On the physical interpretation of material parameters in phase field models for ferroelectrics

This publication intends to clarify the relations between the free energy expansion and the choice of the order parameter in phase field models for ferroelectrics. The free energy is expanded to include the piezoelectric coupling terms, reflecting the symmetry properties of the material below the Curie temperature. The order parameter can then be interpreted as the material polarization less than the dielectric and piezoelectric contributions. Furthermore, a 1d reduction of the problem is used to identify the physical meaning of the remaining model parameters. The theoretical results are verified by numerical simulations of 180^? and 90^? domain walls. Both the static case, where the emphasis lies on the specific energy and the interface width, and the dynamic case, where interfaces are subjected to an electric driving field, are considered in the simulations.     

Generation of polygonal gas interfaces by soap film for Richtmyer–Meshkov instability study

A simple method of generating polygonal gas interfaces is proposed by using the soap film technique. Thin pins are used as angular vertexes to connect the adjacent sides of polygonal soap films in order to avoid the pressure singularities around the vertexes caused by the surface tension. As a demonstration, three polygonal interfaces (i.e., square, equilateral triangle and diamond) are created in the test section of a shock tube. Experiments are then carried out for a planar shock wave (Mach number about 1.2) interacting with air/SF₆ polygonal interfaces. Numerical simulations are also performed to validate the proposed method of the interface formation. Wave systems and interface structures can be clearly identified in experimental schlieren images and agree well with the numerical results. It is also indicated that the presences of thin pins and fine chamfers only have limited effects on the interface evolution and can be ignored at the very early stage. Experimental and numerical results about the movement of the distorted interface, the width and height of the interface structures are further compared and good agreement is achieved. It is then concluded that the polygonal interface formed by the proposed method is applicable for the Richtmyer–Meshkov instability study.     

A Hybrid RANS/LES Simulation of Turbulent Channel Flow

Hybrid models combining large eddy simulation (LES) with Reynolds-averaged Navier–Stokes (RANS) simulation are expected to be useful for wall modeling in the LES of high Reynolds number flows. Some hybrid simulations of turbulent channel flow have a common defect; the mean velocity profile has a mismatch between the RANS and LES regions due to a steep velocity gradient at the interface. This mismatch is reproduced and examined using a simple hybrid model; the Smagorinsky model is switched to a RANS model increasing the filter width. It is suggested that a rapid spatial variation in the eddy viscosity is responsible for an underestimate of the grid-scale shear stress and for the steep velocity gradient. To reduce the mean velocity mismatch a new scheme is proposed; additional filtering is introduced to define two kinds of velocity components at the interface between the two regions. The two components are used to remove inconsistency in the velocity equations due to a rapid variation in the filter width. Using the new scheme, simulations of channel flow are carried out with the simple hybrid model. It is shown that the grid-scale shear stress becomes large enough and most of the mean velocity mismatch is removed. Simulations for higher Reynolds numbers are carried out with the k–ε model and the one-equation subgrid-scale model. Although it is necessary to improve the turbulence models and the treatment of the buffer region, the new scheme is shown to be effective for reducing the mismatch and to be useful for developing better hybrid simulations. Received 5 April 2002 and accepted 8 January 2003 Published online 25 March 2003 Communicated by M.Y. Hussaini     

A hybrid Lagrangian–Eulerian particle‐level set method for numerical simulations of two‐fluid turbulent flows

A coupled Lagrangian interface‐tracking and Eulerian level set (LS) method is developed and implemented for numerical simulations of two‐fluid flows. In this method, the interface is identified based on the locations of notional particles and the geometrical information concerning the interface and fluid properties, such as density and viscosity, are obtained from the LS function. The LS function maintains a signed distance function without an auxiliary equation via the particle‐based Lagrangian re‐initialization technique. To assess the new hybrid method, numerical simulations of several ‘standard interface‐moving’ problems and two‐fluid laminar and turbulent flows are conducted. The numerical results are evaluated by monitoring the mass conservation, the turbulence energy spectral density function and the consistency between Eulerian and Lagrangian components. The results of our analysis indicate that the hybrid particle‐level set method can handle interfaces with complex shape change, and can accurately predict the interface values without any significant (unphysical) mass loss or gain, even in a turbulent flow. The results obtained for isotropic turbulence by the new particle‐level set method are validated by comparison with those obtained by the ‘zero Mach number’, variable‐density method. For the cases with small thermal/mass diffusivity, both methods are found to generate similar results. Analysis of the vorticity and energy equations indicates that the destabilization effect of turbulence and the stability effect of surface tension on the interface motion are strongly dependent on the density and viscosity ratios of the fluids. Copyright © 2007 John Wiley & Sons, Ltd.     

Multiple bifurcations and local energy minimizers in thermoelastic martensitic transformations

Thermoelastic martensitic transformations in shape memory alloys can be modeled on the basis of nonlinear elastic theory.Microstructures of fine phase mixtures are local energy minimizers of the total energy.Using a one-dimensional effective model,we have shown that such microstructures are inhomogeneous solutions of the nonlinear Euler-Lagrange equation and can appear upon loading or unloading to certain critical conditions,the bifurcation conditions.A hybrid numerical method is utilized to calculate the inhomogeneous solutions with a large number of interfaces.The characteristics of the solutions are clarified by three parameters:the number of interfaces,the interface thickness,and the oscillating amplitude.Approximated analytical expressions are obtained for the interface and inhomogeneity energies through the numerical solutions.     

Damping of mesh-induced errors in Free-Lagrange simulations of Richtmyer-Meshkov instability

Mesh-induced errors at material interfaces are identified as a source of unphysical behaviour in Lagrangian numerical simulations of Richtmyer-Meshkov instability. The mesh geometry introduces interface perturbations with wavelengths of the same order as the mesh resolution. When a shock propagates through the interface, these perturbations can grow, severely contaminating the predicted interface development. Here an algorithm is presented which damps small-scale interface perturbations. A body force is applied at the interface which depends upon the disturbance amplitude and growth rate, and which resembles surface tension. Using this technique, qualitative improvements are obtained in Free-Lagrange simulations of single-mode Richtmyer-Meshkov instability. Growth rate behaviour and the evolution of the instability are seen to agree well with previously published results. Received 9 March 2000 / Accepted 30 May 2000     

On a relation between the volume of fluid,level-set and phase field interface models

This paper discusses a relation between the re-initialization equation of the level-set functions derived by Wacławczyk [J. Comput. Phys., 299 (2015)] and the condition for the phase equilibrium provided by the stationary solution to the modified Allen-Cahn equation [Acta Metall., 27 (1979)]. As a consequence, the statistical model of the non-flat interface in the state of phase equilibrium is postulated. This new physical model of the non-flat interface is introduced based on the statistical picture of the sharp interface disturbed by the field of stochastic forces, it yields the relation between the sharp and diffusive interface models. Furthermore, the new techniques required for the accurate solution of the model equations are proposed. First it is shown, the constrained interpolation improves re-initialization of the level-set functions as it avoids oscillatory numerical errors typical for the second-order accurate interpolation schemes. Next, the new semi-analytical, second order accurate Lagrangian scheme is put forward to integrate the advection equation in time avoiding interface curvature oscillations introduced by the second-order accurate flux limiters. These techniques provide means to obtain complete, second-order convergence during advection and re-initialization of the interface in the state of phase equilibrium.     

Traction–separation laws and stick–slip shear phenomenon of interfaces between cellulose nanocrystals

Cellulose nanocrystals (CNCs) are one of nature's most abundant structural material building blocks and possess outstanding mechanical properties including a tensile modulus comparable to Kevlar. It remains challenging to upscale these properties in CNC neat films and nanocomposites due to the difficulty of characterizing interfacial bonding between CNCs that governs stress transfer under deformation. Here we present new analyses based on atomistic simulations of shear and tensile failure of the interfaces between Iβ CNCs, providing new insight into factors governing the mechanical behavior of hierarchical nanocellulose materials. We compare the two most relevant crystal interfaces and find that hydrogen bonded surfaces have greater tensile strength compared to the surfaces governed by weaker interactions. On the contrary, shearing simulations reveal that friction between the atomic interfaces depends not only on surface energy but also the energy landscape along the shear direction. While being a weaker interface, the intersheet plane exhibits greater energy barriers to shear. The molecular roughness of this interface, characterized by a greater energy barrier, exhibits stick–slip deformation behavior as opposed to a more continuous sliding and rebonding mechanism observed for the interfaces with hydrogen bonds. Analytical models to describe the energy landscapes are developed using energy scaling relations for van der Waals surfaces in combination with a modification of the Prandtl–Tomlinson model for atomic friction. Our simulations pave the way for tailoring hierarchical CNC materials by taking a similar approach to techniques employed for describing metals, where mechanical properties can be tuned through a deeper understanding of grain boundary physics and nanoscale interfaces.     

The intersection marker method for 3D interface tracking of deformable surfaces in finite volumes

Currently, the majority of computational fluid dynamics (CFD) codes use the finite volume method to spatially discretise the computational domain, sometimes as an array of cubic control volumes. The Finite volume method works well with single‐phase flow simulations, but two‐phase flow simulations are more challenging because of the need to track the surface interface traversing and deforming within the 3D grid. Surface area and volume fraction details of each interface cell must be accurately accounted for, in order to calculate for the momentum exchange and rates of heat and mass transfer across the interface. To attain a higher accuracy in two‐phase flow CFD calculations, the intersection marker (ISM) method is developed. The ISM method is a hybrid Lagrangian–Eulerian front‐tracking algorithm that can model an arbitrary 3D surface within an array of cubic control volumes. The ISM method has a cell‐by‐cell remeshing capability that is volume conservative and is suitable for the tracking of complex interface deformation in transient two‐phase CFD simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Multiscale mechanics of noncovalent interface in graphene oxide layered nanocomposites

Noncovalent interfaces play a vital role in inelastic deformation and toughening mechanisms in layered nanocomposites due to their dynamical recoverability. When interfacial engineering is applied to design layered nanocomposites, shear-lag analysis is usually implemented to evaluate the capability of interfacial loading transfer. Here, we introduce a multiscale shear-lag model that correlates macroscale mechanical properties with the molecular mechanisms to quantify the effects of interfacial configuration in graphene oxide(GO) layered nanocomposites. By investigating the mechanical responses of commensurate and incommensurate interfaces, we identify that the commensurate interface exhibits a pronounced size effect due to the nucleation and propagation of interfacial defects, whereas the incommensurate interface displays uniform deformation. Our predictions are further validated through large-scale molecular dynamics simulations for GO layered nanocomposites. This work demonstrates how size effects and interfacial configurations can be exploited to fabricate layered nanocomposites with superior mechanical properties despite relying on weak noncovalent interfaces.     

Evolution of Phase Boundaries by Configurational Forces

An initial boundary value problem modeling the evolution of phase interfaces in materials showing martensitic transformations is studied. The model, which is derived rigorously from a sharp interface model with phase interfaces driven by configurational forces and which generalizes that model, consists of the equations of linear elasticity coupled with a nonlinear partial differential equation of hyperbolic character governing the evolution of the order parameter. It is proved that in one space dimension, global solutions exist for which the order parameter belongs to the space of functions of bounded variation. Other models for interface motion by martensitic transformations and by interface diffusion are suggested.     

Shear deformation effect in plates stiffened by parallel beams

In this paper a general solution for the analysis of shear deformable stiffened plates subjected to arbitrary loading is presented. According to the proposed model, the arbitrarily placed parallel stiffening beams of arbitrary doubly symmetric cross section are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. The analysis of the plate is based on Reissner’s theory, which may be considered as the standard thick plate theory with which all others are compared, while the analysis of the beams is performed employing the linearized second order theory taking into account shear deformation effect. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM based method. The solution of the aforementioned plate and beam problems, which are nonlinearly coupled, is achieved using iterative numerical methods. The adopted model permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates. The effectiveness, the range of applications of the proposed method and the influence of shear deformation effect are illustrated by working out numerical examples with great practical interest.     

双材料界面断裂力学模型与实验方法

纤维增强聚合物(FRP)质轻、高强, 可提高结构的刚度、强度、抗震性能和耐久性, 近年来在结构加固及工程改造中得到广泛应用. FRP与传统复合材料之间形成双材料黏结界面, 界面断裂特性是决定双材料结构性能的关键因素. 对双材料界面裂纹尖端应力场理论、界面裂纹模型、黏结界面I型、II型及混合型断裂试验及理论研究现状进行综合评述和分析. 界面模型主要有经典梁/板理论和刚性节点模型、考虑剪切变形的双亚层理论和半刚性节点模型、基于双亚层理论的柔性节点模型、考虑剪切变形的多层亚层理论和多亚层柔性节点模型、弹性地基梁模型以及黏聚模型. 还介绍了双材料界面断裂力学在FRP-混凝土研究中的应用.      

高速冲击过程数值分析的再生核质点法

利用新型的无网格方法-再生核质点方法对高速冲击过程进行数值模拟，给出了控制 方程，分析中引入Bordner-Partom本构模型来实现材料高速冲击条件下的大应变和高应变 率的特性，提出了新的接触面处理方法，介绍了速度配点法来实现接触面及其它本质边界的 速度条件. 数值模拟表明，再生核质点法能够准确模拟高速冲击过程，具有较高的计算精度.     

An unstructured-grid numerical model for interfacial multiphase fluids based on multi-moment finite volume formulation and THINC method

We present a practical numerical framework for incompressible interfacial multiphase flows on unstructured grids with arbitrary and hybrid elements. The numerical framework is constructed by combining VPM (volume-average/point-value multi-moment) and UMTHINC (unstructured multi-dimensional tangent of hyperbola interface capturing) schemes. To facilitate accurate and reliable simulations for interfacial multiphase flows on arbitrary and hybrid unstructured grids, we have made the following major new efforts in this work. (1) UMTHINC scheme on prismatic and pyramidal elements to facilitate computations on hybrid arbitrary unstructured grids; (2) Consistent numerical formulation for mass and momentum transports to simulate multiphase flows of large density ratio; (3) Combined FVM-FEM for accurate solution to diffusion equation; (4) Pressure-projection formulation in consistent with the balanced-force model. Integrating all these numerical techniques effectively enhances the accuracy and robustness in interface capturing and numerical solution of multiphase fluid dynamics, which results in a numerical framework of great significance for practical applications. Numerical verifications have been carried out through benchmark tests ranging from surface tension dominant flows of small scale to large scale flows with violently-changing interfaces. Numerical results demonstrate that the present framework is robust with adequate accuracy for simulating multiphase flows in complex geometries.     

Log-layer mismatch and commutation error in hybrid RANS/LES simulation of channel flow

Hybrid approach combining large eddy simulation (LES) with the Reynolds-averaged Navier–Stokes equation (RANS) is expected to accurately simulate wall-bounded turbulent flows at high Reynolds numbers. As an important issue in developing hybrid methods, it is known that the log layers in the RANS and LES regions are not lined up in hybrid RANS/LES simulations of channel flow. Although several methods including additional filtering near the RANS/LES interface have been proposed to eliminate the log-layer mismatch, there is no obvious physical justification for the methods and some ad hoc tuning is necessary. In this work, the commutation error terms in the filtered velocity equations are investigated to justify the method of additional filtering. It is shown that the additional filtering can be considered as a finite difference approximation to extra terms due to the non-commutivity between the hybrid filter and the spatial derivative. Moreover, an expression determining the filter width and its location for the additional filtering is obtained. To validate the expression, a hybrid simulation of channel flow is carried out. The additional filtering with the filter width derived is shown to be effective in eliminating the log-layer mismatch and improving the mean velocity profile.     

Cohesive fracture simulation and failure modes of FRP–concrete bonded interfaces

A work-of-fracture method using three-point bend beam (3PBB) specimen, commonly employed to determine the fracture energy of concrete, is adapted to evaluate the mode-I cohesive fracture of fiber reinforced plastic (FRP) composite–concrete adhesively bonded interfaces. In this study, a bilinear damage cohesive zone model (CZM) is used to simulate cohesive fracture of FRP–concrete bonded interfaces. The interface cohesive process damage model is proposed to simulate the adhesive–concrete interface debonding; while a tensile plastic damage model is used to account for the cohesive cracking of concrete near the bond line. The influences of the important interface parameters, such as the interface cohesive strength, concrete tensile strength, critical interface energy, and concrete fracture energy, on the interface failure modes and load-carrying capacity are discussed in detail through a numerical finite element parametric study. The results of numerical simulations indicate that there is a transition of the failure modes controlling the interface fracture process. Three failure modes in the mode-I fracture of FRP–concrete interface bond are identified: (1) complete adhesive–concrete interface debonding (a weak bond), (2) complete concrete cohesive cracking near the bond line (a strong bond), and (3) a combined failure of interface debonding and concrete cohesive cracking. With the change of interface parameters, the transition of failure modes from interface debonding to concrete cohesive cracking is captured, and such a transition cannot be revealed by using a conventional fracture mechanics-based approach, in which only an energy criterion for fracture is employed. The proposed cohesive damage models for the interface and concrete combined with the numerical finite element simulation can be used to analyze the interface fracture process, predict the load-carrying capacity and ductility, and optimize the interface design, and they can further shed new light on the interface failure modes and transition mechanism which emulate the practical application.     

Wetting and Prewetting of Anti-Phase Boundaries

A degenerate Allen-Cahn/Cahn-Hilliard system which was developed to describe simultaneous ordering and phase separation, can also be viewed as a diffuse interface approximation for various problems in materials science in which surface diffusion and motion by mean curvature are coupled. In the original context a low temperature coarsening limit, yielding geometric motion in the limit, was designed to describe small particles of a disordered phase whose shape evolves by surface diffusion which are embedded along grain boundaries which partition the system into two ordered variants. While an early analysis focused on systems in the proximity of the complete wetting limit [9], a later analysis extended these results also to the partial wetting setting [11]. We outline here some features which determine whether a given degenerate Allen-Cahn/Cahn-Hilliard system corresponds to complete or partial wetting in the limit, giving some explicit examples of both possibilities.     

Thermomechanics of solids with general imperfect coherent interfaces

The objective of this contribution is to develop a thermodynamically consistent theory for general imperfect coherent interfaces in view of their thermomechanical behavior and to establish a unified computational framework to model all classes of such interfaces using the finite element method. Conventionally, imperfect interfaces with respect to their thermal behavior are often restricted to being either highly conducting (HC) or lowly conducting (LC) also known as Kapitza. The interface model here is general imperfect in the sense that it allows for a jump of the temperature as well as for a jump of the normal heat flux across the interface. Clearly, in extreme cases, the current model simplifies to HC and LC interfaces. A new characteristic of the general imperfect interface is that the interface temperature is an independent degree of freedom and, in general, is not a function of only temperatures across the interface. The interface temperature, however, must be computed using a new interface material parameter, i.e., the sensitivity. It is shown that according to the second law, the interface temperature may not necessarily be the average of (or even between) the temperatures across the interface. In particular, even if the temperature jump at the interface vanishes, the interface temperature may be different from the temperatures across the interface. This finding allows for a better, and somewhat novel, understanding of HC interfaces. That is, a HC interface implies, but is not implied by, the vanishing temperature jump across the interface. The problem is formulated such that all types of interfaces are derived from a general imperfect interface model, and therefore, we establish a unified finite element framework to model all classes of interfaces for general transient problems. Full details of the novel numerical scheme are provided. Key features of the problem are then elucidated via a series of three-dimensional numerical examples. Finally, we recall since the influence of interfaces on the overall response of a body increases as the scale of the problem decreases, this contribution has certain applications to nano-composites and also thermal interface materials.