Cohesive-strength homogenisation model of porous and non-porous materials using linear comparison composites and application

An estimation of the strength of composite materials with different strength behaviours of the matrix and inclusion is of great interest in science and engineering disciplines. Linear comparison composite (LCC) is an approach introduced for estimating the macroscopic strength of matrix-inclusion composites. The LCC approach has however not been expanded to model non-porous composites. Therefore, this paper is to fill this gap by developing a cohesive-strength method for modelling frictional composite materials, which can be porous and non-porous, using the LCC approach. The developed cohesive-strength homogenisation model represents the matrix and inclusion as a two-phase composite containing solids and pores. The model is then implemented in a multiscaling model in which porous cohesive-frictional solids intermix with each other at different scale levels classified as micro, meso and macro. The developed model satisfies an upscaling scheme and is suitable for investigating the effects of the microstructure, the composition, and the interface condition of the materials at micro scales on the macroscopic strength of the composites. To further demonstrate the application of the developed cohesive-strength homogenisation model, the cohesive-strength properties of very high strength concrete are determined using instrumented indentation, nonlinear limit analysis and second-order cone programming to obtain material properties at different scale levels.