Mass transport phenomenon in concrete structures is strongly coupled with their mechanical behavior. The first coupling fabric is the Biot’s theory according to which fluid pressure interacts with solid stress state and volumetric deformation rate of the solid induces changes in fluid pressure. Another coupling mechanism emerges with cracks which serve as channels for the fluid to flow through them and provide volume for fluid storage. Especially the second coupling mechanism presents a challenge for numerical modeling as it requires detailed knowledge about cracking process. Discrete mesoscale mechanical models coupled with mass transport offer simple and robust way to solve the problem. On the other hand, however, they are computationally demanding.

In order to reduce this computational burden, the present paper applies the asymptotic expansion homogenization technique to the coupled problem to deliver (i) continuous and homogeneous description of the macroscopic problem which can be easily solved by the finite element method, (ii) discrete and heterogeneous mesoscale problem in the periodic setup attached to each integration point of the macroscale along with (iii) equations providing communication between these two scales. The transient terms appear at the macroscale only, as well as the Biot’s coupling terms. The coupling through cracking is treated at the mesoscale by changing conductivity of the conduit elements according to the mechanical solution, otherwise the two mesoscale steady state problems are decoupled and can be therefore solved in a sequence. This paper presents verification studies showing performance of the homogenized solution. Further improvement is achieved by pre-computing the initial linear mesoscale solution and adaptively replacing it by the full nonlinear one only at integration points that fulfill Ottosen’s stress-based criterion indicating deviation from linearity.

混凝土结构中的质量传递现象与其力学行为密切相关。第一个耦合结构是Biot理论，根据该理论，流体压力与固体应力状态相互作用，固体的体积变形率引起流体压力的变化。另一种耦合机制出现裂缝，裂缝作为流体流过它们的通道并为流体储存提供体积。特别是第二种耦合机制对数值建模提出了挑战，因为它需要详细了解开裂过程。离散的中尺度力学模型与质量传输相结合，为解决该问题提供了简单而可靠的方法。然而，另一方面，它们对计算的要求很高。

为了减少这种计算负担，本文将渐近展开均匀化技术应用于耦合问题，以提供（i）可以通过有限元方法轻松解决的宏观问题的连续和均匀描述，（ii）离散和附加到宏观尺度的每个积分点的周期性设置中的异构中尺度问题以及（iii）提供这两个尺度之间通信的方程。瞬态项仅出现在宏观尺度，以及 Biot 的耦合项。根据力学解，通过改变管道元件的电导率在中尺度上处理通过开裂的耦合，否则两个中尺度稳态问题被解耦，因此可以顺序求解。本文介绍了验证研究，显示了均质溶液的性能。通过预先计算初始线性中尺度解并仅在满足 Ottosen 的基于应力的指示偏离线性的标准的积分点处将其自适应地替换为完全非线性解，可以实现进一步的改进。