Shahed Rezaei

The optimal design and durable utilization of lithium-ion batteries necessitates an objective modeling approach to understand fracture and failure mechanisms. This paper presents a comprehensive chemo-mechanical modeling study focused on elucidating fracture-induced damage and degradation phenomena in the polycrystalline Li x Ni 0.5 Mn 0.3 Co 0.2 O 2 (NMC532) cathode. An innovative approach that utilizes image-based reconstructed 3D geometry as finite element (FE) mesh input is employed to enhance the precision in capturing the convoluted architecture and morphological features. For accurately representing the intricate crack configurations within the polycrystalline system, we adopted the cohesive phase-field fracture (CPF) model. Through the integration of advanced image-based geometry reconstruction technique and the promising CPF modeling approach, lithium (de) intercalation induced …

Physics‐informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have shown that when designing loss functions for many engineering problems, using first‐order derivatives and combining equations from both strong and weak forms can lead to much better accuracy, especially when there are heterogeneity and variable jumps in the domain. This new approach is called the mixed formulation for PINNs, which takes ideas from the mixed finite element method. In this method, the PDE is reformulated as a system of equations where the primary unknowns are the fluxes or gradients of the solution, and the secondary unknowns are the solution itself. In this work, we propose applying the mixed formulation to solve multi‐physical problems …

Anisotropic volume change of Ni-rich nickel-manganese-cobalt-oxide (NMC) during cycling significantly contributes to mechanical degradation, emerging as a primary factor leading to instability issues in high-capacity cathode active materials for lithium-ion batteries. Despite their commendable energy density, these challenges hinder the broader application of NMC, underscoring the need for rational analysis of and innovative solutions to address the associated mechanical instability. In this contribution, we utilize a chemo-mechanically coupled cohesive fracture model, complemented by its 3D finite element implementation, to simulate and analyze the performance and cracking behavior of polycrystalline high-Ni nickel-manganese-cobalt cathode active materials. Thereby the two-way coupling between mechanics and diffusion is regarded both in the bulk and at grain boundary. In particular, novel algorithms are introduced to model the electrolyte penetration along the inter-granular cracks, capturing its intricate impact on particle performance. Utilizing simulations on synthetic and reconstructed microstructure samples derived from experimental images, extensive parameter studies were conducted. These investigations unveiled the intricate influence of various microstructure aspects, encompassing grain morphology, grain/particle sizes, and texture. The findings indicate that secondary active material particles exhibiting smaller size and radially elongated primary particles, coupled with radially oriented high-diffusivity planes, demonstrate enhanced resistance to mechanical damage.

We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides information about the current material state (i.e., free energy, stress, and the evolution of internal variables) under any given loading scenario without requiring initial data. One advantage of this work is that it bypasses the repetitive Newton iterations needed to solve nonlinear equations in complex material models. Furthermore, after training, the proposed approach requires significantly less effort in terms of implementation and computing time compared to the traditional methods. The trained model can be directly used in any finite element package (or other numerical methods) as a user-defined material model. We tested this methodology on rate-independent processes such as the …

We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase contrast. Similar equations manifest in diverse applications like chemical diffusion, electrostatics, and Darcy flow. The neural network aims to establish the link between the complex thermal conductivity profiles and temperature distributions, as well as heat flux components within the microstructure, under fixed boundary conditions. A distinctive aspect is our independence from classical solvers like finite element methods for data. A noteworthy contribution lies in our novel approach to defining the loss function, based on the discretized weak form of the governing equation. This not only reduces the required order of derivatives but also eliminates the need for automatic differentiation in the construction of loss terms, accepting potential numerical errors from the chosen discretization method. As a result, the loss function in this work is an algebraic equation that significantly enhances training efficiency. We benchmark our methodology against the standard finite element method, demonstrating accurate yet faster predictions using the trained neural network for temperature and flux profiles. We also show higher accuracy by using the proposed method compared to purely data-driven approaches for unforeseen scenarios.

The local geometrical randomness of metal foams brings complexities to the performance prediction of porous structures. Although the relative density is commonly deemed as the key factor, the stochasticity of internal cell sizes and shapes has an apparent effect on the porous structural behavior but the corresponding measurement is challenging. To address this issue, this chapter is aimed to develop an assessment strategy for efficiently examining the foam properties by combining multiscale modeling and deep learning. The multiscale modeling is based on the finite element (FE) simulations employing representative volume elements (RVEs) with random cellular morphologies, mimicking the typical features of closed-cell aluminum foams. A deep learning database is constructed for training the designed convolutional neural networks (CNNs) to establish a direct link between the mesoscopic porosity …

To develop faster solvers for governing physical equations in solid mechanics, we introduce a method that parametrically learns the solution to mechanical equilibrium. The introduced method outperforms traditional ones in terms of computational cost while acceptably maintaining accuracy. Moreover, it generalizes and enhances the standard physics-informed neural networks to learn a parametric solution with rather sharp discontinuities. We focus on micromechanics as an example, where the knowledge of the micro-mechanical solution, i.e., deformation and stress fields for a given heterogeneous microstructure, is crucial. The parameter under investigation is the Young modulus distribution within the heterogeneous solid system. Our method, inspired by operator learning and the finite element method, demonstrates the ability to train without relying on data from other numerical solvers. Instead, we leverage ideas from the finite element approach to efficiently set up loss functions algebraically, particularly based on the discretized weak form of the governing equations. Notably, our investigations reveal that physics-based training yields higher accuracy compared to purely data-driven approaches for unseen microstructures. In essence, this method achieves independence from data and enhances accuracy for predictions beyond the training range. The aforementioned observations apply here to heterogeneous elastic microstructures. Comparisons are also made with other well-known operator learning algorithms, such as DeepOnet, to further emphasize the advantages of the newly proposed architecture.

In the context of computational modeling of fracture in chemo-mechanical environments, physically-sound and strong coupling between different fields is essential. Furthermore, our knowledge of the fracture in a purely mechanical setting should be extended to the new realm adequately. In this work, we apply the cohesive phase-field (CPF) fracture models to address damage initiation and progression in a chemo-mechanical coupled environment. Since CPF models are shown to be independent of the length scale parameter, such models allow a unified simulation framework for bulk and interface damages that concurrently and competitively occur in the battery materials. First, a thermodynamical framework is discussed to obtain all the possible coupling terms consistently. Through a systematic derivation from dissipation inequality and by performing various studies, we intend to comparatively demonstrate the role …

The surging interest in porous lightweight structures has been witnessed in recent years to pursue material innovations in broad engineering disciplines for sustainable developments and multifunctional proposes. Functionally graded (FG) porous composites represent a novel way to adjust mechanical characteristics by controlling the porosity distributions. However, the further advance in this field is challenged by the scale gap between mesoscopic and macroscopic aspects of porous structural analysis, i.e. how the local cellular morphologies impact the overall behaviors. The purpose of this paper is to bridge this gap by conducting a theoretical investigation on the performance of inclined self-weight sandwich beams with FG porous cores, where Young’s modulus is obtained with representative volume elements (RVEs) in a multiscale modeling study and depends on the cellular morphologies: average cell size …

This review presents a thorough survey of the roll bonding process with a focus on the bimetallic bars/tubes as well as the bonding models and criteria. The review aims to provide insight into cold, hot and cryogenic bonding mechanisms at the micro and atomic scale and act as a guide for researchers working on roll bonding, other joining processes and bonding simulation. Meanwhile, the shortcomings of roll bonding processes are presented from the aspect of formable shapes, while bonding models are shown from the aspect of calculation time, convergence, interface behavior of dissimilar materials as well as hot bonding status prediction. Two well-accepted numerical methodologies of bonding models, namely the contact algorithm and cohesive zone model (CZM) of bonding models and in simulations of the bonding process are highlighted. Particularly, recent advances and trends in the application of the …

The prediction of damage and cracking patterns in ceramic thin films plays a vital role in the optimal design thereof. In this study, we focus on developing a numerical framework to predict fracture in ceramic thin films. For accurate and efficient modeling, the fracture energy and the material strength (ultimate stress) are taken into account by the cohesive phase-field damage model. Moreover, we argue that the orientation of the grain morphology induces a preferential direction for the crack which serves as a weak spot for crack initiation and propagation. A novel equivalent fracture energy is introduced into the formulation to account for the effects of microstructure on the cracking behavior of thin films. On the experimental side, tensile tests on (V,Al)N and (V,Al)(O,N) thin films deposited on ductile substrates are performed. It has been shown that this approach is a fast and efficient tracking tool for determining the mode-I …

To circumvent a mesh dependency of damage models, non‐local approaches such as phase‐field and gradient‐extended damage models have shown a good capability and attracted a lot of attention for modeling fracture. These models can predict crack nucleation, kinking, and branching. The gradient‐extended formulation proposed by [1, 2], which includes a micromorphic degree of freedom for damage, is connected to a phase‐field damage model presented in [3]; by connecting fracture parameters in brittle fracture. The latter is followed by comparing the thermodynamic consistency of these models. Despite having similarities in the formulation, gradient‐extended models differ from the standard phase‐field ones by having a damage threshold. Besides that, the local iteration exists in the gradient‐extended damage models. By employing the cohesive phase‐field model or the Angiotensin type 1 (AT1), a …

The potential of the mixed formulation for physics-informed neural networks is investigated in order to find a solution for a non-uniform beam resting on an elastic foundation and subjected to arbitrary external loading. These types of structures are commonly encountered in civil engineering problems at larger scales, as well as in the design of new generation meta-materials at smaller scales. The mixed formulation approach aims to predict not only the primary variable itself but also its higher derivatives. In the context of this work, the primary variable is the beam deflection, while its higher-order derivatives are associated with the shear stress and moment within the beam structure. By employing this new methodology, it becomes possible to reduce the order of the derivatives in the physical constraints used for training the neural networks. As a result, significantly more accurate predictions can be achieved compared …

Thermal fracture is prevalent in many engineering problems and is one of the most devastating defects in metal additive manufacturing. Due to the interactive underlying physics involved, the computational simulation of such a process is challenging. In this work, we propose a thermo-mechanical phase-field fracture model, which is based on a thermodynamically consistent derivation. The influence of different coupling terms such as damage-informed thermomechanics and heat conduction and temperature-dependent fracture properties, as well as different phase-field fracture formulations, are discussed. The model is numerically implemented with the finite element method. Finally, the model is applied to simulate the hot cracking in additive manufacturing. Thereby not only the thermal strain but also the solidification shrinkage is considered. As for the thermal profile, both analytical temperature solution and …

The battery cell performance is determined by electro-chemo-mechanical mechanisms on different length scales. Though there exist multi-field multiscale simulation frameworks, the high computation cost prevents their wide application. It is even more challenging when it comes to all-solid-state batteries where the influence of the interface damage and delamination between the solid electrolyte and cathode active material plays a critical role in cell performance and degradation. In this contribution, we propose a novel multiscale strategy based on large datasets and machine learning. Thereby a large dataset of simulations is obtained at the microscale for electrolyte-active material two-phase representative elements by employing a coupled chemo-mechanical model with varying materials and state variables. The data is then used to train a surrogate model based on a neural network. The surrogate model is …

コウシツマク ニ オケル キレツ ハッセイ オヨビ シンテン オ モデリング スル タメ ノ ケツゴウリョク phase-field ソンショウ モデル ノ サイヨウ

Accurate forecasting of the lifetime and degradation mechanisms of lithium-ion batteries is crucial for their optimization, management, and safety while preventing latent failures. However, the typical state estimations are challenging due to complex and dynamic cell parameters and wide variations in usage conditions. Physics-based models need a tradeoff between accuracy and complexity due to vast parameter requirements, while machine-learning models require large training datasets and may fail when generalized to unseen scenarios. To address this issue, this paper aims to integrate the physics-based battery model and the machine learning model to leverage their respective strengths. This is achieved by applying the deep learning framework called physics-informed neural networks (PINN) to electrochemical battery modeling. The state of charge and state of health of lithium-ion cells are predicted by integrating the partial differential equation of Fick’s law of diffusion from a single particle model into the neural network training process. The results indicate that PINN can estimate the state of charge with a root mean square error in the range of 0.014% to 0.2%, while the state of health has a range of 1.1% to 2.3%, even with limited training data. Compared to conventional approaches, PINN is less complex while still incorporating the laws of physics into the training process, resulting in adequate predictions, even for unseen situations.

Despite their rapid emergence as the dominant paradigm for electrochemical energy storage, the full promise of lithium-ion batteries is yet to be fully realized, partly because of challenges in adequately resolving common degradation mechanisms. Positive electrodes of Li-ion batteries store ions in interstitial sites based on redox reactions throughout their interior volume. However, variations in the local concentration of inserted Li-ions and inhomogeneous intercalation-induced structural transformations beget substantial stress. Such stress can accumulate and ultimately engender substantial delamination and transgranular/intergranular fracture in typically brittle oxide materials upon continuous electrochemical cycling. This perspective highlights the coupling between electrochemistry, mechanics, and geometry spanning key electrochemical processes: surface reaction, solid-state diffusion, and phase nucleation …

We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides information about the current material state (i.e., free energy, stress, and the evolution of internal variables) under any given loading scenario without requiring initial data. One advantage of this work is that it bypasses the repetitive Newton iterations needed to solve nonlinear equations in complex material models. Additionally, strategies are provided to reduce the required order of derivation for obtaining the tangent operator. The trained model can be directly used in any finite element package (or other numerical methods) as a user-defined material model. However, challenges remain in the proper definition of collocation points and in integrating several non-equality constraints that become active or non-active simultaneously. We tested this methodology on rate-independent processes such as the classical von Mises plasticity model with a nonlinear hardening law, as well as local damage models for interface cracking behavior with a nonlinear softening law. Finally, we discuss the potential and remaining challenges for future developments of this new approach.

This study evaluates four fracture simulation methods, comparing their computational expenses and implementation complexities within the Finite Element (FE) framework when employed on multiphase materials. Fracture methods considered encompass the Cohesive Zone Model (CZM) using zero-thickness cohesive interface elements (CIEs), the Standard Phase-Field Fracture (SPFM) approach, the Cohesive Phase-Field fracture (CPFM) approach, and an innovative hybrid model. The hybrid approach combines the CPFM fracture method with the CZM, specifically applying the CZM within the interface zone. The finite element model studied is characterized by three specific phases: Inclusions, matrix, and interface zone. The thorough assessment of these modeling techniques indicates that the CPFM approach stands out as the most effective computational model provided that the thickness of the interface zone is not significantly smaller than that of the other phases. In materials like concrete the interface thickness is notably small when compared to other phases. This leads to the hybrid model standing as the most authentic finite element model, utilizing CIEs within the interface to simulate interface debonding. A significant finding from this investigation is that the CPFM method is in agreement with the hybrid model when the interface zone thickness is not excessively small. This implies that the CPFM fracture methodology may serve as a unified fracture approach for multiphase materials, provided the interface zone's thickness is comparable to that of the other phases. In addition, this research provides valuable insights that can advance efforts …

The goal of the current work is to explore direction-dependent damage initiation and propagation within an arbitrary anisotropic solid. In particular, we aim at developing anisotropic cohesive phase-field (PF) damage models by extending the idea introduced in Rezaei et al. (2021) for direction-dependent fracture energy and also anisotropic PF damage models based on structural tensors. The cohesive PF damage formulation used in the current contribution is motivated by the works of Lorentz et al. (2011), Wu and Nguyen (2018) and Geelen et al. (2019). The results of the such models are shown to be insensitive with respect to the length scale parameter for the isotropic case. This is because they manage to formulate the fracture energy as a function of diffuse displacement jumps in the localized damaged zone. In the present paper, we discuss numerical examples and details on finite element implementations …

The local geometrical randomness of metal foams brings complexities to the performance prediction of porous structures. Although the relative density is commonly deemed as the key factor, the stochasticity of internal cell sizes and shapes has an apparent effect on the porous structural behaviour but the corresponding measurement is challenging. To address this issue, we are aimed to develop an assessment strategy for efficiently examining the foam properties by combining multiscale modelling and deep learning. The multiscale modelling is based on the finite element (FE) simulation employing representative volume elements (RVEs) with random cellular morphologies, mimicking the typical features of closed-cell Aluminium foams. A deep learning database is constructed for training the designed convolutional neural networks (CNNs) to establish a direct link between the mesoscopic porosity characteristics and the effective Youngs modulus of foams. The error range of CNN models leads to an uncertain mechanical performance, which is further evaluated in a structural uncertainty analysis on the FG porous three-layer beam consisting of two thin high-density layers and a thick low-density one, where the imprecise CNN predicted moduli are represented as triangular fuzzy numbers in double parametric form. The uncertain beam bending deflections under a mid-span point load are calculated with the aid of Timoshenko beam theory and the Ritz method. Our findings suggest the success in training CNN models to estimate RVE modulus using images with an average error of 5.92%. The evaluation of FG porous structures can be significantly …

Physics informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. Here, the training of the network is equivalent to the minimization of a loss function that includes the governing (partial differential) equations (PDE) as well as initial and boundary conditions. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering problems. The main contribution of the current work is to promote using the spatial gradient of the primary variable as an output from separated neural networks. Later on, the strong form (given governing equation) which has a higher order of derivatives is applied to the spatial gradients of the primary variable as the physical constraint. In addition, the so-called energy form of the problem (which can be obtained from the weak form) is applied to the primary variable as an additional constraint …

Lithium-ion batteries are yet to realize their full promise because of challenges in the design and construction of electrode architectures that allow for their entire interior volumes to be reversibly accessible for ion storage. Electrodes constructed from the same material and with the same specifications, which differ only in terms of dimensions and geometries of the constituent particles, can show surprising differences in polarization, stress accumulation and capacity fade. Here, using operando synchrotron X-ray diffraction and energy dispersive X-ray diffraction (EDXRD), we probe the mechanistic origins of the remarkable particle geometry-dependent modification of lithiation-induced phase transformations in V2O5 as a model phase-transforming cathode. A pronounced modulation of phase coexistence regimes is observed as a function of particle geometry. Specifically, a metastable phase is stabilized for nanometre …

Substantial improvements in cycle life, rate performance, accessible voltage, and reversible capacity are required to realize the promise of Li-ion batteries in full measure. Here, we have examined insertion electrodes of the same composition (V2O5) prepared according to the same electrode specifications and comprising particles with similar dimensions and geometries that differ only in terms of their atomic connectivity and crystal structure, specifically two-dimensional (2D) layered α-V2O5 that crystallizes in an orthorhombic space group and one-dimensional (1D) tunnel-structured ζ-V2O5 crystallized in a monoclinic space group. By using particles of similar dimensions, we have disentangled the role of specific structural motifs and atomistic diffusion pathways in affecting electrochemical performance by mapping the dynamical evolution of lithiation-induced structural modifications using ex situ scanning …

In the current study, we investigated mechanical strength and fracture behavior of 3D-printed open-hole plates. To this aim, acrylonitrile butadiene styrene (ABS) and polylactic acid (PLA) are used for fabrication of specimens based on FDM technique. Since ratio of the specimen width to the hole diameter (W/D) has influence on the structural integrity of the part, we have printed specimens with two hole diameters. Particularly, specimens with W/D of 3 and 6 were designed and fabricated. Based on a series of tensile tests under static loading conditions, fracture load and stress–strain relationship of the plates are determined. Parallel to the experimental practice, a finite element model a series of finite element analyses were conducted to simulate cracking behavior of the aforementioned specimen. The model is based on phase-field fracture. The model parameters is calibrated based on the data from experiment or …

This paper combines the finite element (FE) homogenisation and structural assessments to conduct the multiscale modelling of laminated functionally graded (FG) porous beams made of closed-cell foams, with a focus on the beam buckling and vibration performances. In the FE homogenisation, representative volume elements (RVEs) are built up according to the relative densities, average cell sizes, and base material properties from foam samples. They are used to predict the foam Young’s modulus and verified against existing studies. A detailed investigation is then carried out to disclose the effects of RVE and porosity features, where the relative density is confirmed as the dominating factor in the calculation of foam modulus. Quantitative relations between pore structure and Young’s modulus are obtained via data fitting.In the subsequent structural assessment, the predicted Young’s modulus is employed in the …

The extrusion-based additive manufacturing (AM) is currently the most common there-dimensional (3D) printing for the fabrication of polymer components. In this study, the fracture behavior of 3D-printed polymer parts is investigated. To this aim, polylactic acid material (PLA) was used to print intact and defected specimens based on the fused deposition modeling (FDM) process. The specimens were printed with three different raster directions to determine their effect on the fracture behavior of the parts. Moreover, wood-reinforced PLA material was used to print another group of test coupons. All specimens were subjected to a series of tensile tests and their fracture behaviors are investigated. Based on the comparison of the results, the influence of reinforcement is determined. In addition, parallel to the experiments, a series of finite element analyses were conducted utilizing the anisotropic phase-field fracture model …

A seamless and lossless transition of the constitutive description of the elastic response of materials between atomic and continuum scales has been so far elusive. Here we show how this problem can be overcome by using artificial intelligence (AI). A convolutional neural network (CNN) model is trained, by taking the structure image of a nanoporous material as input and the corresponding elasticity tensor, calculated from molecular statics (MS), as output. Trained with the atomistic data, the CNN model captures the size- and pore-dependency of the material’s elastic properties which, on the physics side, derive from its intrinsic stiffness as well as from surface relaxation and non-local effects. To demonstrate the accuracy and the efficiency of the trained CNN model, a finite element method (FEM)-based result of an elastically deformed nanoporous beam equipped with the CNN as constitutive law is compared with …

We propose a new phase-field damage formulation which takes into account anisotropic damage evolution in solids. Such anisotropy projects itself in fracture energy values which depend on the direction of the crack surface. Therefore, instead of one constant scalar parameter for the fracture energy value, we use a direction-dependent fracture energy function. By incorporating a direction-dependent fracture energy function, only a single damage variable as well as a first order damage gradient need to be used within the standard phase-field damage model. This is in contrast to other available anisotropic phase-field models which typically use multiple variables or higher order gradient terms. To obtain values for the fracture energy function, atomistic calculations are performed. Here, molecular static simulations are utilized to calculate the energy of free surfaces within an Aluminum crystal. As a result, we report the …

In the present work, a novel cohesive discontinuous Galerkin (CDG) method is proposed to model interfacial failure of brittle materials. Before the failure, an incomplete interior penalty Galerkin (IIPG) variant of discontinuous Galerkin (DG) family is applied for the linear elasticity. Once the failure criterion is met, an extrinsic cohesive zone (CZ) model captures the failure behavior of the interface. Through application of the DG method in combination with reduced integration on the boundary terms, the locking problem of the bulk elements is solved as well as a realistic propagation of the crack is obtained. In addition, due to the presence of the DG elements prior to failure, remeshing of the interface during crack propagation is not required for the proposed extrinsic CZ model. Delamination of a composite structure is simulated in a numerical example. Furthermore, the performance of the CDG element formulation in …

Damage and fracture can be induced not only by mechanical loading but also due to chemical interactions within a solid. On one hand, species concentration may embrittle or toughen the material and on the other hand, the mechanical state adds additional driving force for diffusion. We propose a chemo-mechanically coupled cohesive fracture model with several novel features. It distinguishes the mode-dependent damage progression and its influence on lithium transport. Coupled with mode-dependent cohesive zone damage, the model recaptures both the normal and tangential transport behavior of lithium at the interface. Moreover, it tackles concentration-dependent crack initiation, various softening behavior, as well as the cyclic damage accumulation. The thermodynamic consistency of the proposed model with the mentioned features is demonstrated. The model is numerically implemented with the finite …

The unique mechanical properties and transport features of grain boundaries (GBs) in polycrystalline materials have been widely investigated. However, studies which focus on the unique chemo-mechanics phenomena resulting from GBs’ are exceedingly sparse. In this work, a thermodynamically consistent framework has been developed to explore the multi-physics coupling between mechanics and species diffusion. Constitutive laws for the bulk and the across-GB interaction laws have been derived for large deformations from the system free energies. A chemo-mechanically coupled cohesive zone model is developed which takes into account mode-dependent fracture properties in the presence of GBs. Polycrystalline LiNi x Mn y Co z O 2 (NMC) particles and Li x V 2 O 5 nanowires haveüeen selected to demonstrate the impact of GBs on the modeled and observed chemo-mechanics. The model has been …

In this study, the failure behavior at the interface of ductile materials is investigated. In order to capture the degradation of the tractions at the interface, a cohesive zone (CZ) model is applied. The choice of the type of the CZ approach, ie either intrinsic or extrinsic, brings about different drawbacks. The former includes an elastic regime at the interface prior to the failure, which can result in numerical difficulties whereas the latter necessitates the re-meshing of the structure during crack propagation. In order to overcome these problems, the incomplete interior penalty Galerkin variant of the discontinuous Galerkin (DG) method is applied both at the interface and in the bulk instead of the standard conforming finite element method. In addition, the application of the DG method enables to use nonmatching meshes in the discretized model. To treat the bulk, an elastoplastic material model with isotropic hardening as well as different hardening rules for small strains is incorporated into the DG framework. Two numerical examples are computed to study the convergence behavior of the new cohesive discontinuous Galerkin (CDG) method in comparison to that of the conventional models. The new CDG method outperforms the conventional CZ continuous Galerkin elements in the presence of locking effects as well as hanging nodes.

In this work, modeling of brittle failure of the interface for a linear elastic material is presented. The idea is to integrate a novel extrinsic cohesive zone model into the incomplete interior penalty Galerkin variant of the discontinuous Galerkin (DG) method. As a result, the initial stiffness in the prefailure regime is omitted without having to remesh the crack path during the crack propagation. The interface model is used in combination with different discretization techniques, including matching and nonmatching meshes. This is possible due to the DG method's weak continuity constraint. Moreover, the locking problem in the bulk is cured by the application of a reduced Gaussian integration scheme on the boundary terms. The performance of the new cohesive discontinuous Galerkin elements with different integration schemes is compared with one of the standard intrinsic cohesive models. Due to the elimination of locking …

Understanding and modeling the interface behavior is an important task for predicting materials response in various applications. To formulate the behavior of an arbitrary interface, one needs to construct the relation between acting tractions and displacement jumps at the interface. In addition to capturing the correct physics of the interface, the so-called traction–separation relation must also be thermodynamically consistent and satisfy the basic balance laws. Apart from many attempts in the literature to address these issues, a new and simple method to capture the complex mechanical behavior at an arbitrary interface is proposed. The new formulation is based on introducing a new quantity called “traction density”. As a result, the traction–separation relation for any arbitrary interface is automatically computed by integrating the traction density over the interface. The traction density can be formulated based on …

Ceramic matrix composites (CMCs) as an enhancement of classical technical ceramics overcome limitations such as low fracture toughness and brittle failure under mechanical or thermomechanical loading. Their low weight and high temperature stability makes them attractive for use in various fields, especially aerospace industry, where they improve engine efficiency as substitutions for metal components. Despite their positive attributes current CMCs lack well established material property design databases for a reliable use in critical aerospace structures. Demonstrating the durability and lifespan of this relatively new class of materials is the present task. Therefore their failure mechanisms need to be investigated further, taking into account the extensive range of temperatures the components are subjected to. This contribution deals with the successive development of a woven representative volume element (RVE) for arbitrary CMCs. In contrast to previously developed approaches, the introduced model combines various damage formulations. The fiber bridging effect is governed using a cohesive zone (CZ) formulation to adress the debonding mechanism in the weak interface between matrix and reinforcement and a continuum mechanical approach to account for matrix damage. To cover the temperature dependency of the material parameters, thermal coupling is included in both element formulations.

Despite the extensive use of mortar materials in constructions over the last decades, there is not yet a robust quantitative method, available in the literature, which can reliably predict mortar strength based on its mix components. This limitation is due to the highly nonlinear relation between the mortar's compressive strength and the mixed components. In this paper, the application of artificial neural networks for predicting the compressive strength of mortars has been investigated. Specifically, surrogate models (such as artificial neural network models) have been used for the prediction of the compressive strength of mortars (based on experimental data available in the literature). Furthermore, compressive strength maps are presented for the first time, aiming to facilitate mortar mix design. The comparison of the derived results with the experimental findings demonstrates the ability of artificial neural networks to approximate the compressive strength of mortars in a reliable and robust manner.