Towards quantum computing enhanced general computational homogenization without readout problem

This paper considers modelling strategies for the multiscale analysis of heterogeneous materials. Initial focus is on computational homogenization (e.g. [1-4]) which represents a powerful, albeit computationally intensive, technique for capturing the influence of an evolving microstrucuture on the overall macroscopic behaviour. First-order homogenization assumes that the representative volume element (RVE) is infinitely small compared to the macroscopic characteristic length scale and that there is clear separation of scales. Second-order schemes [2,4,5] are subsequently discussed as a possible solution. This approach introduces a material length scale into the macroscopic constitutive model and potentially enables geometric size effects to be captured. However, the size of the RVE now becomes an important parameter for the macroscopic response and there is no clear way of determining this length scale. Second-order computational homogenization is demonstrated in the context of an indentation problem. In situations where the RVE cannot be defined and there is no clear separation of scales, computational homogenization is not applicable and full resolution of the microstructure may be necessary. This paper summarises an efficient solution strategy for such situations following the work of Miehe and Bayreuther [6], with particular focus on fracturing heterogeneous materials, which utilises a geometric multi-grid preconditioner and the scale transition methodology from computational homogenization. This solution strategy is coupled with the use of the hybrid-Trefftz stress elements for modelling cohesive cracking [7]. The resulting modelling approach is demonstrated with the analysis of concrete dog-bone specimens where the different phases of matrix, aggregate and interfacial transition zone are explicitly modelled. Such an approach is still computationally intensive and so this paper also presents a novel hybrid multiscale approach that avoids the need for the finite element mesh to fully resolve all heterogeneities [8]. Classical micromechanics is utilised to enhance the approximation space in order to capture the effect of microstructural inclusions. In comparison to where the finite element mesh fully resolves the microstructure, this novel approach significantly reduces the number of degrees of freedom required while still accurately capturing the influence of the inclusions.

Homogenization methods can be used to predict the effective macroscopic properties of materials that are heterogenous at micro- or fine-scale. Among existing methods for homogenization, computational homogenization is widely used in multiscale analyses of structures and materials. Conventional computational homogenization suffers from long computing times, which substantially limits its application in analyzing engineering problems. The neural networks can be used to construct fully decoupled approaches in nonlinear multiscale methods by mapping macroscopic loading and microscopic response. Computational homogenization methods for nonlinear material and implementation of offline multiscale computation are studied to generate data set. This article intends to model the multiscale constitution using feedforward neural network (FNN) and recurrent neural network (RNN), and appropriate set of loading paths are selected to effectively predict the materials behavior along unknown paths. Applications to two-dimensional multiscale analysis are tested and discussed in detail.

Micromechanical modeling of cyclic plastic deformation of ZK60 Mg alloy using 3D full-field crystal plasticity coupled with computational homogenization

We present a computational homogenization approach for linear and non‐linear solid mechanics problems, which is fully compatible with conventional finite element code architecture. A seamless implementation in ABAQUS is presented including Python script, validation problems and a web‐link where script files, user‐defined subroutines and input files can be accessed. For linear problems, we demonstrate how to utilize ABAQUS existing facilities to develop analysis attributes required for solving a unit‐cell problem. For non‐linear problems, a Python script invoked by a coarse‐scale stress update procedure is introduced to carry out the scale bridging. The purpose of this paper is twofold: (i) to motivate practitioners to adopt the computational homogenization as an integral part of their analysis and design process; and (ii) to encourage commercial code vendors to seamlessly integrate the architectures proposed in their legacy codes. Copyright © 2007 John Wiley & Sons, Ltd.

Stiffness and strength evaluation of lattice-based mechanical metamaterials by decoupled two-scale analysis

Nano‐particles, as compared to micro‐sized inclusions, result in a much better improvement to the mechanical properties of otherwise brittle polymers. Standard first‐order computational homogenization lacks the length scale necessary to capture this size effect. In this work, a computational homogenization scheme enhanced with interface energetics is considered and its applicability to polymer nano‐composites with different types of filler particles is assessed through systematic numerical experimentation. The study reveals that the method performs quantitatively much better in the case of softer inclusions as compared to the case where the inclusions are much stiffer than the matrix material, which happens in the case of silica nano‐particles.

Anisotropic strain gradient thermoelasticity for cellular structures: Plate models, homogenization and isogeometric analysis

A computational homogenization of heterogeneous solids is presented based on the data-driven approach for both linear and nonlinear elastic responses. Within the Double-Scale Finite Element Method (FE2) framework, a data-driven model is proposed to substitute the micro-level Finite Element (FE) simulations to reduce computational costs in multiscale simulations. The heterogeneity of porous solids at the micro-level is considered in various material properties and geometrical attributes. For material properties, elastic constants, which are Lame’s coefficients, are subjected to be heterogeneous in the linear elastic responses. For geometrical features, different numbers, sizes, and locations of voids are considered to reflect the heterogeneity of porous solids. A database for homogenized microstructural responses is constructed from a series of micro-level FE simulations, and machine learning is used to train and test our proposed model. In particular, four geometrical descriptors are designed, based on N-probability and lineal-path functions, to clearly reflect the geometrical heterogeneity of various microstructures. This study indicates that a simple deep neural networks model can capture diverse microstructural heterogeneous responses well when given proper input sources, including the geometrical descriptors, are considered to establish a computational data-driven homogenization scheme.

The purpose of this paper is to determine the random spatially varying elastic properties of concrete at various scales taking into account its highly heterogeneous microstructure. The reconstruction of concrete microstructure is based on computed tomography (CT) images of a cubic concrete specimen. The variability of the local volume fraction of the constituents (pores, cement paste and aggregates) is quantified and mesoscale random fields of the elasticity tensor are computed from a number of statistical volume elements obtained by applying the moving window method on the specimen along with computational homogenization. Based on the statistical characteristics of the mesoscale random fields, it is possible to assess the effect of randomness in microstructure on the mechanical behavior of concrete.

Multiscale stability analysis of periodic magnetorheological elastomers

Periodic mesh generation and homogenization of inclusion-reinforced composites using an element-carving technique with local mesh refinement

SummaryBuilding upon the equivalence of the basic scheme in the work of Moulinec and Suquet with gradient descent methods, we investigate the effect of using the celebrated Barzilai‐Borwein step size selection technique in this context. We provide an overview of recent convergence theory and present efficient implementations in the context of computational micromechanics, with and without globalization. In contrast to polarization schemes and fast gradient methods, no lower bound on the eigenvalues of the material tangent is necessary for the Barzilai‐Borwein scheme. We demonstrate the power of the proposed method for linear elastic and inelastic large scale problems with finite and infinite material contrast.

This paper reports the results from the European project PROSOFC (funded by FCH-JU, FP7). Within the project an innovative methodology for a production and reliability oriented SOFC cell and stack design is developed. In particular the PROSOFC project aims at improving the robustness, manufacturability, efficiency and cost of SOLIDpowers state-of-the-art SOFC stacks so as to reach market entry requirements. The key issues are the mechanical robustness of solid oxide fuel cells (SOFCs), and the delicate interplay between cell properties, stack design, and operating conditions of the SOFC stack. The novelty of the project lies in combining state of the art methodologies for cost-optimal reliability-based design (COPRD) with actual production optimization. To achieve the COPRD beyond state of the art multi-physical modeling concepts were developed and validated for significantly improved understanding of the production and operation of SOFC stacks. The most critical failure modes for stack operation were identified in order to align the experimental investigations to generate suitable data for modelling these failures. The multi-physics model allows a probabilistic approach to consider statistical variations in production, material and operating parameters for the optimization phase. The project provides a methodology for 3D description of spatial distribution of material properties based on a random field models. The key for the whole methodology are validating experiments, homogenized models on multiple levels of the SOFC system (cell, interconnect, sealings) and introduction of extensive test programs specified by the COPRD methodology. The probabilistic models were related to the experimentally obtained properties of base materials to establish a statistical relationship between the material properties and the most relevant load effects in view of potential damage/failure based on multi-physics simulation can be established. Software algorithms for meta models that allow the detection of relationships between input parameters (materials, loading, etc.) and output parameters and to perform a sensitivity analysis were developed and implemented. The capabilities of the methodology for COPRD being developed is illustrated on two practical cases. A procedure based on meta models has been developed to estimate elastic, primary and secondary creep model parameters from 4-point bending tests. The goal is to (i) account for the effects of the friction between the sample and the rollers, anticlastic curvature, contact point shift and large deflection, which can affect the accuracy of the measurements, and (ii) measure properties which cannot be obtained using closed-form analytical solutions. This could be achieved by model-based parameter estimation with a 3-D continuum finite-element (FE) model, at the cost of very high running time. The proposed approach is computationally much more efficient. It starts with a sensitivity analysis to generate distributed meta models of the displacement at the inner rollers during loading-unloading cycles and creep measurements simulated by the 3-D FE model. The optimization problem for parameter estimation is then solved using the meta models. The accuracy of the approach was tested using a set of numerical experiments and comparison with results from 3-D imaging and computational homogenization. The experiments on Ni-YSZ samples were then analyzed. For the stochastic investigation of the thermo-electrochemical behavior of the stack a multi-physics stack model implemented in gPROMS and Fluent was linked and controlled automatically by optiSlang to perform a sensitivity analysis. The outcome is (i) the identification of the most relevant production and operating parameters which can have a significant impact on the stack lifetime and (ii) meta models of the efficiency and of the 3-D temperature distribution generated in the view of optimization. The tests show for instance that the accuracy of the 3-D meta model of the temperature distribution is sufficient to identify the minimum of variations in the spatial distribution of the temperature during cycling between full and part load by using sets of operating conditions for optimization.

A computational homogenization technique for modeling diffusion in concrete is introduced with emphasis on the influence of the aggregate content and variability. The highly heterogeneous material is investigated on different scales by combining Variationally Consistent Homogenization on numerical microstructures with analytical techniques accounting for lower, unresolved, length scales. The concrete structure consists of the cement paste, the embedded aggregates, and the Interfacial Transition Zone (ITZ) in between the two. Diffusion takes place in the cement phase, as well as in the ITZ. Since the thickness of the ITZ is, typically, much smaller than the diameter of the aggregates, the effect of the ITZ can be modelled as a surface transport around the aggregates. The occurrence of different aggregate sizes is described via the Particle Size Distribution for given sieve curves, as described in design codes. The Particle Size Distribution curve is split into two parts. The effect of smaller aggregates is homogenized analytically using a mixture rule. This results in an effective matrix material consisting of cement paste and the smaller aggregates. Synthetic structures are then generated numerically to account for the larger aggregates. At first, a dense sphere packing is created based on the Particle Size Distribution. This information is used to generate a weighted Voronoi diagram, which is modified by a shrinking process. This procedure allows us to create periodic Representative Volume Elements for numerical investigations.The overall diffusivity of the concrete mixture is evaluated upon using Variationally Consistent Homogenization, in the context of Finite Element analysis, for the generated RVEs and compared with analytical homogenization results and experimental data. It is found that, depending on the Particle Size Distribution, the ITZ has a large effect on the effective properties.

Functional metal oxide particles are often added to the polymers to prepare flexible functional polymer composites with adequate mechanical properties. ZnO and cellulose nanofibrils (CNF) outstand among these metal oxides and the polymer matrices respectively due to their various advantages. Herein, we in situ prepare ZnO microrods in the presence of CNF, which resultes in a layered composite structure. The ZnO microrods are sandwiched between the CNF layers and strongly bind to highly charged CNF, which provides a better stress transfer during mechanical activity. Digital image correction (DIC) and finite element analysis-based computational homogenization methods are used to investigate the relationship between mechanical properties and composite structure, and the stress transfer to the ZnO microrods. Full-field strain measurements in DIC reveal that the in situ ZnO microrods preparation leads to their homogenous distribution in the CNF matrix unlike other methods, which require external means such as ultrasonication. The computational homogenization technique provides a fairly good insight into the stress transfer between constituents in microstructure as well as a good prediction of macroscopic mechanical properties, which otherwise, would be challenging to be assessed by any ordinary mechanical testing in the layered composites. Finally, we also demonstrate that these composites could be used as physiological motion sensors for human health monitoring.