A rate-dependent constitutive model for brittle granular materials based on breakage mechanics

Modeling the rate-dependent mechanical behavior of brittle granular materials is of interest to defense applications, civil and mining engineering, geology, and geophysics. In particular, granulated ceramics in armor systems play a significant role in the overall dynamic material response of ceramics, particularly in their penetration resistance. This paper presents a rate-dependent constitutive model for brittle granular materials based on a recent reformulation of breakage mechanics theory. The rate-dependency is introduced via the overstress theory of viscoplasticity. The proposed formulation incorporates the effects of relative density and particle grading on strength and porous compaction/dilation, and is capable of tracking their evolution. The model is devised with internal variables linked to underlying dissipative micromechanisms including configurational reorganization, particle breakage and frictional dissipation. A strategy for calibrating model parameters and required experiments are described. The impact of loading rate on shear strength and grading evolution are explored through a sensitivity analysis. The presented model is capable of capturing several key features of the experimentally observed behavior of brittle granular materials including stress-, rate- and density-dependent stress-strain and volume change responses, the competition between dilation and breakage-induced compaction, the evolving particle grading due to particle breakage, and the evolution toward a critical (steady) state under shearing. A possible application of this micromechanics-inspired modeling framework involves integrating it into rate-dependent models for ceramics to assist in improving the impact performance of next-generation ceramics.