Two-scale random field model for quasi-brittle materials. (October 2021) - Li, Jie; Hai, Lu; Xu, Taozhi
Abstract: 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. Highlights: A new idea of two-scale random field for the stochastic analysis of engineering structures is proposed. A two-step numerical implementation is introduced for the sample realizations of two-scale random field. The random fluctuation in the micro-mesoscopic levels and spatial correlation of nonlinear mechanical behaviors of materials are incorporated within a unified framework.