A continuum model with microstructures for wave propagation in ultra-thin films

Ultrasonic waves are powerful and popular methods for measuring mechanical properties of solids even at nanoscales. The extraction of material constants from the measured wave data requires the use of a model that can accurately describe the wave motion in the solid. The objective of this paper is to develop a continuum theory with microstructures that can capture the effect of the microstructure or nanostructure in ultra-thin films when waves of short wavelengths are used. This continuum theory is developed from assumed displacement fields for microstructures. Local kinematic variables are introduced to express these local displacements and are subjected to internal continuity conditions. The accuracy of the present theory is verified by comparing the results with those of the lattice model for the thin film. Specifically, dispersion curves for surface wave propagation and wave propagation in a thin film supported by an elastic homogeneous substrate are studied. The inadequacy of the conventional continuum theory is discussed.     

Microelastic wave field signatures and their implications for microstructure identification

This work combines closed-form and computational analyses to elucidate the dynamic properties, termed signatures, of waves propagating through solids defined by the theory of elasticity with microstructure and the potential of such properties to identify microstructure evolution over a material’s lifetime. First, the study presents analytical dispersion relations and frequency-dependent velocities of waves propagating in microelastic solids. A detailed parametric analysis of the results show that elastic solids with microstructure recover traditional gradient elasticity under certain conditions but demonstrate a higher degree of flexibility in adapting to observed wave forms across a wide frequency spectrum. In addition, a set of simulations demonstrates the ability of the model to quantify the presence of damage, just another type of microstructure, through fitting of the model parameters, especially the one associated with the characteristic length scale of the underlying microstructure, to an explicit geometric representation of voids in different damage states.     

A Peridynamic Model of Fracture Mechanics with Bond-Breaking

Wave propagation in elastic dielectrics with flexoelectricity, micro-inertia and strain gradient elasticity is investigated in this paper. Dispersion phenomenon, which does not exist in classical elastic dielectric theory, is observed in the flexoelectric microstructured solids. Analytical solutions for the phase velocity \(C_{p}\), group velocity \(C_{g}\) and their ratio \(\gamma = C_{g} / C_{p}\) are calculated for the case of harmonic decomposition. The magnitudes of the phase velocity and group velocity changed with the increasing of the wave number, while they are constant in the classical elastic dielectric theory. It is shown that the flexoelectricity, micro-inertia and microstructural effects are significant to predict the real behavior of longitudinal wave propagating in flexoelectric microstructured solids. Microstructural effects are not sufficient for dealing with realistic dispersion curves in flexoelectric solids, the micro-inertia and flexoelectricity are needed to obtain a physically acceptable value of the phase and group velocities.     

Nonlinear wave propagation analysis in hyperelastic 1D microstructured materials constructed by homogenization

We analyze the acoustic properties of microstructured beams including a repetitive network material undergoing configuration changes leading to geometrical nonlinearities. The effective constitutive law is evaluated successively as an effective first and second order nonlinear grade 1D continuum, based on a strain driven incremental scheme written over the reference unit cell, taking into account the changes of the lattice geometry. The dynamical equations of motion are next written, leading to specific dispersion relations. The presence of second gradient order term in the nonlinear equation of motion leads to the presence of two different modes: an evanescent subsonic mode for high nonlinearity that vanishes beyond certain values of wave number, and a supersonic mode for a weak nonlinearity. This methodology is applied to analyze wave propagation within different microstructures, including the regular and reentrant hexagons, and plain weave textile pattern.     

High-frequency antiplane wave propagation in ultra-thin films with nanostructures

Ultrasonic wave propagation is one of powerful and popular methods for measuring mechanical properties of solids even at nano scales. The extraction of material constants from the measured wave data may not be accurate and reliable when waves of short wavelengths are used. The objective of this paper is to study the high-frequency antiplane wave propagation in ultra-thin films at nanoscale. A developed continuum microstructure theory will be used to capture the effect of nanostructures in ultra-thin films. This continuum theory is developed from assumed displacement fields for nanostructures. Local kinematic variables are introduced to express these local displacements and are subjected to internal continuity conditions. The accuracy of the theory is verified by comparing the results with those of the lattice model for the antiplane problem in an infinite elastic medium. Specifically, dispersion curves and corresponding displacement fields for antiplane wave propagation in the ultra-thin films are studied. The inadequacy of the conventional continuum theory is discussed.     

Wave propagation and dispersion in elasto-plastic microstructured materials

A Mindlin continuum model that incorporates both a dependence upon the microstructure and inelastic (nonlinear) behavior is used to study dispersive effects in elasto-plastic microstructured materials. A one-dimensional equation of motion of such material systems is derived based on a combination of the Mindlin microcontinuum model and a hardening model both at the macroscopic and microscopic level. The dispersion relation of propagating waves is established and compared to the classical linear elastic and gradient-dependent solutions. It is shown that the observed wave dispersion is the result of introducing microstructural effects and material inelasticity. The introduction of an internal characteristic length scale regularizes the ill-posedness of the set of partial differential equations governing the wave propagation. The phase speed does not necessarily become imaginary at the onset of plastic softening, as it is the case in classical continuum models and the dispersive character of such models constrains strain softening regions to localize.     

Virtual improvement of ice cream properties by computational homogenization of microstructures

Optimal shape design of microstructured materials has recently attracted a great deal of attention in materials science. The shape and the topology of the microstructure have a significant impact on the macroscopic properties. This paper presents different computational models of random microstructures, to virtually improve the physical properties of ice cream. Several sensory properties of this heterogeneous material issued from food industry are directly controlled by the elastic and thermal conducting ones. The material effective elastic and thermal conducting properties are obtained through direct large scale numerical simulations. The different formulations address the problem of finding the shape of the representative microstructural element for random heterogeneous media that increase the elastic moduli and thermal conductivity compared to existing products. The computational models are established using finite element method and images of virtual microstructures. In this paper we propose a new model of microstructures. This model is constructed with hexagonal prismatic rods and plates with volume fractions around 0.7 for the hard phase represented by hexagons of ice. A comparison between three two-phase elastic heterogeneous microstructures models is drawn. This illustrates the concept of design of microstructures using computational homogenization tools.     

A fracture criterion for finitely deforming crystalline solids—The dynamic fracture of single crystals

The major objective of this work has been to develop, within a continuum framework, a microstructurally-based computational theory to investigate dynamic failure in metals. To model the nucleation and propagation of failure surfaces at the microstructural scale, under large deformations and dynamic loading conditions, general finite-deformation theory, as relating to the decomposition of the deformation gradient, was tailored to monitor displacement incompatibilities and fracture in crystalline solids subjected to large deformations. Based on this proposed decomposition, a general fracture criterion for finitely deforming crystals, using the integral law of incompatibility, was developed. The analyses indicate that this newly proposed fracture formulation and criterion can be validated with experimental results, and can be used to accurately predict brittle and ductile failure modes for the large deformation of single crystals. As part of the newly proposed decomposition of the deformation gradient, sub-problems can also be solved for lattice distortions, such as twinning and geometrically necessary dislocation (GND) densities. Accordingly, the interactions of GND densities with cracks were investigated for single crystals. GND densities were shown to form as loops for stationary crack tips, but no loops formed for propagating cracks.     

Heterogeneous deformation and spall of an extruded tungsten alloy: plate impact experiments and crystal plasticity modeling

The role of microstructure in the dynamic deformation and fracture of a dual phase, polycrystalline tungsten alloy under high-rate impact loading is investigated via experiments and modeling. The material studied consists of pure tungsten crystals embedded in a ductile binder alloy comprised of tungsten, nickel, and iron. The tungsten crystals are elongated in a preferred direction of extrusion during processing. Plate impact tests were conducted on samples oriented either perpendicular or parallel to the extrusion direction. Spatially resolved interferometric data from these tests were used to extract wave propagation behavior and spall strength dependent upon position in the sample microstructure. Finite element simulations of impact and spall in digitally reproduced microstructural geometries were conducted in parallel with the experiments. Finite deformation crystal plasticity theory describes the behavior of the pure tungsten and binder phases, and a stress- and temperature-based cohesive zone model captures fracture at grain and phase boundaries in the microstructure. In results from both experiments and modeling, the grain orientations affect the free-surface velocity profile and spall behavior. Some aspects of distributions of free-surface velocity and spall strength among different microstructure configurations are qualitatively similar between experimental and numerical results, while others are not as a result of differing scales of resolution and modeling assumptions. Following a comparison of experimental and numerical results for different microstructures, intergranular fracture is identified as an important mechanism underlying the spall event.     

Numerical simulation of interaction of solitary deformation waves in microstructured solids

In the present paper 1D wave propagation in microstructured solids is modelled based on the Mindlin theory and hierarchical approach. The governing equation under consideration is non-integrable therefore it is analysed numerically. Propagation and interaction of localised initial pulses is simulated numerically over long time intervals by employing the pseudospectral method. Special attention is paid to the solitonic character of the solution.     

基于近场动力学理论的准脆性材料的本构力函数的构建

近场动力学理论(PD)是基于非局部思想的连续介质力学新理论,用于研究材料破坏问题。根据准脆性材料破坏的线性和非线性的力学行为,在初始微观弹脆性材料(PMB)的本构力函数中引入了键的损伤模型,将键的断裂过程分成了线性的弹性变形阶段和非线性的损伤变形阶段,以此构建了准脆性材料的本构力函数的基本形式。以典型的准脆性材料为例构建了其本构力函数,通过在压缩载荷下对含预制不同角度单裂纹缺陷的类岩材料的裂纹扩展进行PD数值模拟仿真,裂纹起裂位置和扩展方向与试样试验结果在一定程度上保持了一致,证明了该基于近场动力学理论的典型准脆性材料的本构力函数可用于该类材料的破坏分析。     

Simulation of the densification of real open-celled foam microstructures

Ubiquitous in nature and finding applications in engineering systems, cellular solids are an increasingly important class of materials. Foams are an important subclass of cellular solids with applications as packing materials and energy absorbers due to their unique properties. A better understanding of foam mechanical properties and their dependence on microstructural details would facilitate manufacture of tailored materials and development of constitutive models for their bulk response. Numerical simulation of these materials, while offering great promise toward furthering understanding, has also served to convincingly demonstrate the inherent complexity and associated modeling challenges.The large range of deformations which foams are subjected to in routine engineering applications is a fundamental source of complication in modeling the details of foam deformation on the scale of foam struts. It requires accurate handling of large material deformations and complex contact mechanics, both well established numerical challenges. A further complication is the replication of complex foam microstructure geometry in numerical simulations. Here various advantages of certain particle methods, in particular their compatibility with the determination of three-dimensional geometry via X-ray microtomography, are exploited to simulate the compression of “real” foam microstructures into densification. With attention paid to representative volume element size, predictions are made regarding bulk response, dynamic effects, and deformed microstructural character, for real polymeric, open-cell foams. These predictions include a negative Poisson's ratio in the stress plateau, and increased difficulty in removing residual porosity during densification.     

PARTITION OF UNITY FINITE ELEMENT METHOD FOR SHORT WAVE PROPAGATION IN SOLIDS

IntroductionIt is known that standard finite element procedure is unable to simulate the wavepropagation with high oscillations or gradients in space in the media with reasonableefficiency and accuracy due to the nature of polynomial interpolation approxi…     

The effect of microstructural representation on simulations of microplastic ratcheting

This paper assesses the sensitivity of cyclic plasticity to microstructure morphology by examining and comparing the microplastic ratcheting behavior of different idealized microstructures (square, hexagonal, tessellated, and digitized from experimental data). This analysis demonstrates the sensitivity of computational accuracy to the various approximations in microstructural representation. The methodology used to perform this study relies on a coupling between microstructural characterization, mechanical testing and numerical simulations to investigate the influence of the microstructure on the purely tensile uniaxial microplastic ratcheting behavior of pure nickel polycrystals. The morphology and deformation behavior of polycrystals were characterized using electron back-scatter diffraction (EBSD), while a finite element model (FEM) of crystal plasticity was used in a computational framework. The predicted cyclic behavior is compared to experimental results both at the macroscopic and microstructural scales. The stress–strain response is less sensitive to the details of the microstructural representation than might be expected with all representations displaying similar macroscopic constitutive response. However, the details of the plastic strain distribution at the microstructural scale and the related estimations of damage mechanics vary substantially from one microstructural representation to another.     

Mesoscopic characterization and modeling of microcracking in cementitious materials by the extended finite element method

This study develops a mesoscopic framework and methodology for the modeling of microcracks in concrete. A new algorithm is first proposed for the generation of random concrete meso-structure including microcracks and then coupled with the extended finite element method to simulate the heterogeneities and discontinuities present in the meso-structure of concrete. The proposed procedure is verified and exemplified by a series of numerical simulations. The simulation results show that microcracks can exert considerable impact on the fracture performance of concrete. More broadly, this work provides valuable insight into the initiation and propagation mechanism of microcracks in concrete and helps to foster a better understanding of the micro-mechanical behavior of cementitious materials.     

Waves in microstructured solids and the Boussinesq paradigm

The emergence of soliton trains and interaction of solitons are analyzed by using a Boussinesq-type equation which describes the propagation of bi-directional deformation waves in microstructured solids. The governing equation in the one-dimensional setting is based on the Mindlin model. This model includes scale parameters which show explicitly the influence of the microstructure in wave motion. As a result the governing equation has a hierarchical structure. The analysis is based on numerical simulation using the pseudospectral method. It is shown how the number of solitons in emerging trains depends on the initial excitation. The head-on collision of emerged solitons is not fully elastic due to radiation but the solitons preserve their identity after collision and the speed of solitons is retained while the radiation keeps a certain mean value. That is why we have kept through this paper the notion of solitons.     

三维气相爆轰动态并行计算程序设计与开发

在三维气相爆轰数值研究中,网格精度和计算域的规模导致网格数占有非常庞大的计算资源,进而给数值模拟带来了极大的挑战。本文针对这一难题,采用5阶WENO格式对带化学反应Euler方程组进行空间离散,基于MPI（MessagePassingInterface）并行模式开发了高精度动态并行代码,并对爆轰波在带有障碍物的三维方形管道中的传播过程进行计算。计算结果表明,高精度动态并行计算能够很好的模拟三维气相爆轰波在大尺寸管道中的传播,不仅提高了计算效率,而且提高了爆轰波阵面的分辨率。与高精度静态并行相比,高精度动态并行计算减少了界面数据通信时间,从而进一步提高了计算效率。因此,高精度动态并行程序为探究三维气相爆轰新的物理机制提供有效的手段。