We study the plane shear flow of a dense assembly of dissipative disks using discrete simulation and prescribing the pressure and the shear rate. Those shear states are steady and uniform, and become intermittent in the quasistatic regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called the inertial number I , which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic critical state of soil mechanics, while large values of I correspond to the fully collisional regime of kinetic theory. When I increases in the intermediate dense flow regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. The mechanical characteristics of the grains (restitution, friction, and elasticity) have a small influence in the dense flow regime. Finally, we show that the evolution of the relative velocity fluctuations and of the contact force anisotropy as a function of I provides a simple explanation of the friction law.

Rheophysics of dense granular materials: Discrete simulation of plane shear flows

Various multiscale methods are reviewed in the context of modelling mechanical and thermomechanical responses of composites. They are developed both at the material level and at the structural analysis level, considering sequential or integrated kinds of approaches. More specifically, such schemes like periodic homogenization or mean field approaches are compared and discussed, especially in the context of non linear behaviour. Some recent developments are considered, both in terms of numerical methods (like FE2) and for more analytical approaches based on Transformation Field Analysis, considering both the homogenization and relocalisation steps in the multiscale methodology. Several examples are shown.

Multiscale Methods for Composites: A Review

The past 20 years have seen substantial work on the modeling of ductile damage and fracture. Several factors explain this interest. (i) There is a growing demand to provide tools which allow to increase the efficiency of structures (reduce weight, increase service temperature or load, etc.) while keeping or increasing safety. This goal is indeed first achieved by using better materials but also by improving design tools. Better tools have been provided which consist (ii) of material constitutive equations integrating a physically-based description of damage processes and (iii) of better numerical tools which allow to use the improved constitutive equations in structural computations which become more and more realistic. This article reviews the material constitutive equations and computational tools, which have been recently developed to simulate ductile rupture.

/pdf/continuum-models-of-ductile-fracture-a-review-35khqjinf0.pdf

Continuum Models of Ductile Fracture: A Review

The objective of this review is to examine how the concept of plasticity is used in geophysical fluid dynamics. Rapid mass movements such as snow avalanches or debris flows involve slurries of solid particles (ice, boulder, clay, etc.) within an interstitial fluid (air, water). The bulk behavior of these materials has often been modeled as plastic materials, i.e., a plastic material yields and starts to flow once its stress state has significantly departed from equilibrium. Two plastic theories are of common use in fluid dynamics: Coulomb plasticity and viscoplasticity. These theories have little in common, since ideal Coulomb materials are two-phase materials for which pore pressure and friction play the key role in the bulk dynamics, whereas viscoplastic materials (e.g., Bingham fluids) typically behave as single-phase fluids on the macroscopic scale and exhibit a viscous behavior after yielding. Determining the rheological behavior of geophysical materials remains difficult because they encompass coarse, irregular particles over a very wide range of size. Consequently, the true nature of plastic behavior for geophysical flows is still vigorously debated. In this review, we first set out the continuum-mechanics principles used for describing plastic behavior. The notion of yield surface rather than yield stress is emphasized in order to better understand how tensorial constitutive equations can be derived from experimental data. The notion of single-phase or two-phase behaviors on the macroscopic scale is then examined using a microstructural analysis on idealized suspensions of spheres within a Newtonian fluid; for these suspensions, the single-phase approximation is valid only at very high or low Stokes numbers. Within this framework, the bulk stress tensor can also be constructed, which makes it possible to give a physical interpretation to yield stress. Most of the time, depending on the bulk properties (especially, particle size) and flow features, bulk behavior is either Coulomb-like or viscoplastic in simple-shear experiments. The consequences of the rheological properties on the flow features are also examined. Some remarkable properties of the governing equations describing thin layers flowing down inclined surfaces are discussed. Finally, the question of parameter fitting is tackled: since rheological properties cannot be measured directly in most cases, they must be evaluated from field data. As an example, we show that the Coulomb model successfully captures the main traits of avalanche motion, but statistical analysis demonstrates that the probability distribution of the friction coefficient is not universal.

/pdf/plasticity-and-geophysical-flows-a-review-4bos64lahx.pdf

Plasticity and geophysical flows: A review

Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the absence of external forces. In this work we present a mathematical framework for such bodies in terms of a covariant theory of linear elasticity, valid for large displacements. We propose the concept of non-Euclidean plates to approximate many naturally formed thin elastic structures. We derive a thin plate theory, which is a generalization of existing linear plate theories, valid for large displacements but small strains, and arbitrary intrinsic geometry. We study a particular example of a hemispherical plate. We show the occurrence of a spontaneous buckling transition from a stretching dominated configuration to bending dominated configurations, under variation of the plate thickness.

http://www.ma.huji.ac.il/~razk/Publications/PDF/ESK08.pdf

Elastic theory of unconstrained non-Euclidean plates

A micromechanical modeling of the Greenwood–Johnson mechanism in transformation induced plasticity

The homogenization techniques allow the macroscopic constitutive equations of a given material to be derived from its microscopic behaviour. The case of granular material is difficult because the microscopic level must be described in discrete terms (contact forces and relative displacements). The present paper is devoted to a general discussion of this problem and to a presentation of different models for granular homogenization. Since we shall primarily be concerned with methodological issues and with comparison to the standard microcontinuous case, attention will be focussed to the simplest case of micro-elasticity assuming a linear contact law

Homogenization for granular materials

A hyperelastic constitutive model is developed for textile composite reinforcement at large strain. A potential is proposed, which is the addition of two tension and one shear energies. The proposed potential is a function of the right Cauchy Green and structural tensor invariants whose choice corresponds to textile composite reinforcement mechanical behavior which exhibits weak elongations in the fiber directions and large angular variations in the fabric plane.The model is implemented in a Vumat user routine of ABAQUS/Explicit. Some elementary tests are performed in order to identify the model and verify its validity. It is then used to simulate the hemispherical punch forming of balanced and unbalanced fabrics. A correct agreement is obtained with experimental forming processes.

A Hyperelastic Approach for Composite Reinforcement Large Deformation Analysis

Some issues about anisotropic elastic–plastic models at finite strain

The description of anisotropic elastic-plastic behaviour at large strain is difficult. In the rigid plastic case, anisotropic plasticity is now reasonably well understood and is based on formulating anisotropic constitutive equations in a moving frame which, correctly chosen, will ensure objectivity and which can be postulated: (i) a priori to follow in some sense the material rotations (kinematical rotating frame); (ii) a posteriori by an appropriate constitutive evolution equation (plastic spin equation). With respect to the classical continuum models this is in fact an alternative for the formulation of frame indifferent constitutive equations. This rotating frame formulation of continuum mechanics is first formally presented and applied to anisotropic elasticity to show that in this case the proper rotating frame must be used to get a true elasticity. The remaining part of the paper is then devoted to the elastic-plastic case starting from a direct extension of the formalism with derivation of the elastic constitutive equation and plastic flow rule which is best written in the so-called isoclinic configuration. Finally the kinematic plastic rotating frames will be introduced and exemplified as the appropriate choice for a correct description of an anisotropic elastic- plastic behaviour.

F. Sidoroff

Papers

A micromechanical modeling of the Greenwood–Johnson mechanism in transformation induced plasticity

Homogenization for granular materials

A Hyperelastic Approach for Composite Reinforcement Large Deformation Analysis

Some issues about anisotropic elastic–plastic models at finite strain

Some issues about anisotropic elastic-plastic models at finite strain