A new idea of two-scale random field is presented by taking the mechanical behaviors of quasi-brittle materials as an example. In this way, the random fluctuation of material damage at the micro-meso-scale and the spatial correlation of mechanical properties at the macro-scale are both well described by the random distribution of fracture strain. Moreover, it is proved that by introducing a transform matrix, the mesoscopic random fields can be described by a two-scale random field. Based on this, a two-step numerical implementation of the two-scale random field is proposed, and the mechanical behaviors of quasi-brittle materials can be analyzed by incorporating the probability density evolution theory. Finally, an experimental example is presented to demonstrate the capability of the proposed model. Ideal agreements are achieved against the experimental results. Particularly, the randomness of material properties at both scales can be well reproduced.

以准脆性材料的力学行为为例，提出了二维随机场的新思路。这样，微观尺度上材料损伤的随机波动和宏观尺度上力学性能的空间相关性都可以通过断裂应变的随机分布来很好地描述。此外，证明了通过引入变换矩阵，细观随机场可以用二维随机场来描述。在此基础上，提出了两尺度随机场的两步数值实现方法，并结合概率密度演化理论对准脆性材料的力学行为进行了分析。最后，给出了一个实验例子来证明所提出模型的能力。根据实验结果实现了理想的协议。特别是，可以很好地再现两个尺度下材料属性的随机性。