arXiv subjects

Ken Kamrin

Publications and source records attributed to Ken Kamrin.

40 records · Page 3Linked to original sources

arXiv2009

An Eulerian approach to the simulation of deformable solids: Application to finite-strain elasticity

We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of large solid-like deformations, in any dimension, of the type that might otherwise require the finite element method. The generality of the method stems from its ability to easily compute kinematic quantities essential to solid mechanics, that are elusive outside of Lagrangian frame. This introductory work focuses on large-strain, hyperelastic materials. After a brief review of hyperelasticity, a discretization of the method is presented and some non-trivial elastic deformations are simulated, both static and dynamic. The method's accuracy is directly verified against known analytical solutions.

cond-mat.soft↗

arXiv2009

Nonlinear elasto-plastic model for dense granular flow

This work proposes a model for granular deformation that predicts the stress and velocity profiles in well-developed dense granular flows. Recent models for granular elasticity (Jiang and Liu 2003) and rate-sensitive plastic flow (Jop et al. 2006) are reformulated and combined into one universal granular continuum law, capable of predicting flowing regions and stagnant zones simultaneously in any arbitrary 3D flow geometry. The unification is performed by justifying and implementing a Kroner-Lee elasto-plastic decomposition, with care taken to ensure certain continuum physical principles are necessarily upheld. The model is then numerically implemented in multiple geometries and results are compared to experiments and discrete simulations.

cond-mat.soft↗

arXiv2006

The stochastic flow rule: A multi-scale model for granular plasticity

In spite of many attempts to model dense granular flow, there is still no general theory capable of describing different types of flows, such as gravity-driven drainage in silos and wall-driven shear flows in Couette cells. Here, we summarize our recent proposal of the Stochastic Flow Rule (SFR), which is able to describe these cases in good agreement with experiments, and we focus on testing the theory in more detail against brute-force simulations with the discrete-element method (DEM). The SFR is a general rate-independent constitutive law for plastic flow, based on diffusing spots of fluidization. In the case of quasi-2D granular materials, we assume limit-state stresses from Mohr-Coulomb plasticity and postulate that spots undergo biased random walks along slip-lines, driven by local stress imbalances. We compare analytical predictions of the SFR against DEM simulations for silos and Couette cells, carrying out several parametric studies in the latter case, and find good agreement.

cond-mat.soft↗

arXiv2006

A stochastic flow rule for granular materials

There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-2D granular materials to calculate (average) stresses and slip planes, but we propose a "stochastic flow rule" (SFR) to replace the principle of coaxiality in classical plasticity. The SFR takes into account two crucial features of granular materials - discreteness and randomness - via diffusing "spots" of local fluidization, which act as carriers of plasticity. We postulate that spots perform random walks biased along slip-lines with a drift direction determined by the stress imbalance upon a local switch from static to dynamic friction. In the continuum limit (based on a Fokker-Planck equation for the spot concentration), this simple model is able to predict a variety of granular flow profiles in flat-bottom silos, annular Couette cells, flowing heaps, and plate-dragging experiments -- with essentially no fitting parameters -- although it is only expected to function where material is at incipient failure and slip-lines are inadmissible. For special cases of admissible slip-lines, such as plate dragging under a heavy load or flow down an inclined plane, we postulate a transition to rate-dependent Bagnold rheology, where flow occurs by sliding shear planes. With different yield criteria, the SFR provides a general framework for multiscale modeling of plasticity in amorphous materials, cycling between continuum limit-state stress calculations, meso-scale spot random walks, and microscopic particle relaxation.

cond-mat.soft↗