Abstract
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.
Highlights
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
The fundamental idea behind the developed approach presented in this paper is that it is possible to assess the cohesive-strength behaviour of composite materials at different scale levels
The novelty of the present model is the incorporation of the two-phase nonlinear relationship of cohesive-strength composites based on a linear comparison composite (LCC) approach
Summary
The macroscopic strain rate energy density Πhom for the upper bound solution can be found by employing the generated expression of the strain rate energy function in Eq (6) and nonlinearity function Eq (8). Consider a two-phase composite material with perfect adherence between interface at Level II as shown, the first phase and second phase are cohesive frictional porous inclusion and matrix, respectively. The mesoscopic cohesive-strength yield criterion of a two-phase composite material formed by pores (voids) and solid frictional matrix phase is established. By substituting the limits, α2 → 0, c2 → 0, rg → 0, f2 → 0, and f1 → η in Eq 13, the cohesive-strength yield criterion of porous solid becomes: Materials Cement Fly ash Slag Silica fume Coarse Aggregate
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