Kinetic wrinkling of an elastic film on a viscoelastic substrate

A compressed elastic film on a compliant substrate can form wrinkles. On an elastic substrate, equilibrium and energetics set the critical condition and select the wrinkle wavelength and amplitude. On a viscous substrate, wrinkle grows over time and the kinetics selects the fastest growing wavelength. More generally, on a viscoelastic substrate, both energetics and kinetics play important roles in determining the critical condition, the growth rate, and the wavelength. This paper studies the wrinkling process of an elastic film on a viscoelastic layer, which in turn lies on a rigid substrate. The film is elastic and modeled by the nonlinear von Karman plate theory. The substrate is linear viscoelastic with a relaxation modulus typical of a cross-linked polymer. Beyond a critical stress, the film wrinkles by the out-of-plane displacement but remains bonded to the substrate. This study considers plane strain wrinkling and neglects the in-plane displacement. A classification of the wrinkling behavior is made based on the critical conditions at the elastic limits, the glassy and rubbery states of the viscoelastic substrate. Linear perturbation analyses are conducted to reveal the kinetics of wrinkling in films subjected to intermediate and large compressive stresses. It is shown that, depending on the stress level, the growth of wrinkles at the initial stage can be exponential, accelerating, linear, or decelerating. In all cases, the wrinkle amplitude saturates at an equilibrium state after a long time. Subsequently, both amplitude and wavelength of the wrinkle evolve, but the process is kinetically constrained and slow compared to the initial growth.     

Buckling and postbuckling of a compressed thin film bonded on a soft elastic layer: a three-dimensional analysis

The wrinkling of a stiff thin film bonded on a soft elastic layer and subjected to an applied or residual compressive stress is investigated in the present paper. A three-dimensional theoretical model is presented to predict the buckling and postbuckling behavior of the film. We obtained the analytical solutions for the critical buckling condition and the postbuckling morphology of the film. The effects of the thicknesses and elastic properties of the film and the soft layer on the characteristic wrinkling wavelength are examined. It is found that the critical wrinkling condition of the thin film is sensitive to the compressibility and thickness of the soft layer, and its wrinkling amplitude depends on the magnitude of the applied or residual in-plane stress. The bonding condition between the soft layer and the rigid substrate has a considerable influence on the buckling of the thin film, and the relative sliding at the interface tends to destabilize the system.     

形状记忆聚合物力学行为及其物理机制

形状记忆聚合物是一类环境响应主动形变智能软材料,是智能材料与结构领域的新兴研究内容之一。宏观概括其物理和力学行为的研究热点,主要包括三个方面：材料与环境之间的信息交换（如热量、能量等）,主动形变控制（如驱动方法、形变行为本构建模等）,软材料及其结构力学（如相变/转变热力学、复合材料设计等）。形状记忆聚合物的记忆效应源于分子链段本征结构的热运动,受外场激励影响,是分子链段结构（包括构型和构象）松弛行为的宏观表象,遵循Arrhenius定律。本文从物理和力学两方面讨论了形状记忆聚合物的分子链段热力学行为及其熵弹效应、分子结构松弛力学行为、环境效应记忆行为的物理和力学机制,系统地对形状记忆聚合物分子结构本征属性及其物理机理、记忆效应转变机制及其力学内涵、温度记忆效应、多场耦合效应响应行为等热点和难点问题进行了分析和讨论。最后,论文展望了形状记忆聚合物力学行为研究的未来发展方向。     

Analytical study of wrinkling in thin-film-on-elastomer system with finite substrate thickness

Surface wrinkling, a film bonded on a pre-strained elastomeric substrate can form periodic wrinkling patterns, is a common phenomenon in daily life. In existing theoretical models, the film is much thinner than the substrate so that the substrate can be considered to be elastomeric with infinite thickness. In this paper, the effect of finite substrate thickness is analyzed theoretically for free boundary condition cases. Based on the minimum potential energy principle, a theoretical model is established, and the wave length and amplitude of the wrinkling pattern are obtained. When the thickness of the substrate is more than 200 times larger than the thickness of the film, the results of this study agree well with the results obtained from the previous models for infinite substrate thickness. However, for thin substrates, the effect of finite substrate thickness becomes significant. The model given in this paper accurately describes the effect of finite substrate thickness, providing important design guidelines for future thin-film-on-substrate systems such as stretchable electronic devices.     

An influence of temperature on reconstructed middle ear with shape memory prosthesis

In the paper idea of reconstructed middle ear with a prosthesis made of shape memory alloy is proposed. The new design of shape memory prosthesis is used to enable adjusting its length to individual patient’s needs which is a novel contribution of the paper. In order to make a proper fit of prosthesis, a surgeon has to adjust its size and position by cutting step by step classical prosthesis. It takes time of a operation and enlarges a period of patient’s esthesia. Therefore, a shape memory prosthesis (SMP) is proposed to shorten operation time and improve fitting through precisely selected length. A reconstructed middle ear is modelled as a two degree of freedom system with nonlinear shape memory element. Finding advisable periodic and undesirable a periodic and irregular behaviour in various temperature is the main aim of the paper. Results of the study should give an answer whether SMP can be useful in medical practice and should also explain dynamics of the middle ear with SMP. The properties of the shape memory prosthesis, in the form of helical spring, are described here by a polynomial dependence. Firstly, free vibrations are investigated and equilibrium points, next forced vibrations are studied under different parameters of external excitations and temperature range. Bifurcation analysis and stability of periodic solutions are performed in order to reveal the system behaviour. Finally, interesting dynamical findings of chaotic vibrations pure regular and regular oscillations with fluctuation are presented. However, from practical point of view only harmonic response of the stapes is advisable. That can be achieved at the normal temperature of a human body only for small excitation amplitude.     

Wrinkle patterns of anisotropic crystal films on viscoelastic substrates

This paper presents a nonlinear mathematical model for evolution of wrinkle patterns of an anisotropic crystal film on a viscoelastic substrate layer. The underlying mechanism of wrinkling has been generally understood as a stress-driven instability. Previously, theoretical studies on wrinkling have assumed isotropic elastic properties for the film. Motivated by recent experimental observations of ordered wrinkle patterns in single-crystal thin films, this paper develops a theoretical model coupling anisotropic elastic deformation of a crystal film with viscoelastic deformation of a thin substrate layer. A linear perturbation analysis is performed to predict the onset of wrinkling instability and the initial evolution kinetics. An energy minimization method is adopted to analyze wrinkle patterns in the equilibrium states. For a cubic crystal film under an equi-biaxial compression, orthogonally ordered wrinkle patterns are predicted in both the initial stage and the equilibrium state. This is confirmed by numerical simulations of evolving wrinkle patterns. By varying the residual stresses in the film, numerical simulations show that a variety of wrinkle patterns (e.g., orthogonal, parallel, zigzag, and checkerboard patterns) emerge as a result of the competition between material anisotropy and stress anisotropy.     

Effects of tension–compression asymmetry on the surface wrinkling of film–substrate systems

Many soft materials and biological tissues are featured with the tension–compression asymmetry of constitutive relations. The surface wrinkling of a stiff thin film lying on a compliant substrate is investigated through theoretical analysis and numerical simulations. It is found that the tension–compression asymmetry of the soft substrate not only affects the critical strain of buckling but, more importantly, may also influence the wrinkling pattern that occurs in the film–substrate system under specified loading conditions. Due to this mechanism, the thin film subjected to equi-biaxial compression may first buckle into a hexagonal array of dimples or bulges, instead of the checkerboard pattern, and consequently evolve into labyrinths with further loading. Under non-equi-biaxial compression, the system may buckle either into a parallel bead-chain pattern or a stripe pattern, depending on the substrate nonlinearity and the loading biaxiality. Phase diagrams are established for the wrinkling patterns in a wide range of geometric and mechanical parameters, which facilitate the design of surface patterns with desired properties and functions.     

Theoretical analysis of the deformation of SMP sandwich beam in flexure

Shape memory polymers (SMPs) can have a large frozen strain but with a very small recovery stiffness in comparison with shape memory metals or ceramics. To provide more deployable stresses for the application of actuators, sandwich beams consisting of a SMP core and two thin metallic skins were considered. The packaging behaviors of two types of SMP sandwich beams, aluminum/SMP/aluminum and steel/SMP/steel, were discussed. Due to the high compliance of SMP core on packaging condition that the testing temperature is above the activation temperature of the material, buckling and post-buckling are the essential deformation mechanisms of SMP sandwich beams under bending. Theoretical solutions were derived in studying such non-linear behaviors, including the initiation of critical buckling, post-buckling response, and final failure modes. Systematic parameter’s analyses, e.g., buckling half-wavelength, amplitude, location of the neutral-strain surface in different packaging curvatures, were also presented.     

Constitutive modeling of shape memory polymer based self-healing syntactic foam

In a previous study, it was found that the shape memory functionality of a shape memory polymer based syntactic foam can be utilized to self-seal impact damage repeatedly, efficiently, and almost autonomously [Li G., John M., 2008. A self-healing smart syntactic foam under multiple impacts. Comp. Sci. Technol. 68(15–16), 3337–3343]. The purpose of this study is to develop a thermodynamics based constitutive model to predict the thermomechanical behavior of the smart foam. First, based on DMA tests and FTIR tests, the foam is perceived as a three-phase composite with interfacial transition zone (interphase) coated microballoons dispersed in the shape memory polymer (SMP) matrix; for simplicity, it is assumed to be an equivalent two-phase composite by dispersing elastic microballoons into an equivalent SMP matrix. Second, the equivalent SMP matrix is phenomenologically assumed to consist of an active (rubbery) phase and a frozen (glassy) phase following Liu et al. [Liu, Y., Gall, K., Dunn, M.L., Greenberg, A.R., Diani J., 2006. Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modeling. Int. J. Plasticity 22, 279–313]. The phase transition between these two phases is through the change of the volume fraction of each phase and it captures the thermomechanical behavior of the foam. The time rate effect is also considered by using rheological models. With some parameters determined by additional experimental testing, the prediction by this model is in good agreement with the 1D test result found in the literature. Parametric studies are also conducted using the constitutive model, which provide guidance for future design of this novel self-healing syntactic foam and a class of light-weight composite sandwich structures.     

Post-buckling evolution of wavy patterns in trapezoidal film/substrate bilayers

This paper investigates quantitatively the post-buckling response of irregular wrinkles in a trapezoidal film/substrate bilayer. The geometric gradient can change the wrinkling profile to create ribbed and graded structural patterns with variations of wave direction, amplitude and wavelength. The tapered angle and edge dimension are examined numerically using a nonlinear shell/solid coupled finite element model that incorporates a path-following continuation technique, which explores their influences on secondary bifurcations, localization and surface mode transition. For instance, the competition between plate-like and beam-like post-buckling behavior is discussed. An analysis of graded amplitude is also provided based on Fourier envelope equations of beam/foundation models, which gives an insightful understanding of these fading wrinkles that differ from the ones usually observed in rectangular geometric cases. The results of this work can be used to guide the design of geometrically gradient film/substrate systems to achieve desired wavy instability patterns.     

Buckling and post-buckling of a stiff film resting on an elastic graded substrate

Systems consisting of a hard layer resting on an elastic graded soft substrate are frequently encountered both in nature and industry. In this paper, we study the surface wrinkling problem of such a composite system subjected to in-plane compression. The Young’s modulus of the elastic substrate is assumed to vary along its depth direction. In particular, we investigate two typical variations in the modulus, described by a power function and an exponential function, respectively. Analytical solutions which permit to determine the critical compressive strain for the onset of wrinkling and the wrinkling wavelength are derived. A series of finite element simulations are performed to validate the theoretical solutions and demonstrate the prominent features of the postbuckling evolution of the system. The results may not only find applications in thin-film metrology and surface patterning but also provide insight into the wrinkling phenomena of various living tissues.     

温度梯度对热致型形状记忆聚合物板力学性能的影响

形状记忆聚合物作为一种新型的智能材料,由于质量轻、成本低以及变形回复率大等优势,已经在航空、医学等领域得到广泛应用。当前对于热致型形状记忆聚合物力学行为的研究,大都集中在整体变温的情况下,随着应用环境的越来越广泛,温度梯度对材料力学性能的影响效果越发重要。本文在均匀应力的假设下,给出材料在不同初始和传热条件下的温度梯度分布情况,结合传热学和热致型形状记忆聚合物相变理论本构模型,分别讨论了不同温度梯度对存储应变、弹性模量等力学性能的影响,通过理论分析和实验数据对比验证了模型正确性。本文研究可为不同导热情况下,对热致型形状记忆聚合物力学行为监测提供思路,也为形状记忆聚合物的进一步工程应用提供理论依据。     

Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam

The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer(SMP) microbeam. Size-dependent constitutive equations, which can capture the size effect of the SMP, are proposed based on the modified couple stress theory(MCST). The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam theory. An SMP microbeam model, which includes the formulations of deflection, strain, curvature, stress and couple stress, is developed by using the principle of minimum potential energy and the separation of variables together. The sizedependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam model. Results show that the size effects of the SMP microbeam are significant when the dimensionless height is small enough. However, they are too slight to be necessarily considered when the dimensionless height is large enough. The bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height, while the couple stress level declines with the increasing dimensionless height.The larger the dimensionless height is, the more obvious the viscous property and shape memory effect of the SMP microbeam are. The Poisson ratio has obvious influence on the size-dependent behaviors of the SMP microbeam. The paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine, microelectronic devices and micro-electro-mechanical system(MEMS) self-assembling.     

Spontaneous instability of soft thin films on curved substrates due to van der Waals interaction

The linear bifurcation theory is used to investigate the stability of soft thin films bonded to curved substrates. It is found that such a film can spontaneously lose its stability due to van der Waals or electrostatic interaction when its thickness reduces to the order of microns or nanometers. We first present the generic method for analyzing the surface stability of a thin film interacting with the substrate and then discuss several important geometric configurations with either a positive or negative mean curvature. The critical conditions for the onset of spontaneous instability in these representative examples are established analytically. Besides the surface energy and Poisson's ratio of the thin film, the curvature of the substrate is demonstrated to have a significant influence on the wrinkling behavior of the film. The results suggest that one may fabricate nanopatterns or enhance the surface stability of soft thin films on curved solid surfaces by modulating the mechanical properties of the films and/or such geometrical properties as film thickness and substrate curvature. This study can also help to understand various phenomena associated with surface instability.     

Nonlinear analysis of photo-induced wrinkling of glassy twist nematic films on compliant substrates

A kinetics approach is developed for the geometrically nonlinear analysis of photo-induced wrinkling of glassy twist nematic films on soft elastic substrates.In this way,the problem is reduced to finding the steady state of an overdamped evolution system according to a kinetic law,rather than directly solving the coupled nonlinear equations.This enables one to account for the complicated director distribution and obtain the precise wrinkling morphology of the film.Though the approach proposed here is for a twist nematic film,it can be extended to study glassy nematic films with other director distributions.     

Switchable dry adhesive based on shape memory polymer with hemispherical indenters for transfer printing

Transfer printing based on switchable adhesive is essential for developing unconventional systems, including flexible electronics, stretchable electronics, and micro light-emitting diode (LED) displays. Here we report a design of switchable dry adhesive based on shape memory polymer (SMP) with hemispherical indenters, which offers a continuously tunable and reversible adhesion through the combination of the preloading effect and the thermal actuation of SMP. Experimental and numerical studies reveal the fundamental aspects of design, fabrication, and operation of the switchable dry adhesive. Demonstrations of this adhesive concept in transfer printing of flat objects (e.g., silicon wafers), three-dimensional (3D) objects (e.g., stainless steel balls), and rough objects (e.g., frosted glasses) in two-dimensional (2D) or 3D layouts illustrate its unusual manipulation capabilities in heterogeneous material integration applications.     

绕水翼空化流动及振动特性的实验研究

空化是发生在水力机械内部的一种水动力现象,其发展具有显著的非定常特性.空化流动中空穴的脱落以及溃灭会诱发结构振动,对水力机械的效率、噪声、安全性等造成影响. 研究空化流动中结构的振动特性具有重要的工程意义. 采用实验的方法研究了绕NACA66 水翼空化流动的空穴形态和水翼振动特性. 实验在一闭式空化水洞中进行. 采用高速摄像技术观测不同空化阶段的空穴形态,应用多普勒激光测振仪测量水翼的振动速度,并通过一套同步系统实现了高速相机和多普勒激光测振仪的同步触发和测量. 采用小波分析方法对不同空化阶段下的空穴形态和水翼振动数据在时域和频域中的特性进行了分析.对云状空化阶段的同步测量结果进行了研究,分析了振动与空穴发展过程的联系. 结果表明,随着空化数的降低,流场经历了无空化、初生空化、片状空化和云状空化4个阶段,水翼的振动强度呈逐渐增大趋势. 在片状空化和云状空化阶段,空穴脱落导致水翼振动,诱发的振动频率与空穴脱落频率相同. 对于云状空化,在附着型空穴生长阶段水翼发生高频小幅度振动,在空穴脉动和断裂脱落期间水翼表现为低频大幅振动.      

An analytic model for transient heat conduction in bi-layered structures with flexible serpentine heaters

Uniform heating of complex surfaces, especially non-developable surfaces, is a crucial problem that traditional rigid heaters cannot solve. Inspired by flexible electronic devices, a novel design for the stretchable heating film is proposed with the flexible serpentine wire embedded in the soft polymer film, which can be attached to non-developable surfaces conformally. It provides a new way for the stretchable heaters to realize uniform heating of complex surfaces. However, the thermal field of flexible serpentine heaters(FSHs) depends on the configurations of the embedded serpentine heating wire, which requires accurate theoretical prediction of real-time temperature distribution. Therefore,the analytical model for the transient heat conduction in FSHs is solved by the separation of variables method and validated by the finite element analysis(FEA) in this paper. Based on this model, the effects of the geometric parameters, such as the radius and the length of the serpentine heaters, on the thermal uniformity are systematically investigated. This study can help to design and fabricate flexible heaters with uniform heating in the future.     

A thermoviscoelastic model for amorphous shape memory polymers: Incorporating structural and stress relaxation

A thermoviscoelastic constitutive model is developed for amorphous shape memory polymers (SMP) based on the hypothesis that structural and stress relaxation are the primary molecular mechanisms of the shape memory effect and its time-dependence. This work represents a new and fundamentally different approach to modeling amorphous SMPs. A principal feature of the constitutive model is the incorporation of the nonlinear Adam–Gibbs model of structural relaxation and a modified Eyring model of viscous flow into a continuum finite–deformation thermoviscoelastic framework. Comparisons with experiments show that the model can reproduce the strain–temperature response, the temperature and strain-rate dependent stress–strain response, and important features of the temperature dependence of the shape memory response. Because the model includes structural relaxation, the shape memory response also exhibits a dependence on the cooling and heating rates.     

超弹性薄膜与可压缩基底双层结构表面失稳分析

当上层超弹性硬质薄膜和下层可膨胀基底构成的双层结构受压时,薄膜的自由表面可通过形成褶皱降低系统能量.研究表明,上下两层的模量比不同时,上层弹性硬质薄膜将表现出不同的表面失稳模式.本文提出了一种新颖的方法可有效抑制双层软材料的表面失稳,即改变基底材料的泊松比,这种方法同时适用于不具有应变硬化的软材料.首先基于Neo-Hookean模型发展了小变形条件下双层结构表面失稳的理论模型,通过半解析的方法得到了表面失稳的临界应变;然后通过有限元计算与模拟,进一步验证了负泊松比基底可延缓表面失稳.结果表明:(1)当双层结构基底泊松比为正且趋于0.5(不可压缩)时,双层结构在较小的压缩应变下出现表面失稳;(2)当基底的泊松比为负且趋于-1时,可被压缩至46%而不出现表面失稳,即可膨胀基底能有效抑制薄膜的表面失稳.本文发展的方法及主要结果可为延展性电子器件的设计提供指导.