Overview
This research introduces a unified viscoelastic-viscoplastic continuum framework designed for modeling rate-dependent granular flows across various regimes. The framework integrates two distinct rate-dependent mechanisms: micro-inertia and viscoelastic dissipation, within a single continuum description. A core element of this model is an explicit relationship between the coefficient of restitution and a continuum viscosity. This relationship is derived through an analysis of wave attenuation in granular assemblies, thereby establishing a direct connection between particle-scale collision physics and macroscopic damping.
The constitutive model structured in this work partitions elastic and plastic responses. This partitioning, along with the corresponding stress-update routine, ensures that viscous dissipation governs wave propagation and collisional processes. It achieves this without altering the plastic flow rule, which retains inertia-dependent plastic flow governed by the classical $\mu(I)$ rheology.
Approach
The continuum granular flow model is constructed to integrate micro-inertia and viscoelastic dissipation. The derivation of the link between the coefficient of restitution and continuum viscosity is based on an analysis of wave attenuation within granular assemblies. This analytical step bridges the gap between particle-scale collisional behavior and the macroscopic damping observed in granular flows.
The framework's implementation utilizes the material point method. This numerical method was selected to simulate transient processes that involve large deformations, material separation, and subsequent reconsolidation events. The model's constitutive framework carefully separates elastic and plastic responses, allowing viscous dissipation to manage wave propagation and collisional activities without modifying the existing plastic flow rule, which relies on the $\mu(I)$ rheology.
Findings
The presented continuum framework successfully unifies viscoelastic and viscoplastic characteristics for modeling granular flows. A direct relationship was established between the coefficient of restitution and a continuum viscosity, linking particle-scale collisions to macroscopic damping through wave attenuation analysis.
The model's constitutive formulation partitions elastic and plastic responses, with viscous dissipation specifically governing wave propagation and collisional processes. This approach maintains the $\mu(I)$ rheology for inertia-dependent plastic flow.
Numerical examples, encompassing steady, transient, vibrational, and impact-driven flows, were used to demonstrate the model's capabilities. These simulations indicated that the model effectively captures wave propagation, diffusion, and rate-dependent granular behavior within a unified continuum setting.
Why This Matters
The development of a unified continuum framework that models rate-dependent granular flows across regimes, incorporating micro-inertia and viscoelastic dissipation, offers a comprehensive tool for understanding complex material behaviors. The explicit link between the coefficient of restitution and continuum viscosity provides a mechanistic understanding of how microscopic particle interactions scale up to macroscopic damping. The ability to simulate transient processes involving large deformations, material separation, and reconsolidation uniformly improves the predictive capabilities for various granular phenomena.
Potential Applications
The model's capacity to capture wave propagation, diffusion, and rate-dependent granular behavior within a unified continuum framework suggests potential utility in fields studying granular materials exhibiting varied flow dynamics. The implementation within the material point method, suitable for transient processes with large deformations and reconsolidation, indicates applicability where such complex material behaviors are critical.