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

Abstract

AbstractModeling 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.