The implementation of M-integral in cross-scale correlation analysis of porous materials

The damage analysis caused by mesoscopic pores has attracted much attention in the development and application of porous materials. In this study, a novel application of M-integral is presented to establish a cross-scale correlation analysis of damaged porous materials. The multiscale damage analysis featured here can be proposed in two main steps. In detail, the first step is to construct a quantitative relationship between M-integral and porosity, where the values of M-integral for different porosity are calculated numerically. Subsequently, it applies the variation of M-integral with the material damage represented by a decrease in effective elastic modulus, and a cross-scale correlation between porosity and effective elastic modulus of porous material can be provided. In addition, an example is discussed to illustrate the specific application of this bridging parameter M-integral. The results confirm that M-integral can be an effective parameter bridging mesoscopic porosity and macroscopic damage, and is expected benefit to propose a convenient damage model of porous material. The findings should be of value in investigating the multiscale damage analysis of porous materials.