Two-scale Approach Research Articles

Mechanical Characterization of Thin SOFC Electrolytes With Honeycomb Support

Planar solid oxide fuel cells are made up of repeating sequences of electrolytes, electrodes, seals, and current collectors. The electrolyte should be as thin as possible for optimal electrochemical efficiency; however, for electrolyte-supported cells, the thin electrolytes are susceptible to damage during production, assembly, and operation. To produce cells that are sufficiently mechanically robust, electrolytes can be made having a cosintered honeycomb structure that supports thin, electrochemically efficient electrolyte membranes. Use of finite element analysis is desirable to mechanically characterize such electrolytes. To maintain reasonable numbers of elements and element aspect ratios, it is not possible to simultaneously model the small-scale details together with the overall membrane response. A two-scale approach is devised: the smaller mesoscale analyzes a representative area of the electrolyte, while the larger macroscale examines the electrolyte as a whole. Elastic properties for the mesoscale model are measured over a range of temperatures using a sonic resonance technique. Effective properties for the macroscale are obtained over a range of mesoscale geometries and can be obtained without needing to rerun the mesoscale simulations. The effective properties are experimentally validated using four-point bend experiments on representative samples. The bulk properties and the effective properties can then be used as material inputs for the macroscale model in order to design cells that are more sufficiently mechanically robust without sacrificing electrochemical performance.

Two-scale Time Homogenization for Isotropic Viscoelastic- Viscoplastic Homogeneous Solids Under Large Numbers of Cycles

A two-scale time homogenization approach for coupled viscoelastic-viscoplatic (VE-VP) homogeneous solids and structures subjected to large numbers of cycles, is proposed. The main aim is to give a description of the long time behaviour, by calculating the evolution of internal variables within the structure, while reducing the computational overhead. This method consists in decomposing the original VE-VP initial-boundary problem into coupled micro-chronological (fast time scale) and macro-chronological (slow time-scale) problems. The proposed methodology was implemented and studied for J2 VP coupled with VE using fully implicit time integration and a return-mapping algorithm. An illustration of the time homogenization on a simple case is presented and a good agreement with the reference solution is observed.

A two-scale Weibull approach to the failure of porous ceramic structures made by robocasting: Possibilities and limits

This paper introduces our approach to modeling the mechanical behavior of cellular ceramics, through the example of calcium phosphate scaffolds made by robocasting for bone-tissue engineering. The Weibull theory is used to deal with the scaffolds' constitutive rods statistical failure, and the Sanchez-Palencia theory of periodic homogenization is used to link the rod- and scaffold-scales. Uniaxial compression of scaffolds and three-point bending of rods were performed to calibrate and validate the model. If calibration based on rod-scale data leads to over-conservative predictions of scaffold's properties (as rods' successive failures are not taken into account), we show that, for a given rod diameter, calibration based on scaffold-scale data leads to very satisfactory predictions for a wide range of rod spacing, i.e. of scaffold porosity, as well as for different loading conditions. This work establishes the proposed model as a reliable tool for understanding and optimizing cellular ceramics' mechanical properties.

Selected Topics in Homogenization of Transport Processes in Historical Masonry Structures

The paper reviews several topics associated with the homogenization of transport processed in historical ma-sonry structures. Since these often experience an irregular or random pattern, we open the subject by summarizing essen-tial steps in the formulation of a suitable computational model in the form of Statistically Equivalent Periodic Unit Cell (SEPUC). Accepting SEPUC as a reliable representative volume element is supported by application of the Fast Fourier Transform to both the SEPUC and large binary sample of real masonry in search for effective thermal conductivities lim-ited here to a steady state heat conduction problem. Fully coupled non-stationary heat and moisture transport is addressed next in the framework of two-scale first-order homogenization approach with emphases on the application of boundary and initial conditions on the meso-scale.

Predicting Local Transport Coefficients at Solid–Gas Interfaces

The regular nanoporous structure make zeolite membranes attractive candidates for separating molecules on the basis of differences in transport rates (diffusion). Since improvements in synthesis have led to membranes as thin as several hundred nanometers by now, the slow transport in the boundary layer separating bulk gas and core of the nanoporous membrane is becoming increasingly important. Therefore, we investigate the predictability of the coefficient quantifying this local process, the surface permeability α, by means of a two-scale simulation approach. Methane tracer-release from the one-dimensional nanopores of an AFI-type zeolite is employed. Besides a pitfall in determining α on the basis of tracer exchange, we, importantly, present an accurate prediction of the surface permeability using readily available information from molecular simulations. Moreover, we show that the prediction is strongly influenced by the degree of detail with which the boundary region is modeled. It turns out that not accounting for the fact that molecules aiming to escape the host structure must indeed overcome two boundary regions yields too large a permeability by a factor of 1.7–3.3, depending on the temperature. Finally, our results have far-reaching implications for the design of future membrane applications.

A two-scale failure analysis of composite materials in presence of fiber/matrix crack initiation and propagation

In this work, a numerical multi-scale failure analysis of locally periodic fiber-reinforced composites is carried out. To this end a two-scale finite element continuum approach is proposed, in which coupling between the two scales is obtained by using a unit cell model with evolving microstructure due to mixed-mode crack initiation and propagation at the fiber/matrix interface. Innovative computational techniques have been introduced to perform the localization and homogenization exchanges between the two scales during microstructural damage evolution. The method is able to predict local failure quantities in an arbitrary cell from the results of the macroscopic analysis. These local quantities are then adopted to predict crack initiation by using a coupled stress and energy failure criterion and subsequent propagation.In order to investigate the accuracy of the method in the prediction of failure mechanisms related to the interfacial crack growth at microstructural level, comparisons with a direct analysis adopting a fine-scale modeling of the composite structure, are developed for a 2D fiber-reinforced composite beam with initially undamaged fibers. Numerical calculations demonstrate the effectiveness of the proposed approach and show the accuracy of the proposed method in terms of both macroscopic load–deflection curves and local failure quantities.

Elastic waves in layered media: Two-scale homogenization approach

Using the two-scale convergence approach, we derive equations which govern transversal time-harmonic waves through a layered medium taking the form of a poroelastic composite saturated with a viscous fluid. To improve convergence, we construct a corrector. We study how wave speed and attenuation time depend on porosity and frequency. We prove that the Darcy permeability and the acoustic permeability in the Biot equations do not coincide.

Hysteretic upscaled constitutive relationships for vertically integrated porous media flow

Subsurface two-phase flow in porous media often takes place in reservoirs with a high ratio between the associated lateral and vertical extent and the lateral and vertical flow time scales. This allows for a two-scale approach with effective quantities for two-dimensional horizontal flow equations obtained from reconstructed hydrostatic vertical pressure and saturation distributions. Here, we derive explicit expressions for the two dimensional constitutive relationships for a play-type hysteretic Brooks---Corey capillary pressure function with a pore-size distribution index of 2 and quadratic relative permeabilities. We obtain an explicit hysteretic parametrization for the upscaled capillary pressure function and the upscaled relative permeabilities. The size of the hysteresis loop depends on the ratio between buoyancy and the entry pressure, i.e. it scales with the reservoir height and the ratio between drainage and imbibition capillary pressure. We find that the scaling for the relative permeability is non-monotonic and hysteresis vanishes for both small and large reservoirs.

Two-scale homogenization in transmission problems of elasticity with interface jumps

The elasticity problem in a periodic structure with prescribed interface jumps in displacements and tractions and oscillating Neumann condition on a part of the external boundary is considered. This work is just a generalization of inhomogeneous Dirichlet and Neumann conditions on the oscillating interface. Such interface jumps arise, e.g. in contact problems with known periodic contact interface. Two-scale approach was applied to the problem and the two-scale convergence was proven. This article also provides a detailed auxiliary analysis for Sobolev functions with interface jumps.

Two-scale homogenization of electromechanically coupled boundary value problems

The contribution addresses a direct micro-macro transition procedure for electromechanically coupled boundary value problems. The two-scale homogenization approach is implemented into a so-called FE2-method which allows for the computation of macroscopic boundary value problems in consideration of microscopic representative volume elements. The resulting formulation is applicable to the computation of linear as well as nonlinear problems. In the present paper, linear piezoelectric as well as nonlinear electrostrictive material behavior are investigated, where the constitutive equations on the microscale are derived from suitable thermodynamic potentials. The proposed direct homogenization procedure can also be applied for the computation of effective elastic, piezoelectric, dielectric, and electrostrictive material properties.

Modeling high flux hollow fibers dialyzers

In hollow fibres dialyzers blood flows in the fibres channel and plasmafiltrates through their permeable wall to feed the flow of the permeate(dialyzate), which takes place among the fibres in the opposite direction.We investigate this fluid dynamical problem exploiting the existence of twoseparate scales: the one in the fibres direction ($\sim \,20\,cm$), and theone along the fibre radius ($\sim \,0.1\,mm$). We formulate a mathematicalmodel based on a two-scale approach providing a full description of theflows of the blood, of the dialyzate and the of the plasma through themembrane, as well as of the progressive increase of the hematocrit. Theproblem is characterized by various rather unusual features like the slipcondition of blood on the membrane and the feedback loop of boundary datafor the hematocrit. Blood rheology is assumed to be of shear-thinning type,with hematocrit dependent coefficients. Under some simplifications explicitsolutions are found. We show how the necessity of respecting severalconstraints and of reaching some specific targets influences the selectionof the geometrical and physical parameters of the system. Once the fluiddynamical problem has been solved, the removal from blood of chemicals likeurea, etc. has been studied.

Flow of a Bingham-like fluid in a finite channel of varying width: A two-scale approach

In this paper we consider the flow of a Bingham-like fluid driven by a known pressure gradient in a channel of finite width and length. We model the continuum as a linear viscous fluid when the stress is above a certain threshold and as a linear elastic solid when the stress is below such a threshold. We consider a channel of varying width. Moreover, the ratio, denoted by ε, between the channel width and length is small. This allows for a two-scale approach. Indeed, we seek a solution performing an asymptotic expansion in powers of ε of the main variables. Under specific assumptions on the model characteristic parameters, we prove some analytical results for the zero order approximation. In particular, we show that, when the deformations of the inner elastic core are non-negligible, its width may vary along the longitudinal coordinate. On the other hand, when the core deformations are negligible, the Bingham model is retrieved along with the well known “lubrication paradox”. We also show some numerical simulations.

Interactive two-scale color-to-gray

Current color-to-gray methods compute the grayscale results by preserving the discriminability among individual pixels. However, human perception tends to firstly group the perceptually similar elements while looking at an image, according to the Gestalt principles. In this paper, we propose a novel two-scale approach for converting color images to grayscale. First, we decompose the input image into multiple soft segments where each segment represents a perceptual group of content. Second, we determine the grayscale of each perceptual group via a global mapping by solving a quadratic optimization. Last, the local details are added into the final result. Our approach is efficient and provides users quick feedback on adjusting the prominent gray tones of the results. As an important aspect of algorithm, our approach offers users an easy, intuitive interactive tool for creating art-like black-and-white images from input color images. Experimental results show that our approach better preserves the overall perception and local details. User studies have been conducted to show the applicability of our approach.

High-frequency asymptotics for microstructured thin elastic plates and platonics

We consider microstructured thin elastic plates that have an underlying periodic structure, and develop an asymptotic continuum model that captures the essential microstructural behaviour entirely in a macroscale setting. The asymptotics are based upon a two-scale approach and are valid even at high frequencies when the wavelength and microscale length are of the same order. The general theory is illustrated via one- and two-dimensional model problems that have zero-frequency stop bands that preclude conventional averaging and homogenization theories. Localized defect modes created by material variations are also modelled using the theory and compared with numerical simulations.

Efficient Two-Scale Optimization of Manufacturable Graded Structures

A new method for the optimal design of inhomogeneous meso-structured components is presented. The method is based on a variant of the free material optimization (FMO) method. Instead of coupling a macroscopic model directly with the meso-scale in the framework of a two-scale approach, information from the meso-scale is incorporated into the FMO model by additional constraints. The FMO result, given in terms of optimized tensors, is interpreted by the inverse homogenization approach. Rather than only computing the meso-structure for each “FMO cell” independently, approximate continuity of the meso-structure is enforced. Thus, the final result is a manufacturable structurally graded material. The feasibility of the whole method is demonstrated by means of an academic example.

Homogenisation theory for deterministic and random bianisotropic media

Homogenisation theory may play an important role in the understanding, modelling and design of multifunctional materials. A homogenisation theory for periodic and random bianisotropic electromagnetic media is presented. Starting with a formal two-scale approach we motivate an auxiliary elliptic homogenisation problem which plays a crucial role in the construction of the homogenised bianisotropic medium which is subsequently supported by rigorous mathematical arguments based on the notion of weak convergence. Comments on the potential implementation of this theory in the modelling of complex electromagnetic media are provided.

LSI for Kawasaki Dynamics with Weak Interaction

We consider a large lattice system of unbounded continuous spins that are governed by a Ginzburg-Landau type potential and a weak quadratic interaction. We derive the logarithmic Sobolev inequality (LSI) for Kawasaki dynamics uniform in the boundary data. The scaling of the LSI constant is optimal in the system size and our argument is independent of the geometric structure of the system. The proof consists of an application of the two-scale approach of Grunewald, Otto, Westdickenberg & Villani. Several ideas are needed to solve new technical difficulties due to the interaction. Let us mention the application of a new covariance estimate, a conditioning technique, and a generalization of the local Cramer theorem.

A Two-Scale Numerical Approach to Granular Systems / Wybrane Problemy Szacowania Prawdopodobienstwa Zawodu W Sytuacji Pozaru

Abstract A two-scale numerical homogenization approach was used for granular materials. At small-scale level, granular micro-structure was simulated using the discrete element method. At macroscopic level, the finite element method was applied. An up-scaling technique took into account a discrete model at each Gauss integration point of the FEM mesh to derive numerically an overall constitutive response of the material. In this process, a tangent operator was generated with the stress increment corresponding to the given strain increment at the Gauss point. In order to detect a loss of the solution uniqueness, a determinant of the acoustic tensor associated with the tangent operator was calculated. Some elementary geotechnical tests were numerically calculated using a combined DEM-FEM technique

Long-term deformation analysis of historical buildings through the advanced SBAS-DInSAR technique: the case study of the city of Rome, Italy

Monitoring of deformation phenomena affecting urban areas and man-made structures is of key relevance for the preservation of the artistic, archaeological and architectural heritage. The differential SAR interferometry (DInSAR) technique has already been demonstrated to be an effective tool for non-invasive deformation analyses over large areas by producing spatially dense deformation maps with centimetre to millimetre accuracy. Moreover, by exploiting long sequences of SAR data acquired by different sensors, the advanced DInSAR technique referred to as the small baseline subset (SBAS) approach allows providing long-term deformation time series, which are strategic for guaranteeing the monitoring of urban area displacements. In this work, we investigate the effectiveness of the two-scale multi-sensor SBAS-DInSAR approach to detect and monitor displacements affecting historical and artistic monuments. The presented results, achieved by applying the full resolution SBAS technique to a huge set of ERS-1/2 and ENVISAT data, spanning the 1992–2010 time interval and relevant to the city of Rome (Italy), show the capability of this approach to detect and analyse the temporal evolution of possible deformation phenomena affecting historical buildings and archaeological sites. Accordingly, our analysis demonstrates the effectiveness of the full resolution multi-sensor SBAS approach to operate as a surface deformation tool for supporting the study and conservation strategies of the historical, cultural and artistic heritage.

A two-scale approach for the analysis of propagating three-dimensional fractures

This paper presents a generalized finite element method (GFEM) for crack growth simulations based on a two-scale decomposition of the solution—a smooth coarse-scale component and a singular fine-scale component. The smooth component is approximated by discretizations defined on coarse finite element meshes. The fine-scale component is approximated by the solution of local problems defined in neighborhoods of cracks. Boundary conditions for the local problems are provided by the available solution at a crack growth step. The methodology enables accurate modeling of 3-D propagating cracks on meshes with elements that are orders of magnitude larger than those required by the FEM. The coarse-scale mesh remains unchanged during the simulation. This, combined with the hierarchical nature of GFEM shape functions, allows the recycling of the factorization of the global stiffness matrix during a crack growth simulation. Numerical examples demonstrating the approximating properties of the proposed enrichment functions and the computational performance of the methodology are presented.