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Using the classical catenary as a motivating example, we use slender-body theory to derive a general theory for thin filaments of arbitrary rheology undergoing large combined stretching and bending, which correctly accounts for the nonlinear geometry of deformation and uses integrated state variables to properly represent the complete deformation state. We test the theory for soft catenaries made of a Maxwell fluid and an elastic yield-stress fluid using a combination of asymptotic and numerical analyses to analyse the dynamics of transient sagging and arrest. We validate our results against three-dimensional finite element simulations of drooping catenaries, and show that our minimal models are easier and faster to solve, can capture all the salient behaviours of the full three-dimensional solution, and provide physical insights into the basic mechanisms involved. [ABSTRACT FROM PUBLISHER]

This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer equation, effectively capturing flows in both non-porous and porous domains. In contrast to the conventional Eulerian computational fluid dynamics (CFD) solver, which solves the velocity and pressure fields as unknown variables, the proposed method employs a monolithic displacement-pressure formulation adopted from the mixed-form updated-Lagrangian finite element method (FEM). To satisfy the discrete inf-sup stability condition, a stabilization strategy based on the variational multiscale method (VMS) is derived and integrated into the proposed formulation. Another distinctive feature is the implementation of blurred interfaces, which facilitate a seamless and stable transition of flows between free and porous domains, as well as across two distinct porous media. The efficacy of the proposed formulation is verified and validated through several benchmark cases in 1D, 2D, and 3D scenarios. Conducted numerical examples demonstrate enhanced accuracy and stability compared to analytical, experimental, and other numerical solutions. • The coupled Navier-Stokes/Darcy-Brinkman-Forchheimer flow is consistently derived, resulting in a unified formulation. • The derived formulation is implemented in the updated Lagrangian mixed MPM framework. • The VMS method is adopted to the formulation to satisfy the inf-sup condition. • The blurred interface approach is employed for a smooth and stable transition of free surface to porous flow. • A verification suite is developed in 1D, 2D, and 3D to verify and validate accuracy, stability, and efficiency. [ABSTRACT FROM AUTHOR]

Based on discrete element method simulations, we propose a new form of the constitutive equation for granular flows independent of packing fraction. Rescaling the stress ratio µ by a power of dimensionless temperature T makes the data from a wide set of flow geometries collapse to a master curve depending only on the inertial number I. The basic power-law structure appears robust to varying particle properties (e.g., surface friction) in both 2D and 3D systems. We show how this rheology fits and extends frameworks such as kinetic theory and the nonlocal granular fluidity model. [ABSTRACT FROM AUTHOR]

A recent granular rheology based on an implicit "granular fluidity" field has been shown to quantitatively predict many nonlocal phenomena. However, the physical nature of the field has not been identified. Here, the granular fluidity is found to be a kinematic variable given by the velocity fluctuation and packing fraction. This is verified with many discrete element simulations, which show that the operational fluidity definition, solutions of the fluidity model, and the proposed microscopic formula all agree. Kinetic theoretical and Eyring-like explanations shed insight into the obtained form. [ABSTRACT FROM AUTHOR]

This paper proposes novel and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). To address the modeling of Newtonian fluids with incompressibility constraints, a new mixed implicit MPM formulation is proposed. Here, instead of solving the velocity and pressure fields as the unknown variables like the typical Eulerian computational fluid dynamics (CFD) solver, the proposed approach adopts a monolithic displacement–pressure formulation inspired by the mixed-form updated-Lagrangian Finite Element Method (FEM). To satisfy the inf–sup stability condition, two stabilization strategies are integrated into the formulation: the variational multiscale method (VMS) and the pressure-stabilization Petrov–Galerkin method (PSPG). By concurrently solving the displacement and pressure fields, the developed monolithic solver obviates the need for free-surface detection as well as Dirichlet and Neumann pressure imposition, in contrast to the fractional-step method. This attribute mitigates spurious pressure and velocity oscillations in simulating dynamic and transient flow problems. This study also addresses other prevalent challenges in MPM simulations, such as the pressure oscillations triggered by cell-crossing errors, particle-distribution-induced quadrature errors, and particle-grid information transfer. To resolve these issues, the quadratic B-Spline basis function, the delta-correction method, and the Taylor particle-in-cell method are incorporated into the proposed mixed MPM formulation, thereby enhancing numerical stability. The efficacy of the proposed stabilized incompressible MPM framework is validated through several benchmark cases, comparing the obtained results with other numerical methods and analytical solutions. Furthermore, the method's capability in simulating real-world problems involving violent free-surface fluid motion is demonstrated through comparisons with experimental results of water sloshing and dam break scenarios. • A mixed updated-Lagrangian MPM is proposed for simulations of incompressible fluids. • The VMS and PSPG methods are adopted to the MPM to satisfy the inf–sup condition. • Numerical accuracy and stability are enhanced through the mitigation of numerical errors. • Objective comparisons with the fractional-step MPM are conducted. [ABSTRACT FROM AUTHOR]

We outline a continuum approach for treating discrete granular flows that holds across multiple scales: from experiments that focus on centimeter-size control volumes, to tests that involve landslides and large buildings. The time evolution of the continuum used to capture the granular dynamics is resolved in space via the smoothed particle hydrodynamics (SPH) method. The interaction between the granular material and immersed rigid bodies is posed and solved as a "fluid"–solid interaction (FSI) problem using boundary conditions enforcing (BCE) SPH particles rigidly attached onto the boundary of the body interacting with the granular material. A new penetration-based particle shifting technique (PPST) is proposed to enforce the particle regularity and thus a stable simulation. Several numerical experiments (angle of repose, ball drop, and cone penetration) are carried out to validate the accuracy of the proposed methodology. The approach is subsequently demonstrated in conjunction with a 3D landslide simulation and a plowing operation. The approach discussed has been implemented and can be used in an open source simulation platform publicly available on GitHub. The implementation leverages GPU computing. • A coupling approach is proposed to model the two-way interaction between granular material and moving solid bodies. • An SPH-based approach is used to model the deformation of dry granular material much faster than allowed by DEM. • A new penetration-based particle shifting technique is proposed to enforce particle regularity. • The GPU-based software implementation is open source and available for unfettered use and distribution. [ABSTRACT FROM AUTHOR]

Bed load sediment transport, in which wind or water flowing over a bed of sediment causes grains to roll or hop along the bed, is a critically important mechanism in contexts ranging from river restoration 1 to planetary exploration 2 . Despite its widespread occurrence, predictions of bed load sediment flux are notoriously imprecise 3,4 . Many studies have focused on grain size variability 5 as a source of uncertainty, but few have investigated the role of grain shape, even though shape has long been suspected to influence transport rates 6 . Here we show that grain shape can modify bed load transport rates by an amount comparable to the scatter in many sediment transport datasets 4,7,8 . We develop a theory that accounts for grain shape effects on fluid drag and granular friction and predicts that the onset and efficiency of transport depend on the coefficients of drag and bulk friction of the transported grains. Laboratory experiments confirm these predictions and reveal that the effect of grain shape on sediment transport can be difficult to intuit from the appearance of grains. We propose a shape-corrected sediment transport law that collapses our experimental measurements. Our results enable greater accuracy in predictions of sediment transport and help reconcile theories developed for spherical particles with the behaviour of natural sediment grains., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Granular intrusion is commonly observed in natural and human-made settings. Unlike typical solids and fluids, granular media can simultaneously display fluid-like and solid-like characteristics in a variety of intrusion scenarios. This multi-phase behavior increases the difficulty of accurately modeling these and other yielding (or flowable) materials. Micro-scale modeling methods, such as DEM (Discrete Element Method), capture this behavior by modeling the media at the grain scale, but there is often interest in the macro-scale characterizations of such systems. We examine the efficacy of a macro-scale continuum approach in modeling and understanding the physics of various macroscopic phenomena in a variety of granular intrusion cases using two basic frictional yielding constitutive models. We compare predicted granular force response and material flow to experimental data in four quasi-2D intrusion cases: (1) depth-dependent force response in horizontal submerged-intruder motion; (2) separation-dependent drag variation in parallel-plate vertical-intrusion; (3) initial-density-dependent drag fluctuations in free surface plowing, and (4) flow zone development during vertical plate intrusions in under-compacted granular media. Our continuum modeling approach captures the flow process and drag forces while providing key meso- and macro-scopic insights. The modeling results are then compared to experimental data. Our study highlights how continuum modeling approaches provide an alternative for efficient modeling as well as a conceptual understanding of various granular intrusion phenomena.

Fine-particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Examination of these mixtures in simple flow geometries suggests intergranular repulsion and its influence on the frictional nature of granular contacts is central to this effect-for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to 2D, steady, simple shearing flows. In this work, we introduce a predictive and general, 3D continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a microstructural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, nonuniform flow configurations where it is shown to accurately capture a variety of key behaviors: 1) the continuous shear-thickening (CST) and discontinuous shear-thickening (DST) behavior observed in steady flows, 2) the time-dependent propagation of "shear jamming fronts," 3) the time-dependent propagation of "impact-activated jamming fronts," and 4) the non-Newtonian, "running on oobleck" effect, wherein fast locomotors stay afloat while slow ones sink., Competing Interests: The authors declare no conflict of interest.

Generalizing Maxwell's (Maxwell 1867 IV. Phil. Trans. R. Soc. Lond. 157 , 49-88 (doi:10.1098/rstl.1867.0004)) classical formula, this paper shows how the dissipation potentials for a dissipative system can be derived from the elastic potential of an elastic system undergoing continual failure and recovery. Hence, stored elastic energy gives way to dissipated elastic energy. This continuum-level response is attributed broadly to dissipative microscopic transitions over a multi-well potential energy landscape of a type studied in several previous works, dating from Prandtl's (Prandtl 1928 Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM 8 , 85-106) model of plasticity. Such transitions are assumed to take place on a characteristic time scale T , with a nonlinear viscous response that becomes a plastic response for T → 0 . We consider both discrete mechanical systems and their continuum mechanical analogues, showing how the Reiner-Rivlin fluid arises from nonlinear isotropic elasticity. A brief discussion is given in the conclusions of the possible extensions to other dissipative processes., Competing Interests: We declare we have no competing interests.