of representative simulations. [ABSTRACT FROM AUTHOR]

In this work, a consistent viscoplasticity formulation is derived from thermodynamical principles and employing the concept of continuum elastic corrector rate. The proposed model is developed based on the principle of maximum viscoplastic dissipation for determining the flow direction. The model uses both the equivalent viscoplastic strain and its rate as state variables. Power balance and energy balance give, respectively, separate evolution equations for the equivalent viscoplastic strain rate and the viscoplastic strain, the former written in terms of inviscid rates. Several key points distinguish our formulation from other proposals. First, the viscoplastic strain rate (instead of a yield function) consistently distinguishes conservative from dissipative behaviours during reverse loading; and the discrete implicit integration algorithm is an immediate discretization of the continuum theory based on the mentioned principles considered as separate equations. Second, the inviscid solution is recovered in a well-conditioned manner by simply setting the viscosity to zero. Indeed, inviscid plasticity, viscoelasticity and viscoplasticity are particular cases of our formulation and integration algorithm, and are recovered just by setting the corresponding parameters to zero (viscosity or yield stress). Third, the linear viscoplasticity solution is obtained in an exact manner for proportional loading cases, independently of the time step employed. Four, general nonlinear models (Perzyna, Norton, etc) may be immediately incorporated as particular cases both in the theory and the computational implementation. [ABSTRACT FROM AUTHOR]