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

Abstract

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.

Quasi‐static confined uniaxial compaction of granular alumina and boron carbide observing the particle size effects

“…In this paper, we explored the mechanical response of alumina and boron carbide powder for better understanding the effects of particle size and shape on the uniaxial compaction response under quasi‐static strain rates. In the literature, there exists only limited studies on the behavior of granular ceramics, with many authors noting this shortcoming . Few studies have accounted for particle size effects .…”

“…Classical failure models often do not account for grain size but rather only account for strength to void ratios . Recently, a study by Cil et al noted the importance of incorporating relative density, porosity, particle size distribution, and particle breakage into constitutive modeling of brittle granular materials. The micromechanical model in Cil et al is referred to as a breakage model, and it initially was developed for soil mechanics .…”

“…Recently, a study by Cil et al noted the importance of incorporating relative density, porosity, particle size distribution, and particle breakage into constitutive modeling of brittle granular materials. The micromechanical model in Cil et al is referred to as a breakage model, and it initially was developed for soil mechanics . The breakage term, described by Equation , represents as an internal state variable in a computational modeling framework that accounts for how the particle sizes evolve and become smaller during loading.…”

“…The breakage term, described by Equation , represents as an internal state variable in a computational modeling framework that accounts for how the particle sizes evolve and become smaller during loading. The breakage model is calculated as given by Cil et al:…”

“…In the literature, there exists only limited studies on the behavior of granular ceramics, 19,21,33,[39][40][41] with many authors noting this shortcoming. 42,43 Few studies have accounted for particle size effects. 44,45 To address the gap in understanding granular ceramic behavior, this study focused on the mechanical response (eg, hydrostatic pressure, bulk | 2205 NICEWICZ Et al.…”