Fatigue fracture simulations with the phase‐field method (PFM) lack efficiency due to the fine meshes required, especially when each load cycle is simulated explicitly. Recent developments in ...combining the phase‐field method for brittle fracture with the extended/generalised finite element method (XFEM/GFEM) show a remarkable reduction of the number of degrees of freedom and thus a reduction of computational effort while retaining or even improving accuracy. In this paper, the combined extended phase‐field method (XPFM) is expanded to fatigue processes in a two‐dimensional setting. A new stabilisation of the phase‐field transformation function is proposed and a convergence criterion for the nested staggered solution process and enrichment scheme update procedure as well as an adaptive integration technique for the non‐polynomial ansatz functions is incorporated. Several numerical examples emphasise the benefits and the efficiency of the newly developed method.
Summary
Phase‐field modeling, which introduces the regularized representation of sharp crack topologies, provides a convenient strategy for tackling 3D fracture problems. In this work, an adaptive ...isogeometric‐meshfree approach is developed for the phase‐field modeling of brittle fracture in a 3D polycrystalline material. The isogeometric‐meshfree approach uses moving least‐squares approximations to construct the equivalence between isogeometric basis functions and meshfree shape functions, thus inheriting the flexible local mesh refinement scheme from a meshfree method. This refinement scheme is improved by introducing an error estimator that includes both the phase field and its gradient. With the present approach, numerical implementations of the adaptive phase‐field modeling that introduces the anisotropy of fracture resistance in polycrystals are proposed. In this way, propagating cracks can be dynamically tracked, and the mesh near cracks is refined in a meshfree manner without requiring a priori knowledge of crack paths. Furthermore, the intergranular and transgranular crack propagation patterns in polycrystalline materials can be simulated by the present approach. A series of numerical examples that deal with the isotropic and anisotropic fracture are investigated to demonstrate the robustness and effectiveness of the proposed approach.
With the theme of fracture of finite-strain plates and shells based on a phase-field model of crack regularization, we introduce a new staggered algorithm for elastic and elasto-plastic materials. To ...account for correct fracture behavior in bending, two independent phase-fields are used, corresponding to the lower and upper faces of the shell. This is shown to provide a realistic behavior in bending-dominated problems, here illustrated in classical beam and plate problems. Finite strain behavior for both elastic and elasto-plastic constitutive laws is made compatible with the phase-field model by use of a consistent updated-Lagrangian algorithm. To guarantee sufficient resolution in the definition of the crack paths, a local remeshing algorithm based on the phase-field values at the lower and upper shell faces is introduced. In this local remeshing algorithm, two stages are used: edge-based element subdivision and node repositioning. Five representative numerical examples are shown, consisting of a bi-clamped beam, two versions of a square plate, the Keesecker pressurized cylinder problem, the Hexcan problem and the Muscat-Fenech and Atkins plate. All problems were successfully solved and the proposed solution was found to be robust and efficient.
The domain is an important characteristic of ferroelectric materials, and the type of domain can have significant effects on the performance of ferroelectric materials. In particular, the unique ...wake-up and fatigue effects of Hf0.5Zr0.5O2 (HZO) films severely restrict improvements in terms of film performance. Recently, using integrated differential phase contrast (iDPC) scanning transmission electron microscopy (STEM) imaging, we observed the existence of intrinsic tail-to-tail 90° domain structures, charged domain walls (CDWs), and polarization relaxation on the TiN/HZO/TiN interfaces of HZO films. Based on this experimental investigation, we establish a phase-field model of the tail-to-tail 90°CDWs based on the time-dependent Ginzburg–Landau equation. In our model, the tail-to-tail 90°CDW affects the mesoscopic domain switching through a built-in electric field, which, in turn, affects the macroscopic ferroelectric properties of the thin film. The following conclusions are drawn: (a) the CDWs that are distributed horizontally or vertically along the thickness of the film cause a A-wake-up effect (antiferroelectric-like wake-up) with double hysteresis loops or a S-wake-up effect (spindle-like wake-up), with thick portions in the middle and both ends points of the hysteresis loop; (b) the S-wake-up caused by the CDWs distributed along the thickness of the film performs badly in fatigue tests and is easier to break down. The model proposed herein reveals the mechanism of the wake-up effect in hafnium oxide-based ferroelectric films. It provides a theoretical basis for the development of a new type of hafnium oxide-based ferroelectric memory system.
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Nonuniform electrodeposition of lithium during charging processes is the key issue hindering development of rechargeable Li metal batteries. This deposition process is largely controlled by the solid ...electrolyte interphase (SEI) on the metal surface and the design of artificial SEIs is an essential pathway to regulate electrodeposition of Li. In this work, an electro‐chemo‐mechanical model is built and implemented in a phase‐field modelling to understand the correlation between the physical properties of artificial SEIs and deposition of Li. The results show that improving ionic conductivity of the SEI above a critical level can mitigate stress concentration and preferred deposition of Li. In addition, the mechanical strength of the SEI is found to also mitigate non‐uniform deposition and influence electrochemical kinetics, with a Young's modulus around 4.0 GPa being a threshold value for even deposition of Li. By comparison of the results to experimental results for artificial SEIs it is clear that the most important direction for future work is to improve the ionic conductivity without compromising mechanical strength. In addition, the findings and methodology presented here not only provide detailed guidelines for design of artificial SEI on Li‐metal anodes but also pave the way to explore strategies for regulating deposition of other metal anodes.
An electro‐chemo‐mechanical model is built and implemented in phase‐field modelling to understand the correlation between the physical properties of artificial solid electrolyte interphases (SEIs) and the electrodeposition of Li. Both the ionic conductivity and mechanical strength of SEIs are found to be crucial to electrochemical kinetics the and resulting morphology. The direction for uniform electrodeposition is to improve ionic conductivity without compromising the mechanical strength of SEIs.
Understanding the dielectric breakdown behavior of polymer nanocomposites is crucial to the design of high‐energy‐density dielectric materials with reliable performances. It is however challenging to ...predict the breakdown behavior due to the complicated factors involved in this highly nonequilibrium process. In this work, a comprehensive phase‐field model is developed to investigate the breakdown behavior of polymer nanocomposites under electrostatic stimuli. It is found that the breakdown strength and path significantly depend on the microstructure of the nanocomposite. The predicted breakdown strengths for polymer nanocomposites with specific microstructures agree with existing experimental measurements. Using this phase‐field model, a high throughput calculation is performed to seek the optimal microstructure. Based on the high‐throughput calculation, a sandwich microstructure for PVDF–BaTiO3 nanocomposite is designed, where the upper and lower layers are filled with parallel nanosheets and the middle layer is filled with vertical nanofibers. It has an enhanced energy density of 2.44 times that of the pure PVDF polymer. The present work provides a computational approach for understanding the electrostatic breakdown, and it is expected to stimulate future experimental efforts on synthesizing polymer nanocomposites with novel microstructures to achieve high performances.
A comprehensive phase‐field model is developed to investigate the breakdown behavior of polymer nanocomposites with different microstructures under electrostatic stimuli, whose results agree with existing experimental measurements. Based on the phase‐field model, a high throughput calculation is performed to design and optimize a sandwich microstructure for PVDF–BaTiO3 nanocomposites, obtaining an enhanced energy density of 2.44 times than that of the pure polymer.
The next‐generation wearable biosensors with highly biocompatible, stretchable, and robust features are expected to enable the change of the current reactive and disease‐centric healthcare system to ...a personalized model with a focus on disease prevention and health promotion. Herein, a muscle‐fiber‐inspired nonwoven piezoelectric textile with tunable mechanical properties for wearable physiological monitoring is developed. To mimic the muscle fibers, polydopamine (PDA) is dispersed into the electrospun barium titanate/polyvinylidene fluoride (BTO/PVDF) nanofibers to enhance the interfacial‐adhesion, mechanical strength, and piezoelectric properties. Such improvements are both experimentally observed via mechanical characterization and theoretically verified by the phase‐field simulation. Taking the PDA@BTO/PVDF nanofibers as the building blocks, a nonwoven light‐weight piezoelectric textile is fabricated, which hold an outstanding sensitivity (3.95 V N−1) and long‐term stability (<3% decline after 7,400 cycles). The piezoelectric textile demonstrates multiple potential applications, including pulse wave measurement, human motion monitoring, and active voice recognition. By creatively mimicking the muscle fibers, this work paves a cost‐effective way to develop high‐performance and self‐powered wearable bioelectronics for personalized healthcare.
To mimic muscle fibers, polydopamine is dispersed into the electrospun barium titanate/polyvinylidene fluoride nanofibers to enhance the interfacial‐adhesion, mechanical strength, and piezoelectric properties. The muscle‐fiber‐inspired nonwoven piezoelectric textile is demonstrated for pulse wave measurement, human motion monitoring, and active voice recognition.
This paper proposes a phase field model for fracture in poroelastic media. The porous medium is modeled based on the classical Biot poroelasticity theory and the fracture behavior is controlled by ...the phase field model. Moreover, the fracture propagation is driven by the elastic energy where the phase field is used as an interpolation function to transit fluid property from the intact medium to the fully broken one. We use a segregated (staggered) scheme and implement our approach in Comsol Multiphysics. The proposed model is verified by a single-phase solid subjected to tension and a 2D specimen subjected to an increasing internal pressure. We also compare our results with analytical solutions. Finally, we show 2D and 3D examples of internal fluid injection to illustrate the capability of the proposed approach.
•A phase-field modeling approach of fracture propagation in poroelastic media is proposed.•The fracture propagation is driven by the elastic energy and no stress threshold is set.•2D and 3D examples are presented.
The phase-field method is lately one of the most popular approaches for modelling of complex fracture phenomena. As known, the displacement field and phase-field variable cannot be determined ...simultaneously, except for easy problems, due to non-convexity of the energy functional. As a remedy, several staggered solution strategies have been proposed, where two PDE system is solved. Materials produced by powder metallurgy, such as sintered materials are increasingly in use. Compared to materials produced by traditional metallurgical production procedures, they possess exceptionally good vibration and noise reduction properties, and high rate of material utilisation. This makes this class of materials highly attractive for application in many fields of industry, especially for production of the complex geometry components. In this work, experimental investigation results performed on Astaloy Mo+0.2C, with density 6.5 g/cm3, will be used for validation of the phase field staggered algorithm. The proposed algorithm consists of two mesh layers (displacement- and phase field mesh layer), and it is implemented into FE software Abaqus via user subroutines UMAT and UEL. The numerical results obtained show good agreement to experimental testing.
We study microstructure selection during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with ...three-dimensional phase-field simulations. We explore a range of temperature gradient G and growth velocity V and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing Λ and tip radius ρ. While ρ shows a good agreement between experimental measurements and dendrite growth theory, with ρ∼V−1/2, Λ is observed to increase with V (∂Λ/∂V>0), in apparent disagreement with classical scaling laws for primary dendritic spacing, which predict that ∂Λ/∂V<0. We show through simulations that this trend inversion for Λ(V) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical diffusion boundary-layer approximation to semi-quantitatively incorporate the effect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely diffusive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V. We explain the observed inversion of ∂Λ/∂V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.
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