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.

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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.

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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.

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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.

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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.

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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.

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This paper presents a methodology for the analysis of three-dimensional static fractures in fiber-reinforced materials. Fibers are discretely modeled using a modification of the embedded reinforcement method with bond Slip (mERS) that allows its combination with a generalized finite element method (GFEM) for three-dimensional fractures. Since the GFEM mesh does not need to fit fracture surfaces or fibers, the GFEM–mERS can handle fibers bridging across crack faces at arbitrary angles. The method is verified against three-dimensional FEM solutions using conformal discretizations for crack surfaces and fiber boundaries. The comparison of the method against experimental data and convergence studies of the h- and p-version of the method is also presented.

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We report the results of a comparative analysis of mesh independent discrete inclusion models and point out some shortcomings of classical approaches in the approximation of the strain field across an inclusion (artificial continuity) and the slip profile along an inclusion (oscillatory behavior). We also present novel embedded reinforcement models based on partition of unity enrichment strategies, adaptive h-refinement, and order/regularity extensions. These novel models are assessed by means of mesh convergence studies and it is shown that they improve the quality of the solution by significantly decreasing local spurious oscillations in the slip profile along an inclusion.@en

FE² multiscale simulations of history-dependent materials are accelerated by means of a recurrent neural network (RNN) surrogate for the history-dependent micro level response. We propose a simple strategy to efficiently collect stress–strain data from the micro model, and we modify the RNN model such that it resembles a nonlinear finite element analysis procedure during training. We then implement the trained RNN model in the FE² scheme and employ automatic differentiation to compute the consistent tangent. The exceptional performance of the proposed model is demonstrated through a number of academic examples using strain-softening Perzyna viscoplasticity as the nonlinear material model at the micro level.

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We analyze the effects of mechanical stresses arising in a solid polymer electrolyte (SPE) on the electrochemical performance of the electrolyte component of a lithium ion battery. The SPE is modeled with a coupled ionic conduction-deformation model that allows to investigate the effect of mechanical stresses induced by the redistribution of ions. The analytical solution is determined for a uniform planar cell operating under galvanostatic conditions with and without externally induced deformations. The roles of the polymer stiffness, internally-induced stresses, and thickness of the SPE layer are investigated. The results show that the predictions of the coupled model can strongly deviate from those obtained with an electrochemical model—up to +38% in terms of electrostatic potential difference across the electrolyte layer—depending on the combination of material properties and geometrical features. The predicted stress level in the SPE is considerable as it exceeds the threshold experimentally detected for irreversible deformation or fracture to occur in cells not subjected to external loading. We show that stresses induced by external solicitations can reduce the concentration gradient of ions across the electrolyte thickness and prevent salt depletion at the electrode-electrolyte interface.@en

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.

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We report numerical evidence for neutrality of thin fibers to a prescribed uniform stress field in a fiber-reinforced composite. Elastic finite element analyses of fiber-reinforced composites are carried out with a conventional fully-resolved model and a novel dimensionally-reduced fiber model.The two modeling approaches are compared in the analysis of mechanical properties and matrix-fiber slip profiles. An analysis of the effectiveness of various fiber orientations with respect to the loading direction shows that the notion of inclusion neutrality, originally formulated for rigid line inclusions by Wang et al. [Journal of Applied Mechanics, 52(4), 814–822, 1985], holds also for linear elastic thin fibers with imperfect interface.@en

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.

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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.@en

We report the results of a computational study regarding the mechanical properties of a lithiated Si/SiO2 interface using reactive molecular dynamics. The study is motivated by an intended application of SiO2-coated Si
nanotubes as fibers in structural batteries with a fiber-reinforced composite architecture while serving as anodes. According to the results, main failure properties due to partly irreversible bond breakage during mechanical deformation are identified, indicating agreement with bond energy/bond order based estimates. Microscopic failure properties are also identified and interpreted in view of the observed processes of bonding degradation. In particular, the effect of Li distribution on the shear deformation response is evaluated as significant.@en

The study explores the use of a composite, graphitic carbon (GC) – sulfur (S) based cathode in laminated structural batteries. Specifically, failure by delamination is studied with regards to the applicability of a double-walled tube architecture obtained by coating the inner surfaces of hollow carbon nanofibers with sulfur. Differences between the material responses of various Li_X S (X ∈ (0, 2)) compounds under bulk-like and interface confined conditions are discussed in terms of the shear response of physically and chemically bonded interfaces, formed with non-functionalized and H/OH/O-functionalized GC surfaces. The study indicates that only a chemically bonded interface with non-functionalized GC yields bulk-compatible mechanical behavior, with the exception of concentrations of X ∈ (0.8, 1.1). To strengthen the interface at low Li concentrations, at which a pronounced inhomogeneity in mass density in terms of interface debonding occurs, a modified transition layer was tested. The results indicate a distinct improvement in terms of homogeneity of mass density and plastic strain localization. The effect of delithiation at high rates on the interface structural stability is investigated at different concentrations of Li in structures of initially uniform Li distribution. According to the results, delamination failure is likely to occur.

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This reactive molecular dynamics study explores the salt concentration dependence of the viscoelastic and mechanical failure properties of a poly(propylene glycol)/LiPF₆-based solid polymer electrolyte (SPE) at a graphitic carbon electrode interface. To account for the finite-size effect of interface-confined SPE films, the properties of two distinct film thicknesses are compared with the respective bulk properties. Additionally, the effect of uniaxial compression in the interface-normal direction on free energy profiles of Li-ion SPE-desolvation is studied.

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Two anisotropic stress-based gradient-enhanced damage models are proposed to address the issue of spurious damage growth typical of continuous standard gradient-enhanced damage models. Both models are based on a decreasing interaction length upon decreasing stresses and do not require additional model parameters or extra degrees of freedom when compared to standard gradient-enhanced models. It is observed that with the proposed models damage spreading is significantly reduced due to the occurrence of non-physical oscillations in the nonlocal strain field near the strain localization band. Model improvements to eliminate these strain oscillations upon vanishing length scale values are proposed. The capability of the models and their patched versions to correctly simulate damage initiation and propagation is investigated by means of mode-I failure, shear band and four-point bending tests.

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Pseudoelasticity in NiTi shape memory alloy single crystals depends on the loading direction. Here, we present a comprehensive study in which molecular dynamics simulations of austenitic bulk single crystals under strain-controlled tensile and compressive loading along the 〈110〉,〈111〉 and 〈100〉 directions are performed, and the mechanical response of the crystals are contrasted. All simulations are performed using the MEAM interatomic potential proposed by Ko et al. (2015). The transformation strains and the Young's modulus of the initial austenitic and the final martensitic phases are compared with values obtained from the lattice deformation model and experimental results from the literature. Results show that depending on orientation the transformation occurs either through the formation of martensitic Lüders bands or through the transient formation of a multivariant martensite which, upon reorientation, becomes a dominant final single variant. Simulations are also performed to assess the orientation-dependent behavior of nano-wires subjected to bending, since the flexibility of the wires is orientation dependent.

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We propose a computational procedure to assess size effects in nonfunctionalized single-walled carbon nanotube (CNT)-polymer composites. The procedure upscales results obtained with atomistic simulations on a composite unit cell with one CNT to an equivalent continuum composite model with a large number of CNTs. Molecular dynamics simulations demonstrate the formation of an ordered layer of polymer matrix surrounding the nanotube. This layer, known as the interphase, plays a central role in the overall mechanical response of the composite. Due to poor load transfer from the matrix to the CNT, the reinforcement effect attributed to the CNT is negligible; hence the interphase is regarded as the only reinforcement phase in the composite. Consequently, the mechanical properties of the interface and the CNT are not derived since their contribution to the elastic response of the composite is negligible. To derive the elastic properties of the interphase, we employ an intermediate continuum micromechanical model consisting of only the polymer matrix and a three-dimensional fiber representing the interphase. The Young's modulus and Poisson's ratio of the equivalent fiber, and therefore of the interphase, are identified through an optimization procedure based on the comparison between results from atomistic simulations and those obtained from an isogeometric analysis of the intermediate micromechanical model. Finally, the embedded reinforcement method is employed to determine the macroscopic elastic properties of a representative volume element of a composite with various fiber volume fractions and distributions. We then investigate the role of the CNT diameter on the elastic response of a CNT-polymer composite; our simulations predict a size effect on the composite elastic properties, clearly related to the interphase volume fraction.

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