Of interest in this paper is a modeling 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.

中文翻译：

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用于 3D 混凝土打印建模的几何非线性增量公式

本文感兴趣的是当本构关系以增量形式给出时的建模框架。对于因水合作用而老化的混凝土尤其如此。此外，考虑到 3D 混凝土打印的应用，由于新鲜材料的柔软性质，必须考虑几何非线性。然后必须充分调整运动学以获得理论上合理的公式。为此，这里选择乘法分割，将变形梯度分为较早时间的已知部分和相对变形梯度。从几何角度来看，这产生了一种中间配置，在将增量本构关系传输回拉格朗日公式的参考配置之前，可以在该配置上理想地定义增量本构关系。给出的模型示例用于演示目的，一组模拟说明了所提出框架的有效性。