arXiv subjects

Matthew R. Kuhn

Publications and source records attributed to Matthew R. Kuhn.

23 records · Page 2Linked to original sources

arXiv2018

The critical state of granular media: Convergence, stationarity, and disorder

Discrete-element simulations are used to monitor several micro-scale characteristics within a granular material, demonstrating their convergence during loading toward the critical state, their stationarity at the critical state, and the evolution of their disorder toward the critical state. Convergence, stationarity and disorder are studied in the context of the Shannon entropy and two forms of Kullback-Leibler relative entropy. Probability distributions of 20 aspects of micro-scale configuration, force and movement are computed for three topological objects: particles, voids and contacts. The probability distributions of these aspects are determined at numerous stages during quasi-static biaxial compression and unloading. Not only do stress and density converge to the critical state, but convergence and stationarity are manifested in all of the micro-scale aspects. The statistical disorder (entropy) of micro-scale movements and strains generally increases during loading until the critical state is reached. When the loading direction is reversed, order is briefly restored, but continued loading induces greater disorder in movements and strains until the critical state is reached again.

cond-mat.soft↗

arXiv2018

Stiffness pathologies in discrete granular systems: bifurcation, neutral equilibrium, and instability in the presence of kinematic constraints

The paper develops the stiffness relationship between the movements and forces among a system of discrete interacting grains. The approach is similar to that used in structural analysis, but the stiffness matrix of granular material is inherently non-symmetric because of the geometrics of particle interactions and of the frictional behavior of the contacts. Internal geometric constraints are imposed by the particles' shapes, in particular, by the surface curvatures of the particles at their points of contact. Moreover, the stiffness relationship is incrementally non-linear, and even small assemblies require the analysis of multiple stiffness branches, with each branch region being a pointed convex cone in displacement-space. These aspects of the particle-level stiffness relationship gives rise to three types of micro-scale failure: neutral equilibrium, bifurcation and path instability, and instability of equilibrium. These three pathologies are defined in the context of four types of displacement constraints, which can be readily analyzed with certain generalized inverses. That is, instability and non-uniqueness are investigated in the presence of kinematic constraints. Bifurcation paths can be either stable or unstable, as determined with the Hill-Bazant-Petryk criterion. Examples of simple granular systems of three, sixteen, and sixty four disks are analyzed. With each system, multiple contacts were assumed to be at the friction limit. Even with these small systems, micro-scale failure is expressed in many different forms, with some systems having hundreds of micro-scale failure modes. The examples suggest that micro-scale failure is pervasive within granular materials, with particle arrangements being in a nearly continual state of instability.

cond-mat.soft↗

arXiv2018

Multi-directional behavior of granular materials and its relation to incremental elasto-plasticity

The complex incremental behavior of granular materials is explored with multi-directional loading probes. An advanced discrete element model (DEM) was used to examine the reversible and irreversible strains for small loading probes, which follow an initial monotonic axisymmetric triaxial loading. The model used non-convex non-spherical particles and an exact implementation of the Hertz-like Cattaneo-Mindlin model for the contact interactions. Rectilinear true-triaxial probes were used in the study (i.e., no direct shear strain or principal stress rotation), with small strains increments of $2\times 10^{-6}$. The reversible response was linear but exhibited a high degree of stiffness anisotropy. The irreversible behavior, however, departed in several respects from classical elasto-plasticity. A small amount of irreversible strain and contact slipping occurred for all directions of the stress increment (loading, unloading, transverse loading, etc.), demonstrating that an elastic domain, if it exists at all, is smaller than the strain increment used in the simulations. Irreversible strain occurred in directions tangent to the primary yield surface, and the direction of the irreversible strain varied with the direction of the stress increment. For stress increments within the deviatoric pi-plane, the irreversible response had rounded-corners, evidence of multiple plastic mechanisms. The response at these rounded corners varied in a continuous manner as a function of stress direction. The results are placed in the context of advanced elasto-plasticity models: multi-mechanism plasticity and tangential plasticity. Although these models are an improvement on conventional elasto-plasticity, they do not fully fit the simulation results.

cond-mat.soft↗

arXiv2018

Quasi-static incremental behavior of granular materials: elastic-plastic coupling and micro-scale dissipation

The paper addresses a common assumption of elastoplastic modeling: that the recoverable, elastic strain increment is unaffected by alterations of the elastic moduli that accompany loading. This assumption is found to be false for a granular material, and discrete element (DEM) simulations demonstrate that granular materials are coupled materials at both micro- and macro-scales. Elasto-plastic coupling at the macro-scale is placed in the context of thermomechanics framework of Tomasz Hueckel and Hans Ziegler, in which the elastic moduli are altered by irreversible processes during loading. This complex behavior is explored for multi-directional loading probes that follow an initial monotonic loading. An advanced DEM model is used in the study, with non-convex non-spherical particles and two different contact models: a conventional linear-frictional model and an exact implementation of the Hertz-like Cattaneo-Mindlin model. Rectilinear true-triaxial probes were used in the study (i.e., no direct shear strain), with tiny strain increments of $2\times 10^{-6}$. At the micro-scale, contact movements were monitored during small increments of loading and load-reversal, and results show that these movements are not reversed by a reversal of strain direction, and some contacts that were sliding during a loading increment continue to slide during reversal. The probes show that the coupled part of a strain increment, the difference between the recoverable (elastic) increment and its reversible part, must be considered when partitioning strain increments into elastic and plastic parts. Small increments of irreversible (and plastic) strain and contact slipping and frictional dissipation occur for all directions of loading, and an elastic domain, if it exists at all, is smaller than the strain increment used in the simulations.

cond-mat.soft↗

arXiv2018

Measurement of higher-order stress-strain effects in granular materials undergoing non-uniform deformation

Discrete element (DEM) simulations demonstrate that granular materials are non-simple, meaning that the incremental stiffness of a granular assembly depends on the gradients of the strain increment as well as on the strain increment itself. In quasi-static simulations, two-dimensional granular assemblies were stiffer when the imposed deformation was non-uniform than for uniform deformation. The contacts between particles were modeled as linear-frictional contacts with no contact moments. The results are interpreted in the context of a higher-order micro-polar continuum, which admits the possibility of higher-order stress and couple-stress. Although the behavior was non-simple, no evidence was found for a couple-stress or an associated stiffness. The experimental results apply consistently to three particle shapes (circles, ovals, and a non-convex cluster shape), to assemblies of three sizes (ranging from 250 to 4000 particles), and at pre-peak and post-peak strains.

cond-mat.soft↗