Micromechanical model for viscoelastic materials undergoing damage

We have derived a stress–strain relationship for viscoelastic materials undergoing damage using a granular micromechanics approach. This approach assumes the material to possess a granular meso-structure such that the material is treated as a discrete or a particulate system. By considering the particle kinematics in terms of Taylor series expansion, a continuum model of the discrete system is obtained. The material rate-dependence and damage are modeled by assuming appropriate inter-granular force–displacement relationships that satisfy thermodynamic constraints. The advantage of this micromechanical approach is that the resultant continuum model retains the discrete nature by incorporating the effect of nearest neighbor grain interactions through the inter-granular force–displacement relationship and orientation vector. As a result, the derived model has the ability to predict a number of material phenomena, such as loading-induced anisotropy, dilation or pressure sensitivity, and secondary creep, which often manifest due to material granularity.