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 secondorder cone programming to obtain material properties at different scale levels.Development of composite materials is on-going to meet the demand for high standard of performance and in-service reliability. It has been pointed out that one of the most important factors that controls the elastic and plastic fields of composite materials is their local properties 1-5 . An estimation of the effective mechanical properties of composite materials based on microstructural properties and a suitable homogenisation model is of great interest in science and engineering disciplines 6,7 . Several homogenisation models have been developed based on continuum micromechanics which have enabled predicting macroscopic strength criteria for composite materials from considering the strength behaviour of the materials 3,4,6-9 . In the field of strength homogenisation, Dormieux et al. 8 have extended the model with cohesive strength attributes. They have derived the strength domain of the materials in a form of cohesive-frictional solids with porosity. Furthermore, Ortega et al. 9 introduced the strength domain for cohesive-frictional composite materials with porosity based on an application of a linear comparison composite (LCC) approach 6,7 . LCC is a homogenisation model of heterogeneous composites. The basic principle of LCC approach is to evaluate the plastic dissipation potential of nonlinear composites for selected linear comparison composites with a similar underlying microstructure 9 . Furthermore, a general type of second-order LCC has been introduced by Castaneda 6,7 . The LCC approach has however not been expanded for modelling non-porous composite materials. ...