Cohesive-strength homogenisation model of porous and non-porous materials using linear comparison composites and application
Hyuk Lee, Vanissorn Vimonsatit, Wai Yeong Huen, Priyan Mendis & Kasun Shanaka Kristombu Baduge
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.
Introduction
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 properties1,2,3,4,5. 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 disciplines6,7. 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 materials3,4,6,7,8,9. 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) approach6,7. 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 microstructure9. Furthermore, a general type of second-order LCC has been introduced by Castaneda6,7. The LCC approach has however not been expanded for modelling non-porous composite materials. Therefore, this work is to develop a cohesive-strength method for modelling frictional composite materials, which are porous and non-porous, based on the LCC approach. The developed cohesive-strength homogenisation model is then implemented in a multiscaling scheme which is extended from existing formulation to investigate the effects of the material’s microstructure, composition, and interface condition, on the macroscopic strength. A multiscaling approach satisfies an upscaling scheme (micro to macro) in which porous cohesive-frictional solids intermix with each other.
The rest of the paper is organised as follows: Section 2 describes the cohesive-strength homogenisation model based on a second-order homogenisation and LCC approach. Section 3 proposes the concept of a multiscale-link approach for determining properties of materials at micro, meso and macro scales. Section 4 demonstrates the application of the proposed approach on very high strength concrete to investigate the cohesive-strength properties at different scales.
