We propose and numerically implement a constitutive framework for granular media that allows the material to traverse through its many common phases during the flow process. When dense, the material is treated as a pressure sensitive elasto-viscoplastic solid obeying a yield criterion and a plastic flow rule given by the µ(I) inertial rheology of granular materials. When the free volume exceeds a critical level, the material is deemed to separate and is treated as disconnected, stress-free media. A Material Point Method (MPM) procedure is written for the simulation of this model and many demonstrations are provided in different geometries. By using the MPM framework, extremely large strains and nonlinear deformations, which are common in granular flows, are representable. The method is verified numerically and its physical predictions are validated against known results. BackgroundGranular materials present several modeling challenges when considering a continuum approach. During dense flow, the material can be characterized as an elasto-viscoplastic material with a frictional yield criterion. Extremely high levels of strain often occur, which challenge certain computational techniques, but the material can also behave as a solid, able to support shear loads in a static configuration. Moreover, because dry grains do not support tension, their constitutive behavior changes from that of a dense plastic media to a gas-like disconnected state during extension, a dramatic switch that is difficult to represent in a unified modeling and numerical framework.Several approaches have been used to simulate granular flow. One of the most accurate methods is the discrete element method (DEM), first described in Cundall & Strack (1979). While accurate, DEM solves the classical equations of motion on each grain individually, resulting in untenable computational expense over the large physical domains in many industrial and geological applications. A recent set of continuum rheological models for granular flow, such as the µ(I) relation in da Cruz et al. (2005) (later extended to 3D in Jop et al. (2006)) and the nonlocal extension in Kamrin & Koval (2012), offer a number of improvements over the commonly used rate-independent Drucker-Prager and Mohr-Coulomb models for problems with zones of dense, rapid flow (as is common in industrial settings) where rate-sensitivity is more pronounced and particle size-effects can play a role. The incompressible Navier-Stokes solver Gerris has been used in Staron et al. (2012) and Staron et al. (2014) with the µ(I) relation, while the commercial finite-element software Abaqus was used in Kamrin (2010) and appended with the nonlocal model in Henann & Kamrin (2013). While both methods can yield good results in certain regimes, the fluid solvers have difficulties with extensional disconnection and truly static zones cannot be represented, while the finite-element method (FEM) has issues when mesh distortion becomes large. Fixes such as Arbitrary-Lagrangian Eulerian (ALE) re-meshing may cause los...
We study the wave propagation in a curved chain of spherical particles constrained by elastic guides under the axial impact of a falling mass. We characterize the force transmission properties of the chain by varying the striker's mass and the chain's curvature. Experimental tests demonstrate amplitude-dependent attenuation of compressive waves propagating through the curved chain. In particular, we observe that the curved systems present an improved transmission of small dynamic disturbances relative to that of strong excitations, resulting from the close interplay between the granular particles and the softer elastic medium. We also find that the transmission of the compressive waves through the chains is dependent on the initial curvature imposed to the system. Numerical simulations, based on an approach that combines discrete element and finite element methods, corroborate the experimental results. The findings suggest that hybrid structures composed of granular particles and linear elastic media can be employed as new passive acoustic filtering materials that selectively transmit or mitigate excitations in a desired range of pressure amplitudes.
Domain swapping in proteins is an important mechanism of functional and structural innovation. However, despite its ubiquity and importance, the physical mechanisms that lead to domain swapping are poorly understood. Here, we present a simple two-dimensional coarse-grained model of protein domain swapping in the cytoplasm. In our model, two-domain proteins partially unfold and diffuse in continuous space. Monte Carlo multiprotein simulations of the model reveal that domain swapping occurs at intermediate temperatures, whereas folded dimers and folded monomers prevail at low temperatures, and partially unfolded monomers predominate at high temperatures. We use a simplified amino acid alphabet consisting of four residue types, and find that the oligomeric state at a given temperature depends on the sequence of the protein. We also show that hinge strain between domains can promote domain swapping, consistent with experimental observations for real proteins. Domain swapping depends nonmonotonically on the protein concentration, with domain-swapped dimers occurring at intermediate concentrations and nonspecific interactions between partially unfolded proteins occurring at high concentrations. For folded proteins, we recover the result obtained in three-dimensional lattice simulations, i.e., that functional dimerization is most prevalent at intermediate temperatures and nonspecific interactions increase at low temperatures.
Granular flow in a silo demonstrates multiple non-local rheological phenomena due to the finite size of grains. We solve the non-local granular fluidity continuum model in quasi-two-dimensional silo geometries and evaluate its ability to predict these non-local effects, including flow spreading and, importantly, clogging (arrest) when the opening is small enough. The model is augmented to include a free-separation criterion and is implemented numerically with an extension of the trans-phase granular flow solver described in Dunatunga & Kamrin (J. Fluid Mech., vol. 779, 2015, pp. 483–513), to produce full-field solutions. The implementation is validated against analytical results of the model in the inclined chute geometry, such as the solution for the critical thickness for flow arrest, and the velocity profile as a function of layer height. We then implement the model in the silo geometry and vary the apparent grain size. The model predicts a clogging criterion when the opening competes with the scale of the mean grain size, which agrees with previous experimental studies. For larger openings, the flow within the silo obtains a diffusive characteristic whose spread depends on the model's non-local amplitude and the mean grain size. The numerical tests are controlled for grid effects and a comparison study of coarse vs refined numerical simulations shows agreement in the pressure field, the shape of the arch in a clogged silo configuration and the velocity field in a flowing configuration.
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