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Complex grain-boundary structures, such as the 1-2 nm thick intergranular glassy films (IGF), play a prominent role in the failure behavior of nano-phased ceramics. The IGF plays the role of an imperfection and serves as the location of strain localization and failure. We have recently performed “theoretical” mechanical loading experiments on very large atomic models of IGF in silicon nitride using ab initio simulation to obtain their failure behavior. The ab initio simulations yield characteristic post-peak softening accompanied by strain localization zone. In this paper a micro-structural granular mechanics based higher-order continuum theory is applied to model the failure behavior of these types of material systems. The results obtained from the ab initio simulations are compared with those predicted by the higher order continuum theory.

International audience; Gradient theories have found wide applications in modeling of strain softening phenomena. This paper presents a higher order stress-strain theory to describe the damage behavior of strain softening materials. In contrast to most conventional gradient approaches for damage modeling, the present higher order theory considers strain gradients and their conjugate higher-order stress such that stable numerical solutions may be achieved. We have described the derivation of the required constitutive relationships, the governing equations and its weak form for this higher-order theory. The constitutive coefficients were obtained from a granular media approach such that the internal length scale parameter reflects the natural granularity of the underlying microstructure. The weak form was discretized using an element-free Galerkin (EFG) formulation that readily admits approximation functions of higher-order continuity. We have also discussed the implementation of essential boundary conditions and linearization of the derived discrete equations. Finally, the applicability of the derived model is demonstrated through two examples with different imperfections designed to initiate dislocation bands and shear bands, respectively.