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.

在 3D 混凝土打印过程中，新拌混凝土会因水合作用而老化。从纯机械的观点来看，其结果之一是它的本构关系必须以比率形式定义。在这个贡献中考虑了这个限制，除了增量弹性之外，我们还引入了内部应力的松弛，以描述早期的蠕变。另一方面，由于材料的软性质，有限应变范围在此是先验假设的。因此也可以预测打印过程中最终的结构不稳定性。另一方面，对于边值问题的增量公式，运动学也必须进行调整。为此，我们将实际变形梯度乘法分解为早期已知部分以及相对于当时配置的相对变形梯度。在拉格朗日公式中，增量本构关系和演化方程可以在上述中间配置上理想地定义，然后再传输回参考配置。特别是，这里通过内部变量方法来描述早期的蠕变，该方法的演变是由广义麦克斯韦模型驱动的。在这项工作中，后者适用于增量粘弹性。提出了模型示例，并通过一组具有代表性的模拟说明了所提出框架的数值效率。