Effective transient behaviour of heterogeneous media in diffusion problems with a large contrast in the phase diffusivities

This paper presents a homogenisation-based constitutive model to describe the effective tran- sient diffusion behaviour in heterogeneous media in which there is a large contrast between the phase diffusivities. In this case mobile species can diffuse over long distances through the fast phase in the time scale of diffusion in the slow phase. At macroscopic scale, contrasted phase diffusivities lead to a memory effect that cannot be properly described by classical Fick's second law. Here we obtain effective governing equations through a two-scale approach for composite materials consisting of a fast matrix and slow inclusions. The micro-macro transition is similar to first-order computational homogenisation, and involves the solution of a transient diffusion boundary-value problem in a Representative Volume Element of the microstructure. Different from computational homogenisation, we propose a semi-analytical mean-field estimate of the composite response based on the exact solution for a single inclusion developed in our previous work [Brassart, L., Stainier, L., 2018. Effective transient behaviour of inclusions in diffusion problems. Z. Angew Math. Mech. 98, 981-998]. A key outcome of the model is that the macroscopic concentration is not one-to-one related to the macroscopic chemical potential, but obeys a local kinetic equation associated with diffusion in the slow phase. The history-dependent macroscopic response admits a representation based on internal variables, enabling efficient time integration. We show that the local chemical kinetics can result in non-Fickian behaviour in macroscale boundary-value problems.Comment: 36 pages, 14 figure

Effective transient behaviour of inclusions in diffusion problems

This paper is concerned with the effective transport properties of heterogeneous media in which there is a high contrast between the phase diffusivities. In this case the transient response of the slow phase induces a memory effect at the macroscopic scale, which needs to be included in a macroscopic continuum description. This paper focuses on the slow phase, which we take as a dispersion of inclusions of arbitrary shape. We revisit the linear diffusion problem in such inclusions in order to identify the structure of the effective (average) inclusion response to a chemical load applied on the inclusion boundary. We identify a chemical creep function (similar to the creep function of viscoelasticity), from which we construct estimates with a reduced number of relaxation modes. The proposed estimates admit an equivalent representation based on a finite number of internal variables. These estimates allow us to predict the average inclusion response under arbitrary time-varying boundary conditions at very low computational cost. A heuristic generalisation to concentration-dependent diffusion coefficient is also presented. The proposed estimates for the effective transient response of an inclusion can serve as a building block for the formulation of multi-inclusion homogenisation schemes.Comment: 24 pages, 9 figures. Submitted to ZAMM (under review

Model-Free Data-Driven Methods in Mechanics: Material Data Identification and Solvers

This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a specific constitutive model. A material data identification procedure, allowing to infer strain-stress pairs from displacement fields and boundary conditions, is used to build a material database from a set of mutiaxial tests on a non-conventional sample. This database is in turn used by a data-driven solver, based on an algorithm minimizing the distance between manifolds of compatible and balanced mechanical states and the given database, to predict the response of structures of the same material, with arbitrary geometry and boundary conditions. Examples illustrate this modelling cycle and demonstrate how the data-driven identification method allows importance sampling of the material state space, yielding faster convergence of simulation results with increasing database size, when compared to synthetic material databases with regular sampling patterns.Comment: Revised versio

A Micromechanical Model of Hardening, Rate Sensitivity and Thermal Softening in BCC Single Crystals

The present paper is concerned with the development of a micromechanical model of the hardening, rate-sensitivity and thermal softening of bcc crystals. In formulating the model we specifically consider the following unit processes: double-kink formation and thermally activated motion of kinks; the close-range interactions between primary and forest dislocations, leading to the formation of jogs; the percolation motion of dislocations through a random array of forest dislocations introducing short-range obstacles of different strengths; dislocation multiplication due to breeding by double cross-slip; and dislocation pair annihilation. The model is found to capture salient features of the behavior of Ta crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.Comment: 27 pages (LaTeX) and 15 Figures (jpg

Consistent incremental approximation of dissipation pseudo-potentials in the variational formulation of thermo-mechanical constitutive updates

International audienceIn this paper, we detail a consistent approximate expression for incremental dissipation pseudo-potentials which appear in the variational formulation of coupled thermo-mechanical boundary-value problems. We explain why the most intuitive expression does not work in the case of an explicit temperature dependence in the dissipation, and propose an alternative expression ensuring consistent results when reducing the time increment towards zero

Shear localization as a mesoscopic stress-relaxation mechanism in fused silica glass at high strain rates

Molecular dynamics (MD) simulations of fused silica glass deforming in pressure-shear, while revealing useful insights into processes unfolding at the atomic level, fail spectacularly in that they grossly overestimate the magnitude of the stresses relative to those observed, e. g., in plate-impact experiments. We interpret this gap as evidence of relaxation mechanisms that operate at mesoscopic lengthscales and which, therefore, are not taken into account in atomic-level calculations. We specifically hypothesize that the dominant mesoscopic relaxation mechanism is shear banding. We evaluate this hypothesis by first generating MD data over the relevant range of temperature and strain rate and then carrying out continuum shear-banding calculations in a plate-impact configuration using a critical-state plasticity model fitted to the MD data. The main outcome of the analysis is a knock-down factor due to shear banding that effectively brings the predicted level of stress into alignment with experimental observation, thus resolving the predictive gap of MD calculations

Lessons from “Lower” Organisms: What Worms, Flies, and Zebrafish Can Teach Us about Human Energy Metabolism

A pandemic of metabolic diseases (atherosclerosis, diabetes mellitus, and obesity), unleashed by multiple social and economic factors beyond the control of most individuals, threatens to diminish human life span for the first time in the modern era. Given the redundancy and inherent complexity of processes regulating the uptake, transport, catabolism, and synthesis of nutrients, magic bullets to target these diseases will be hard to find. Recent studies using the worm Caenorhabditis elegans, the fly Drosophila melanogaster, and the zebrafish Danio rerio indicate that these "lower" metazoans possess unique attributes that should help in identifying, investigating, and even validating new pharmaceutical targets for these diseases. We summarize findings in these organisms that shed light on highly conserved pathways of energy homeostasis