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

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.Comment: In press, International Journal of Solids and Structures, 201

Relaxed micromorphic broadband scattering for finite-size meta-structures -- a detailed development

The conception of new metamaterials showing unorthodox behaviors with respect to elastic wavepropagation has become possible in recent years thanks to powerful dynamical homogenization techniques. Such methods effectively allow to describe the behavior of an infinite medium generated by periodically architectured base materials. Nevertheless, when it comes to the study of the scattering properties of finite-sized structures, dealing with the correct boundary conditions at the macroscopicscale becomes challenging. In this paper, we show how finite-domain boundary value problems canbe set-up in the framework of enriched continuum mechanics (relaxed micromorphic model) by imposing continuity of macroscopic displacement and of generalized traction when non-local effects areneglected.The case of a metamaterial slab of finite width is presented, its scattering properties are studied viaa semi-analytical solution of the relaxed micromorphic model and compared to numerical simulationsencoding all details of the selected microstructure. The reflection coefficient obtained via the twomethods is presented as a function of the frequency and of the direction of propagation of the incidentwave. We find excellent agreement for a large range of frequencies going from the long-wave limitto frequencies beyond the first band-gap and for angles of incidence ranging from normal to nearparallel incidence. The case of a semi-infinite metamaterial is also presented and is seen to be areliable measure of the average behavior of the finite metastructure. A tremendous gain in termsof computational time is obtained when using the relaxed micromorphic model for the study of theconsidered metastructure

Numerical modeling of pile penetration in silica sands considering the effect of grain breakage

International audienceCurrent numerical platforms rarely consider the effect of grain breakage in the design of sandy soil foundations. This paper presents an enhanced platform for large deformation analyses which considers the effect of grain breakage during pile penetration in silica sand. For this purpose, a model based on critical state theory has been developed within the framework of multisurface plasticity to account in the same constitutive platform the effect of stress dilatancy and particle fragmentation. Furthermore, to implement the underlying constitutive equations into a finite element code, a stress integration scheme has been adopted by extending a cutting plane algorithm to the model with multiple yielding mechanisms. A laboratory model test and a series of centrifuge tests of pile penetration are simulated to verify the performance of the selected constitutive approach in terms of pile resistance and grain breakage distribution, with the parameters of sand calibrated through a set of drained triaxial compression tests from low to very high confining pressure. Some extra features of the enhanced platform are also discussed, such as: i) the effect of sand crushability on pile resistance and ii) the nonlinear relation of pile resistance to sand density. The proposed findings demonstrate the capability of this numerical platform to proper design of pile foundation in sandy soils and highlight the interplay between stress dilatancy and grain breakage mechanisms during pile penetration processes

Relaxed micromorphic broadband scattering for finite-size meta-structures - a detailed development

The conception of new metamaterials showing unorthodox behaviors with respect to elastic wavepropagation has become possible in recent years thanks to powerful dynamical homogenization techniques. Such methods effectively allow to describe the behavior of an infinite medium generated by periodically architectured base materials. Nevertheless, when it comes to the study of the scattering properties of finite-sized structures, dealing with the correct boundary conditions at the macroscopicscale becomes challenging. In this paper, we show how finite-domain boundary value problems canbe set-up in the framework of enriched continuum mechanics (relaxed micromorphic model) by imposing continuity of macroscopic displacement and of generalized traction when non-local effects areneglected.The case of a metamaterial slab of finite width is presented, its scattering properties are studied viaa semi-analytical solution of the relaxed micromorphic model and compared to numerical simulationsencoding all details of the selected microstructure. The reflection coefficient obtained via the twomethods is presented as a function of the frequency and of the direction of propagation of the incidentwave. We find excellent agreement for a large range of frequencies going from the long-wave limitto frequencies beyond the first band-gap and for angles of incidence ranging from normal to nearparallel incidence. The case of a semi-infinite metamaterial is also presented and is seen to be areliable measure of the average behavior of the finite metastructure. A tremendous gain in termsof computational time is obtained when using the relaxed micromorphic model for the study of theconsidered metastructure

Integration of material and process modelling in a business decision support system: Case of COMPOSELECTOR H2020 project

This paper shares and contributes to a ground-breaking vision developed and being implemented which consists in the integration of materials modelling methodologies and knowledge-based systems with business process for decision making. The proposed concept moves towards a new paradigm of material and process selection and design by developing and implementing an integrated multi-disciplinary, multi-model and multi-field approach together with its software tool implementation for an accurate, reliable, efficient and cost effective prediction, design, fabrication, Life Cycle Engineering (LCE), cost analysis and decision making. This new paradigm of integrated material design is indeed endowed with a great potential by providing further insights that will promote further innovations on a broad scale

Etude expérimentale du comportement pseudoelastique dans les argiles surconsolidées

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