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Employing direct numerical simulations, we investigate water and water-glycerol (85 wt%) droplets (∼ 25 µL) moving on smooth surfaces, with contact angles of around 90 ∘ , at varying inclinations. Our focus is on elucidating the relative contribution of local viscous forces in the wedge and bulk regions in droplets to the total viscous force. We observe that, for fast-moving droplets, both regions contribute comparably, while the contribution of the wedge region dominates in slow-moving cases. Comparisons with existing estimates reveal the inadequacy of previous predictions in capturing the contributions of wedge and bulk viscous forces in fast-moving droplets. Furthermore, we demonstrate that droplets with identical velocities can exhibit disparate viscous forces due to variations in internal fluid dynamics. [ABSTRACT FROM AUTHOR]

Many geo‐engineering applications, for example, enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase‐field method has grown in popularity as a valid approach to modeling hydraulic fracturing because of the ease of handling complex fracture propagation geometries. However, existing phase‐field methods cannot appropriately capture nucleation of hydraulic fractures because their formulations are solely energy‐based and do not explicitly take into account the strength of the material. Thus, in this work, we propose a novel phase‐field formulation for hydraulic fracturing with the main goal of modeling fracture nucleation in porous media, for example, rocks. Built on the variational formulation of previous phase‐field methods, the proposed model incorporates the material strength envelope for hydraulic fracture nucleation through two important steps: (i) an external driving force term, included in the damage evolution equation, that accounts for the material strength; (ii) a properly designed damage function that defines the fluid pressure contribution on the crack driving force. The comparison of numerical results for two‐dimensional test cases with existing analytical solutions demonstrates that the proposed phase‐field model can accurately model both nucleation and propagation of hydraulic fractures. Additionally, we present the simulation of hydraulic fracturing in a three‐dimensional domain with various stress conditions to demonstrate the applicability of the method to realistic scenarios. [ABSTRACT FROM AUTHOR]

Metal foams constitute a promising and emerging material class in the context of lightweight construction. There exists a variety of different foam topologies, on which resulting mechanical properties depend. To maximize the potential of foams in material use under mechanical load, the present work addresses the question how different geometrical parameters influence the material behaviour. Therefore, an algorithm for digital generation and design of open pore foam structures is presented, that allows to regulate the geometry precisely. A method for retrieving effective mechanical properties from numerical simulations of compression tests in the elastic regime is introduced. Additionally, the representativeness of foam volumes considered for simulations is investigated. This yields a fully digital workflow, which enables the investigation of geometry influence on mechanical properties. This approach is used to conduct simulation studies on generated foam structures with a systematic variation of geometrical parameters. Herein, a range of effective Young's moduli varying by up to a factor of 1.3 for different foam structures at the same porosity is found. This shows a significant impact of the foam geometry on the elastic properties of metal foams. The presented methodology yields insights, which can guide design and optimization of materials for specific applications. [ABSTRACT FROM AUTHOR]

Martensite is a common metallographic structure. Accurately revealing the objective law of the martensite transformation process is of great significance for controlling material organization and design materials. Herein, based on the phase‐field method, a 3D three‐variant martensite transformation model from the metastable to steady state is established based on the Khachaturyan. A. G. dislocation dynamic model. The transformation mechanism of martensite is analyzed and the transformation law and the law of growth behavior of variants is obtained. The research reveals the growth mechanism of martensite in multivariant martensite transformation, verifies the microstructure of steel after the quenching process, and proposes the "phagocytic" behavior of martensite transformation process and the prediction method of transforming variants. Finally, an interpretation of the interface fluctuations and residual austenite appearing during the transformation process is made. Herein, the objective law of martensite transformation is revealed, the universal prediction of martensite transformation morphology is realized, and an important theoretical basis for quenching tissue regulation and large‐scale high‐precision phase‐transition simulation is provided. [ABSTRACT FROM AUTHOR]

In the present study, a general numerical approach, consisting of a consistent limiter and the multiphase reduction-consistent formulation , is developed to solve the multiphase Euler/Phase-Field model for compressible N -phase (N ⩾ 1) flows in a consistent and conservative fashion. The proposed method is general in the sense that it admits N different phases and is not restricted to a specific Phase-Field formulation. Not only is the volume fraction bounded and the mass non-negative, the volume fractions also sum up to unity, preventing the production of fictitious phases, local voids, or overfilling. Velocity, pressure, and temperature equilibria are maintained across material interfaces. Various compressible N -phase problems including shocks and interfaces are performed to verify the analysis and demonstrate the efficacy of the method for N ⩾ 2. Unphysical behavior in N -phase calculations (production of fictitious phases, local voids, and overfilling) due to inappropriate numerical treatment is discussed. Three variants for the Phase-Field mechanism are proposed, one of which is most efficient with increasing number of phases. Including the Phase-Field mechanism produces controllable interface thickness, thus effectively preventing numerical mixing of different phases due to numerical diffusion in shock-capturing schemes. • A general numerical approach is developed for compressible N-phase flows. • A consistent limiter prevents fictitious phases, local voids, or overfilling. • The multiphase reduction-consistent formulation tackles the Phase-Field mechanisms. • The proposed approach maintains equilibrium and preserves physical bounds. • The Phase-Field mechanism prevents the numerical mixing of different phases. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present a phase-field method applied to the fluid-based shape optimization. The fluid flow is governed by the incompressible Navier–Stokes equations. A phase field variable is used to represent material distributions and the optimized shape of the fluid is obtained by minimizing the certain objective functional regularized. The shape sensitivity analysis is presented in terms of phase field variable, which is the main contribution of this paper. It saves considerable amount of computational expense when the meshes are locally refined near the interfaces compared to the case of fixed meshes. Numerical results on some benchmark problems are reported, and it is shown that the phase-field approach for fluid shape optimization is efficient and robust. [ABSTRACT FROM AUTHOR]

A key challenge with interface-capturing methods for compressible multiphase flows is that the numerical diffusion of upwind schemes causes material interfaces to continuously diffuse over time, possibly in a non-uniform fashion. In the present study, a consistent and conservative Phase-Field model for compressible multiphase flows is derived to control mixing between different fluids at material interfaces due to numerical diffusion. The model is general as it admits an arbitrary number of phases and has no prior assumption of the formulation of the Phase-Field mechanism. Necessary physical constraints to formulate the Phase-Field mechanism are obtained by analyzing physical principles, including the second law of thermodynamics. To numerically solve the model, two consistency requirements and a general numerical strategy, called reduction consistent formulation , are proposed. The proposed approach is consistent, conservative, bound/positivity preserving for the volume fraction/mass, and prevents spurious errors at interfaces. Various two-phase compressible flow problems including shocks and interfaces are performed to verify the analysis and demonstrate the efficacy of the method. Finally, temperature equilibrium and the incompressible limit are also discussed. [ABSTRACT FROM AUTHOR]

The effects of the antiphase domain (APD) and the elastic energy on the morphology evolution of γ′ precipitates in Ni-Al binary alloy during aging process are studied with the phase-field method. The merging-splitting phenomenon between the two neighboring γ′ precipitates is observed. The changes of γ′ area fraction and average γ′ size are analyzed for different APDs and for different elastic energies, respectively. It is shown that the merging-splitting phenomenon may occur when the radii of neighboring γ′ precipitates with different APDs are smaller than 24 nm and the critical size for the merged γ′ precipitate splitting is about 108 nm. Besides, the coarsening of γ′ precipitates is significantly impeded by the APDs but accelerated by the elastic energy, and the change of average γ′ size can be divided into two stages with different mechanisms. [ABSTRACT FROM AUTHOR]

In heterogeneous materials, such as fiber-reinforced composites, composite laminates, and coating systems, failure depends on the fracture behavior of the component materials and their interfaces. Modeling crack evolution in heterogeneous materials has been a significant challenge due to the complex interactions between the cracking at the interface and within the material. This paper proposes a cohesive phase-field model based on diffused interface to deal with failure at interfaces. The effective interfacial fracture toughness is obtained based on the fracture toughness of the diffused interface being equivalent to a sharp representation. The effective interfacial fracture strength is approximated using the brittle fracture condition. Then, we propose an approach to minimize the modification of the interfacial fracture parameters. The novelties of this approach are that 1) it is flexible enough to handle brittle and cohesive failure in the interface and bulk; 2) it can capture the crack nucleation at weakly singular interfaces in heterogeneous materials; and 3) compared with other approaches, the calculated fracture behavior is insensitive to the width of the diffused interface. The approach is verified under cases of brittle and cohesive failure. In addition, we demonstrate the approach in describing the fracture behavior of fiber-reinforced composites and ceramic coating systems, finding it to conform exactly with theoretical and experimental results. Hence, the proposed approach shows great potential in predicting crack evolution in heterogeneous materials. [ABSTRACT FROM AUTHOR]

In this article, we focus on the validation of Francfort and Marigo’s variational approach to fracture based on some classical fracture experiments. We show that this approach can be used to faithfully account for unknown crack paths even for complex loadings and geometry. We revisit the backtracking algorithm, aimed at avoiding some spurious local minimizers of the total fracture energy and introduce a variant: the deep backtracking algorithm. [ABSTRACT FROM AUTHOR]

Abstract: The coarsening kinetics of Cu-rich precipitates in an α-Fe matrix for thermally aged Fe–Cu alloys at temperatures above 700°C is studied using a kinetic Monte Carlo (KMC) simulation and a phase-field method (PFM). In this work, the KMC approach adequately captures the early stage of the system evolution which involves nucleation, growth and coarsening, while the PFM provides a suitable framework for studying late-stage coarsening at large precipitate volume fraction regimes. Hence, both models complement each other by transferring the results of KMC along with precipitate–matrix interface energies from a broken-bond model to a quantitative PFM based on a grand chemical potential formulation and the CALPHAD database. Furthermore, molecular dynamics simulations provide information on the structural coherency of the precipitates and hence justify the sequential parameter transfer. We show that our PFM can be validated quantitatively for the Gibbs–Thomson effect and that it also predicts the coarsening kinetics correctly. It is found that the kinetics closely follow the LSW (Lifshitz–Slyozov–Wagner) law, whereas the coarsening rate constant increases with an increase in volume fraction of precipitates. [Copyright &y& Elsevier]

We introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase-field method. In the basic formulation we have a PDE-constrained optimization problem, where the finite element and design analysis are solved simultaneously. The starting point of the relaxation is a reformulation of the material problem involving linear and 0-1 constraints only. The 0-1 constraints are then relaxed and approximated by a Cahn—Hilliard-type penalty in the objective functional, which yields convergence of minimizers to 0-1 designs as the penalty parameter decreases to zero. A major advantage of this kind of relaxation opposed to standard approaches is a uniform constraint qualification that is satisfied for any positive value of the penalization parameter. The relaxation scheme yields a large-scale optimization problem with a high number of linear inequality constraints. We discretize the problem by finite elements and solve the arising finite-dimensional programming problems by a primal-dual interior point method. Numerical experiments for problems with local stress constraints based on different criteria indicate the success and robustness of the new approach. [ABSTRACT FROM AUTHOR]

Abstract: The integration of the laser annealing process in metal-oxide-semiconductor (MOS) technology requires predictive codes for the simulation of the material modification due to the interaction between the laser radiation and the structure. These computational tools have a two-fold aim, i.e. (a) the estimate of the heat sources space distribution in the specimen, and (b) the simulation of the phenomena occurring inside the specimen during the irradiation (thermal field evolution, melting and re-growth of localised zones, dopant re-distribution). Our modelling is based on a coupled finite-difference-time-domain and phase-field method, which is applied in the simulation of the irradiation and the structural evolution, respectively. We considered a simulation framework of a typical transistor structure, i.e. the implanted impurity profiles in two-dimensional (2D) samples containing a SiO2/a-Si/c-Si stack. The model is calibrated for the cases of different impurity atoms. Our results demonstrate the necessity of a complete numerical approach. In particular, the effects of the device geometry and the optical/thermal properties of the material used are discussed in detail. [Copyright &y& Elsevier]

• Variational phase-field adhesive/brittle fracture model. • Electromechanical resonant ice protection systems. • Numerical experiments to highlight the fracture path leading to ice shedding. • Adhesive modelling at the ice/substrate interface. • Choice of input parameters. Electromechanical resonant de-icing systems provide a low-energy solution against ice accumulation on aircraft. Recent researches show a growing interest towards these systems in the context of more electrical aircraft. Electromechanical de-icing systems consists in electric actuators producing stress within the ice, through micro-vibrations of the surface to be protected, leading to bulk or adhesive failure and, ultimately, ice shedding. The understanding of the mechanisms at play is of prime importance in order to design efficient ice protection systems. Despite a large number of studies in the literature, there is still a lack when dealing with fracture propagation phenomena in this context. In this work the authors propose a model based on the well established phase-field variational approach to fracture. The approach is applied to the study of crack propagation and debonding of ice under the effect of an electromechanical resonant de-icing system. Numerical experiments are performed in order to assess possible ice shedding mechanisms. [ABSTRACT FROM AUTHOR]