Micromechanical modelling of elastic continuum with virtual multi-dimensional internal bonds

A micromechanical model is developed for the elastic continua with virtual multi-dimensional internal bonds. The basic idea of the presented model is that materials are discretized into mass particles and these mass particles are connected with randomized normal and shear bonds. Based on the Cauchy-born rules and the hyperelastic theory, a constitutive relationship is derived. The constitutive relationship bridges the virtual bond stiffness and the macromaterial constants, i.e. Young’s modulus and Poisson ratio. The presented model could represent the diversity of Poisson ratio. The motivation of the presented work is to provide a useful micromechanical model for the numerical simulation of material failure behaviours and improve the understanding of material failure mechanisms. To show the application of the presented model, a tensile failure example of brittle materials is analysed and numerically simulated. By comparison, a good agreement is found between the predicted and the experimental. The prospect of the presented model seems to be highly promising