Depending on the synthesis methods employed, nanowires for flexible electronics are either single crystals or possess a penta-twinned nanostructure. This nanostructure, along with the relative crystallographic orientation of the nanowires and the welding temperature, determines the degree of interpenetration between wires and the nanostructure of the junction. This study tracks, by means of atomistic simulations performed at various temperatures, the formation and evolution of the joint between pairs of nanowires. The results show that penta-twinned nanowires generally yield the greatest interpenetration between wires and the most significant nanostructural changes, driven by atomic diffusion facilitated by the presence of twin boundaries. In contrast, single-crystal nanowires can form, in specific orientations, nearly defect-free yet poorly interpenetrated junctions. While surface curvature is an important parameter that drives atomic diffusion and thus promotes interpenetration, it is the presence of twin boundaries that has a dominant role in triggering nanostructural variation in the nanowires during welding.

A continuum-discrete model for failure in quasi-brittle materials is presented. The continuum is regularised through the introduction of gradient terms into the constitutive model. At the transition to discrete failure, the problem fields are enhanced through the use of a discontinuous interpolation. The continuum model is able to simulate micro-cracking, while a traction-free discontinuity represents the macro crack. The discretisation procedure is described in detail.

A network of metallic nanowires (NWs) is a suitable alternative to thin-film oxides for the production of flexible transparent electrodes. Currently available assembly strategies allow for the deposition of NWs in a highly ordered state, with cross-aligned arrangements achieved by stacking layers of NWs with perpendicular preferential orientations. Experimental investigations indicate that the optoelectrical performance of electrodes with a cross-aligned arrangement is superior to that of those with a random arrangement, but the underlying reasons remain unclear. We therefore conduct an extensive set of numerical simulations to compare the performance of networks with cross-aligned and random arrangements in terms of percolative behavior, electrical conductivity, and electrical homogeneity across a wide range of NW densities. Despite the common misconception that the percolation threshold of cross-aligned arrangements is lower than that of random arrangements, we demonstrate that this is not the case. Moreover, our findings indicate that topology alone does not account for the advantages observed in cross-aligned arrangements. We further demonstrate that junction resistanceRjis the key parameter influencing electrical conductivity and homogeneity, estimating thatRjis approximately 20% lower in real cross-aligned arrangements compared to random arrangements. NW assembly strategies also facilitate a spatially homogeneous distribution of NWs, which is rarely observed in real random arrangements, further enhancing the performance of cross-aligned arrangements.

We extend the Discontinuity-Enriched Finite Element Method (DE-FEM) to simulate intersecting discontinuities, such as those encountered in polycrystalline materials, multi-material wedge problems, and branched cracks. The proposed hierarchical enrichment functions capture weak and strong discontinuities at junctions within a single formulation. Several numerical applications to branched cracks and polycrystalline microstructures under both thermal and mechanical loads are presented to demonstrate the proposed method. Results indicate that DE-FEM can accurately capture complex discontinuous primal and gradient fields and attain convergence rates comparable to those of standard FEM using fitted meshes. The main advantages of DE-FEM equipped with the proposed junction enrichment functions lie in the method’s ability to model intersecting discontinuities using meshes that are completely decoupled from them and its robustness in reproducing correct displacement and strain jumps across them, as demonstrated by a patch test. This work thus highlights the potential of DE-FEM for applications to problems characterized by the presence of multiple intersecting discontinuities, posing a valid alternative to traditional FEM and eXtended/Generalized Finite Element (X/GFEM) Methods.

Flexible transparent electrodes employing metal nanowires (NWs) find extensive use in various applications such as optoelectronic devices, solar cells, light-emitting diodes, and transparent heaters. NW networks in flexible transparent electrodes can withstand mechanical deformations and conduct electricity but are susceptible to localized damage caused by mechanical stress and current density concentration. This localized damage ultimately results in electrode failure. Our study aims to track locally induced damage from both mechanical and electrical sources and assess their collective influence on electrode performance until failure occurs. To this end, we create two-dimensional digital samples that represent the NW networks, transform them into beam networks and equivalent resistor networks, and perform finite element simulations of the mechanical and electrical network responses while varying the NW content.Our simulations reveal crack-like patterns in the distribution of damaged elements at network failure that depend on the process inducing the damage. While our results suggest that the impact of electrically induced damage on overall network stability is more significant than that of mechanically induced damage, the latter must not be ignored.

Transparent electrodes made of random distributions of metal nanowires (NWs) are appealing for optoelectronic devices, solar cells, light emitting diodes, and transparent heaters. While these electrodes are comparable to thin films in terms of electrical conductivity and transparency, their network structure allows limiting the amount of conductive material and makes them suitable for low-cost solution-based deposition methods, contributing to an overall costs reduction. Despite these advantages, an even material utilization at different length scales is difficult to achieve. The homogeneous distribution of electric current (electrical homogeneity) is indeed not guaranteed in nanowire electrodes but is crucial for the stability of the electrode and actually desirable in most applications. Despite the relevance of this feature, it is common practice to perform qualitative assessments at the electrode scale, overlooking local effects. To address this issue, we have developed a computational strategy to aid in the design of nanowire electrodes with improved electrical homogeneity. We present a computational approach that allows an objective, quantitative, and systematic assessment of the electrical homogeneity. The approach enables a multiscale comparison of electrodes with different NW content and material properties. Nanowire electrodes are modeled as two-dimensional networks of stick and junction resistors (with resistance Rw and Rj, respectively) to simulate the electric conduction process. Electrodes are discretized into regular grids of squares and the electrical power of the network contained in each square is computed. The mismatch between the areal power density of the entire electrode and that of the squares provides a quantitative electrical homogeneity evaluation. Repeating the analysis with squares of different size yields an evaluation that spans across length scales. A scalar indicator, coined the homogeneity index, summarizes the results of the multiscale evaluation. Parametric studies are performed by varying nanowire content and nanowire-to-junction resistance ratio Rw/Rj. We show that electrical homogeneity improves as i) NW density increases, and ii) junction resistance reduces. The ideal condition of negligible junction resistance (Rw >> Rj) leads to the best-case scenario and guarantees the highest rate of improvement of electrical homogeneity with NW content. Nevertheless, we observe that under condition Rw ≈ Rj the response of the system approaches the response of a system meeting the ideal condition Rw >> Rj (15% difference at most in terms of homogeneity index). We therefore conclude that reducing the junction resistance excessively (with the aim of achieving Rw/Rj > 1) may not always be a worthwhile strategy, as it results in only a marginal improvement in terms of electrical homogeneity. The proposed strategy is employed to assess the electrical homogeneity of silver nanowire electrodes through the analysis of scanning electron microscopy images. Our results agree with the outcomes of the experimental assessment performed on the same electrodes.

The homogeneous distribution of electric current (electrical homogeneity) is not guaranteed in nanowire electrodes but is crucial for the stability of the electrode and actually desirable in most applications. Despite the relevance of this feature, it is common practice to perform qualitative assessments at the electrode scale, thus masking local effects. To address this issue, we have developed a computational strategy to aid in the design of nanowire electrodes with improved electrical homogeneity. Nanowire electrodes are modeled as two-dimensional networks of stick and junction resistors (with resistance Rw and Rj, respectively) to simulate the electric conduction process. Electrodes are discretized into regular grids of squares and the electrical power of the network contained in each square is computed. The mismatch between the areal power density of the entire electrode and that of the squares provides a quantitative electrical homogeneity evaluation. Repeating the analysis with squares of different size yields an evaluation that spans across length scales. A scalar indicator, coined the homogeneity index, summarizes the results of the multiscale evaluation. The proposed strategy is employed to assess the electrical homogeneity of silver nanowire electrodes through the analysis of scanning electron microscopy images. Our results agree with the outcomes of the experimental assessment performed on the same electrodes. Parametric studies are performed by varying nanowire content and nanowire-to-junction resistance ratio Rw/Rj. We observe that a significant reduction of contact resistance is not necessary to ensure a high degree of homogeneity. The ideal condition of negligible junction resistance (Rw ≫ Rj) leads to the best-case scenario, a situation which is closely approached if Rw ≈ Rj (15% difference at the most in terms of homogeneity index).

We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched terms that are associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces. The enrichment strategy effectively produces an enriched node-to-node discretization that can be used with any constraint enforcement criterion; this is demonstrated with both multi-point constraints and Lagrange multipliers, the latter in a generalized Newton implementation where both primal and Lagrange multiplier fields are updated simultaneously. We show that the node-to-node enrichment ensures continuity of the displacement field—without locking—in mesh coupling problems, and that tractions are transferred accurately at contact interfaces without the need for stabilization. We also show the formulation is stable with respect to the condition number of the stiffness matrix by using a simple Jacobi-like diagonal preconditioner.

Fibrous electrodes are a promising alternative to conventional particle-based lithium-ion battery electrodes. In this contribution, we propose an efficient computational approach for the modeling and simulation of electrochemical phenomena taking place in fibrous electrodes during battery charge/discharge processes. Since each fiber is explicitly modeled by means of a dimensionally reduced embedded fiber model, the framework enables simulations in a three-dimensional setting with relatively modest discretization and computational requirements compared to simulations with fully resolved fiber discretizations. The approach is applied to electrodes with high volume fractions of high aspect ratio fibers. Various local and global quantities are analyzed and results are compared to those obtained with the standard finite element method and the pseudo-2D model.

A combined experimental and numerical investigation of the roughness of intergranular cracks in two-dimensional disordered solids is presented. We focus on brittle materials for which the characteristic length scale of damage is much smaller than the grain size. Surprisingly, brittle cracks do not follow a persistent path with a roughness exponent ζ≈0.6-0.7 as reported for a large range of materials. Instead, we show that they exhibit monoaffine scaling properties characterized by a roughness exponent ζ=0.50±0.05, which we explain theoretically from linear elastic fracture mechanics. Our findings support the description of the roughening process in two-dimensional brittle disordered solids by a random walk. Furthermore, they shed light on the failure mechanism at the origin of the persistent behavior with ζ≈0.6-0.7 observed for fractures in other materials, suggesting a unified scenario for the geometry of crack paths in two-dimensional disordered solids.

Existing battery modeling works have limitations in addressing the dependence of transport properties on local field variations and characterizing the response of anisotropic media. These limitations are tackled by means of a nested finite element (FE2) multiscale framework in which microscale simulations are employed to comprehensively characterize an anisotropic medium (macroscale). The approach is applied to the numerical simulation of transport processes in lithium ion battery separators. From the microscale solution, homogenized fluxes and their dependence on the downscaled macroscale variables are upscaled, thereby replacing otherwise assumed macroscale constitutive laws. The tensorial nature of macroscale effective transport properties stems from the numerical treatment. The proposed approach is verified against full-scale simulations. Several numerical examples are used to demonstrate the perils associated with accepted procedures, leading in some cases to severe discrepancies in the prediction of field quantities (from differences in the potential drop across the separator of about 27% for a fixed microstructure to more than 100% in the case of an evolving microstructure). Despite the use of simplified assumptions (e.g., synthetic microstructures), the numerical results demonstrate the importance of a tensorial description of transport properties in the modeling of battery processes. (C) 2021 The Author(s). Published by Elsevier Ltd.

A dispersion of stiff and thin (‘rigid line’) inclusions (RLIs) in a matrix material may result beneficial for stiffening in the elastic range, but might be detrimental to strength, as material instabilities may be triggered by inclusions when the matrix is brought to a viscoplastic-damaging state. This dual role of RLIs is investigated by means of the embedded reinforcement model. Validated against available analytical predictions, this numerical model is employed to assess the roles of RLIs’ orientation, interaction, volume fraction, and distribution, considering up to 1500 inclusions. When the matrix material deforms inelastically, RLIs produce stress concentrations that promote the nucleation of shear bands. These are characterized at collapse for many distributions of RLIs, showing that their effects range from almost negligible to a disrupting alteration of the dominant failure mechanism. In the latter case, it is shown that the dominant shear bands can be fragmented by RLIs into a mosaic of tiny localization bands. These results offer new insights into energy dissipation mechanisms of reinforced materials, as they are promoted or inhibited by the interactions of rigid line inclusions.

This study presents a three-dimensional computational model to evaluate effective conductivity and capacity of fiber-based battery electrodes. We employ electrodes composed of conductive and active material nanofibers dispersed in an electrolyte matrix. The effective conductivity is calculated by means of an equivalent resistor network model, while capacity evaluation is based on the identification of active material fibers that are accessible to electrons (i.e., those connected with the electronically conductive network). When a constraint is applied to the total fiber content, an optimal active-conductive material ratio is determined that maximizes the active material utilization and the electrode capacity. We also study fiber orientation effects on the electrode electrochemical properties. It is found that fiber orientation has a strong impact on the percolation threshold, and this impact also reflects on the active material utilization: the more the fiber orientation deviates from the ideal isotropic distribution, the lower the utilization of active material fibers. This is of special interest for practical applications where geometrical constraints on fiber orientation arise, as in the case of electrospun fibers deposited on a substrate. The results of this study are therefore meant to give an insight into how a fibrous electrode architecture performs and suggest effective design solutions.

In this thesis project, an originally very simple Finite Element Method (FEM) code written in Python is accelerated using well-known techniques: sparse format for matrices and vectorization of operations. The estimate of the transverse elastic modulus of unidirectional fiber-reinforced composite is used as a real-world testing situation for the FEM package called feat [9]. For this purpose, a simple Representative Volume Element (RVE) analysis is created. The performance of the FEM code is very satisfying, the code being able to solve a 2D problem in linear elasticity with about 1 million degrees of freedom in around 30 seconds. Regarding the transverse modulus estimate, taking into account all the simplifications employed in the modeling, we can consider the result as reasonable. This project shows that a very good computational performance can be achieved even with a simple didactic code as a starting point.

The subject paper purportedly proposes a novel enriched finite element method for modeling problems with strong discontinuities such as those encountered in fracture mechanics. The purpose of this document is to demonstrate that the method in the subject paper (Non-nodal eXtended Finite Element Method, NXFEM) is conceptually identical to the Discontinuity-Enriched Finite Element Method (DE-FEM) [Int. J. Numer. Meth. Eng. 2017; 112:1589–1613] proposed by Aragón and Simone.

Crack propagation in polycrystalline specimens is studied by means of a generalized finite element method with linear elastic isotropic grains and cohesive grain boundaries. The corresponding mode-I intergranular cracks are characterized using a grain boundary brittleness criterion that depends on cohesive law parameters and average grain boundary length. It is shown that load–displacement curves for specimens with the same microstructure and for various cohesive law parameters can be obtained from a master load–displacement curve by means of simple linear elastic fracture mechanics scaling relations. This property is a consequence of the independence of intergranular crack paths from cohesive law parameters. Perfect scaling is obtained for cases characterized by the same grain boundary brittleness number, irrespective of its value, whereas scaling is approximated for cases with different but relatively large values of the grain boundary brittleness number. The former case corresponds to grain boundary traction profiles that are identical apart from a scale factor; in the latter case, a large grain boundary brittleness number implies similar, apart from a scale factor, traction profiles. By exploiting this property, it is demonstrated that computationally expensive simulations can be avoided above a certain grain boundary brittleness threshold value.

Fiber-based electrodes represent viable solutions for high-performance and multifunctional batteries. Thanks to the establishment of production techniques such as electrospinning, batteries can nowadays be devised using a fiber-reinforced composite material in which active and conductive material fibers are dispersed in a solid polymer electrolyte matrix. In order to maximize the active material utilization in fiber-based electrodes, the most suitable fiber arrangement can be identified so that internal pathways for electrons and ions are ensured. In particular, the optimal mixture of fibers (active and conductive) and electrolyte in structural batteries is a compromise between several requirements. First, conductive fibers have to form a conductive network for electrons. Second, the space left for the active material must be sufficient to guarantee a reasonable energy storage capacity. Third, mechanics requires enough fibers to attain a specific load bearing capacity without additional electrochemically-inactive reinforcement. Fourth, the solid polymer electrolyte must provide mechanical connection between fibers and, at the same time, the path for ionic conduction. The electrode design-battery performance relationship is investigated by means of numerical simulations. Three-dimensional composite structures are generated by randomly distributing fibers in the electrolyte hosting matrix. Effective electrode properties and charge/discharge performance are evaluated by means of Monte Carlo and finite element simulations. To ease the generation of the finite element mesh, fibers are reduced to mathematically equivalent one-dimensional objects using a mesh-independent embedded fiber method. In the numerical simulations, results of the dimensionally-reduced model are validated against reference finite element solutions.

One of the effective potentials that has proven to be very versatile and useful for describing metals is the modified embedded atom method (MEAM) potential. The reference-free version of the MEAM (RF-MEAM) potential provides more flexibility for fitting than the 2NN-MEAM because it also describes the pair potential as an explicit function. In this work, we present a methodology to fit RF-MEAM potentials to DFT data. We then evaluate the performance of the fitted potential by comparing MD simulations with experimental and DFT data. As an example, the methodology is applied to a binary and a quaternary alloy, namely NiTi and NbMoTaW. In the case of the equi-atomic NiTi shape memory alloy, our attention focuses on designing a potential that properly captures its mechanical behavior, given that the existing potentials fail to predict elastic constants in agreement with experiments. To reach our aim, we included the stress tensors of different high temperature NiTi configurations in the fitting database. The obtained RF-MEAM potential outperforms existing EAM and MEAM potentials in predicting the lattice and elastic constants of austenitic and martensitic phases as well as the corresponding transformation temperatures. To demonstrate the suitability of this methodology also for more complex systems, a RF-MEAM potential is fitted to model the multi-component NbMoTaW high-entropy alloy. Validation is achieved through comparison between observables obtained through the MD output and ab initio data. The article also reports key improvements to the optimization code MEAMfit v2 and the freely-available LAMMPS implementation of the RF-MEAM formalism. Most notably, resorting to analytic derivatives of the objective function with respect to the potential parameters rather than derivatives through finite differences, the time necessary for fitting has decreased by an order of magnitude.

We study the effect of mechanical stresses arising in solid polymer electrolytes (SPEs) on the electrochemical performance of lithium-ion (Li-ion) solid-state batteries. Time-dependent finite element analyses of interdigitated plate cells during a discharge process are performed with a constitutive model that couples ionic conduction within the SPE with its deformation field. Due to the coupled nature of the processes taking place in the SPE, the non-uniform ionic concentration profiles that develop during the discharge process induce stresses and deformations within the SPE; at the same time the mechanical loads applied to the cell affect the charge conduction path. Results of a parametric study show that stresses induced by ionic redistribution favor ionic transport and enhance cell conductivity-up to a 15% increase compared to the solution obtained with a purely electrochemical model. We observe that, when the contribution of the mechanical stresses is included in the simulations, the localization of the electric current density at the top of the electrode plates is more pronounced compared to the purely electrochemical model. This suggests that electrode utilization, a limiting factor for the design of three-dimensional battery architectures, depends on the stress field that develops in the SPE. The stress level is indeed significant, and mechanical failure of the polymer might occur during service. (C) 2018 The Authors. Published by Elsevier Ltd.