Stretchability and compliance of freestanding serpentine-shaped ribbons

High-performance stretchable electronics have to utilize high-quality inorganic electronic materials such as silicon, oxide or nitride dielectrics, and metals. These inorganic materials usually crack or yield at very small intrinsic strains, for example, 1%, whereas bio-integrated electronics are expected to at least match the stretchability of bio-tissues (20%) and deployable structure health monitoring networks are expected to expand from wafer scale (several centimeters) to cover macroscopic structures (several meters). To minimize strains in inorganic materials under large deformation, metallic and ceramic films can be patterned into serpentine-shaped ribbons. When the ribbon is stretched, some sections of the ribbon can rotate and/or buckle to accommodate the applied displacement, leaving much smaller intrinsic strain in the materials compared to the applied strain. The choice of the shape of the serpentine depends on systematic studies of the geometric variables. This paper investigates the effect of serpentine shapes on their stretchability and compliance through theoretical, numerical, and experimental means. Our closed-form curved beam solutions, FEM results, and experimental measurements have found good agreement with one another. Our results conclude that in general, the narrower ribbon, the larger arc radius and arc angle, and the longer arm length will yield lower intrinsic strain and effective stiffness. When the arm length approaches infinite, the stretchability can be enhanced by several orders. A few unexpected behaviors are found at arc angles that are close to straight bars. With additional practical constraints such as minimum ribbon width and finite overall breadth, the optimal serpentine shape can be accurately determined using our closed-form analytical solution.     

Post-buckling analysis for the precisely controlled buckling of thin film encapsulated by elastomeric substrates

The precisely controlled buckling of stiff thin films (e.g., Si or GaAs nano ribbons) on the patterned surface of elastomeric substrate (e.g., poly(dimethylsiloxane) (PDMS)) with periodic inactivated and activated regions was designed by Sun et al. [Sun, Y., Choi, W.M., Jiang, H., Huang, Y.Y., Rogers, J.A., 2006. Controlled buckling of semiconductor nanoribbons for stretchable electronics. Nature Nanotechnology 1, 201–207] for important applications of stretchable electronics. We have developed a post-buckling model based on the energy method for the precisely controlled buckling to study the system stretchability. The results agree with Sun et al.’s (2006) experiments without any parameter fitting, and the system can reach 120% stretchability.     

Reprint of “Post-buckling analysis for the precisely controlled buckling of thin film encapsulated by elastomeric substrates” [In. J. Solids Struct. 45 (2008) 2014–2023]

The precisely controlled buckling of stiff thin films (e.g., Si or GaAs nano ribbons) on the patterned surface of elastomeric substrate (e.g., poly(dimethylsiloxane) (PDMS)) with periodic inactivated and activated regions was designed by Sun et al. [Sun, Y., Choi, W.M., Jiang, H., Huang, Y.Y., Rogers, J.A., 2006. Controlled buckling of semiconductor nanoribbons for stretchable electronics. Nature Nanotechnology 1, 201–207] for important applications of stretchable electronics. We have developed a post-buckling model based on the energy method for the precisely controlled buckling to study the system stretchability. The results agree with Sun et al.’s (2006) experiments without any parameter fitting, and the system can reach 120% stretchability.     

Mechanical response of a short fiber-reinforced thermoplastic: Experimental investigation and continuum mechanical modeling

The present work can be regarded as a first step toward an integrated modeling of mold filling during injection molding process of polymer composites and the resulting material behavior under service loading conditions. More precisely, the emphasis of the present paper is laid on how to account for local fiber orientation in the ground matrix on the prediction of the mechanical response of the composite at its final solid state. To this end, a set of experiments which captures the mechanical behavior of an injection molded short fiber-reinforced thermoplastic under different strain histories is described. It is shown that the material exhibits complex response mainly due to non-linearity, anisotropy, time/rate-dependence, hysteresis and permanent strain. Furthermore, the relaxed state of the material is characterized by the existence of an equilibrium hysteresis independently of the applied strain rate. A three-dimensional phenomenological model to represent experimentally observed response is developed. The microstructure configuration of the material is simplified and assumed to be entirely represented by a distributed fiber orientation in the ground matrix. In order to account for distributed short fiber orientations in a continuum sense, a concept of (symmetric) generalized structural tensor (tensor of orientation) of second order is adopted. The proposed model is based on assumption that the strain energy function of the composite is given by a linear mixture of the strain energy of each constituent: an isotropic part representing Phase 1 which is essentially related to the ground matrix and an anisotropic part describing Phase 2 which is mainly related to the fibers and the interphase as a whole. Hence, taking into account the fiber content and orientation, the efficiency of the model is assessed and perspectives are drawn.     

Modeling for piezoelectric-shape memory alloy composites

A new concept of a piezoelectric ceramic/shape memory alloy (SMA) composite is proposed with aim of using this as a new actuator material with fast actuation speed and large strain. To prove the new concept, a new model is constructed based on Eshelby formulation where linear piezoelectric constitutive equations and bi-linear superelastic equations of SMA are used. The predictions of the strain induced by applied stress and electric field are made for two simple designs of piezo–SMA composites, 1-D series and 1-D parallel laminated composites. The proposed model indicated that 1-D parallel laminate provides the highest strain induced under bias stress and applied electric field among other composite geometries.     

Large amplitude oscillatory shear behavior of graphene derivative/polydimethylsiloxane nanocomposites

Rheological properties of three different nanocomposites, consisting of graphene oxide (GO), reduced graphene oxide (rGO), and polyhedral oligomeric silsesquioxane grafted reduced graphene oxide (rGO-POSS) as nanofillers and polydimethylsiloxane (PDMS), were investigated by large amplitude oscillatory shear (LAOS). The viscoelastic nonlinearity of the three nanofluids groups was studied by Lissajous curves, local nonlinear viscoelastic moduli of an oscillatory shear cycle, and Fourier transform rheology as a function of filler concentration and increasing and decreasing strain magnitude. The nonlinear behavior of the nanofluids was compared to understand the variation of internal microstructures. Firstly, GO/PDMS composites behave with higher moduli and smaller linear viscoelastic range comparing to that of other two composites. Secondly, the elastic stress Lissajous curves of these composites changed from elliptic to rectangular with round the corner with increasing the filler level and strain amplitude. Thirdly, all these three nanofluids exhibited intra-cycle strain stiffening with increasing strains and shear thickening at intermediate strain and then shearing thinning with increasing strain further. Fourthly, higher harmonic intensity of rGO/PDMS increased with increasing strain and came to a plateau, while that of other two nanofluids reached a maximum and then decreased. It suggested that different surface functionalization of nanoparticles will present different rheological behavior due to formed different network and LAOS could be used as a potential helpful method to characterize rheological properties of nanocomposites, especially at higher shear strain.     

聚酰亚胺/二硫化钼插层复合材料的制备及其摩擦磨损性能研究

用插层法制备了聚酰亚胺/二硫化钼插层复合材料(PI/MoS2),采用X射线衍射仪、红外光谱仪以及扫描电子显微镜等对材料的结构进行表征,采用四球长磨摩擦磨损试验机考察了聚酰亚胺/二硫化钼插层复合材料作为润滑脂添加剂的摩擦磨损行为.结果表明,所合成的PI/MoS2插层复合材料作为锂基脂添加剂对钢-钢摩擦副表现出良好的减摩抗磨作用.这主要是由于在摩擦过程中钢球表面形成了由FeSO4、MoO3及Fe的氧化物等组成的边界润滑及防护薄膜所致.     

Optimization of Digital Image Correlation for High-Resolution Strain Mapping of Ceramic Composites

Digital image correlation (DIC) is assessed as a tool for measuring strains with high spatial resolution in woven-fiber ceramic matrix composites. Using results of mechanical tests on aluminum alloy specimens in various geometric configurations, guidelines are provided for selecting DIC test parameters to maximize the extent of correlation and to minimize errors in displacements and strains. The latter error is shown to be exacerbated by the presence of strain gradients. In a case study, the resulting guidelines are applied to the measurement of strain fields in a SiC/SiC composite comprising 2-D woven fiber. Sub-fiber tow resolution of strain and low strain error are achieved. The fiber weave architecture is seen to exert a significant influence over strain heterogeneity within the composite. Moreover, strain concentrations at tow crossovers lead to the formation of macroscopic cracks in adjacent longitudinal tows. Such cracks initially grow stably, subject to increasing app lied stress, but ultimately lead to composite rupture. Once cracking is evident, the composite response is couched in terms of displacements, since the computed strains lack physical meaning in the vicinity of cracks. DIC is used to identify the locations of these cracks (via displacement discontinuities) and to measure the crack opening displacement profiles as a function of applied stress.     

高体积含量非线性黏弹复合材料有效性质

提出了一个细观力学模型,可用于预测高体积含量非线性黏弹复合材料有效性质.该模型基于广义割线模量法、双球法以及Laplace-Carson变换技术.所提出的模型对玻璃微珠填充高密度聚乙烯(GB/HDPE)复合材料的应力应变关系进行了预测,结果与文献实验结果吻合;计算结果还表明在高体积百分比下文中所提出的方法比基于MT方法预测的粘性效应明显减弱;最后还将所提方法与线黏弹框架下的均质化模型做了比较,结果表明GB/HDPE表现出明显的非线性,线黏弹本构无法描述应变率对其力学行为的影响.     

Relaxation modes of molten polydimethylsiloxane

Although it is known that chain reptation with contour length fluctuations and tube constraint release are the relevant mechanisms of chain relaxation, only applications of the theory to specific polymers could allow one to determine the relative importance of these relaxation modes. With this purpose we study the relation between the shear relaxation modulus of entangled, linear and flexible polydimethylsiloxane (PDMS) samples with narrow molecular weight distribution (MWD) and some of their blends. The linear PDMS are synthesized by anionic polymerization. Binary blends having different concentrations of the linear PDMS with narrow MWD are also prepared.  A theory developed by some of the authors has been proposed previously and is based on the double reptation mixing rule and a law for the relaxation time of the chains. Since, calculations in the theory must be carried out with rheometric data of linear viscoelasticity, the time-temperature superposition principle is used at a reference temperature of 20°C to obtain the and master curves. We conclude that the PDMS chains in a matrix with 1.5 relax predominantly by reptation while the tube renewal follows Rouse mode, which is proportional to chain molecular weight raised to the square power. It is also shown that dilution effects due to short chains start to be important in the binary blends of PDMS samples due to the presence of Zimm mode of relaxation, which is suggested by the theory for linear polymers of relatively high polydispersity. Received: 27 January 1998 Accepted: 13 August 1998     

Determination of effective thermomechanical parameters of a mixture of two elastothermoviscoplastic constituents

We analyze plane strain deformations of a representative volume element (RVE) to evaluate effective thermophysical parameters of a particulate composite comprised of two perfectly bonded heat conducting elasto-thermo-visco-plastic constituents. It is assumed that the composite is also isotropic and its response elasto-thermo-visco-plastic. Effective values of material parameters so computed are compared with those obtained from either existing micromechanics models or the rule of mixtures or both. It is found that values computed from the rule of mixtures differ at most by 10% from those obtained by using the RVE. Effective stress versus effective strain curves obtained by analyzing simple shearing and axisymmetric deformations of the RVE and of the homogenized material, and also those obtained in plane strain deformations involving loading/unloading/reloading are found to be very close to each other. Time histories of the effective plastic strain at two neighboring points, one in each constituent, are quite different. The effective stress computed by the rule of mixtures from the average effective stress in each constituent and its volume fraction is very close to that obtained from surface tractions acting on the specimen boundaries. The average effective stress in a constituent is computed from the effective plastic strain averaged over that constituent. This also holds for a composite comprised of three constituents.     

A constitutive model of nanocomposite hydrogels with nanoparticle crosslinkers

Nanocomposite hydrogels with only nanoparticle crosslinkers exhibit extraordinarily higher stretchability and toughness than the conventional organically crosslinked hydrogels, thus showing great potential in the applications of artificial muscles and cartilages. Despite their potential, the microscopic mechanics details underlying their mechanical performance have remained largely elusive. Here, we develop a constitutive model of the nanoparticle hydrogels to elucidate the microscopic mechanics behaviors, including the microarchitecture and evolution of the nanoparticle crosslinked polymer chains during the mechanical deformation. The constitutive model enables us to understand the Mullins effect of the nanocomposite hydrogels, and the effects of nanoparticle concentrations and sizes on their cyclic stress–strain behaviors. The theory is quantitatively validated by the tensile tests on a nanocomposite hydrogel with nanosilica crosslinkers. The theory can also be extended to explain the mechanical behaviors of existing hydrogels with nanoclay crosslinkers, and the necking instability of the composite hydrogels with both nanoparticle crosslinkers and organic crosslinkers. We expect that this constitutive model can be further exploited to reveal mechanics behaviors of novel particle-polymer chain interactions, and to design unprecedented hydrogels with both high stretchability and toughness.     

Effects of non-uniform strains on tensile fracture of fiber-reinforced ceramic composites

Effects of non-uniform strains on tensile fracture of fiber-reinforced ceramic–matrix composites have not been satisfactorily explained by existing mechanics-based models. In this paper, we use an exact model of fiber fragmentation under global load sharing conditions to predict fracture in three model problems in which non-uniform strains occur: (i) an end-constrained plate subject to a linear transverse temperature gradient; (ii) an internally-pressurized cylindrical tube with a linear through-thickness temperature gradient; and (iii) a rectangular beam under combined bending and tension. Fracture is assumed to occur when the global load reaches a maximum value. Approximations to the exact fragmentation model are also assessed, with the goal of decoupling the effects of two important parts of the computed stress–strain response: the rate of post-peak strain softening and the magnitude of the plateau “flow” stress once fiber fragmentation is complete. We find that for cases in which the fiber Weibull modulus is low and hence its plateau strength is high relative to its peak and the loading yields a sufficiently high strain gradient, the failure strain lies in the plateau regime. Consequently, the results can be predicted with good accuracy using a perfectly-plastic representation of the post-peak response. In contrast, for cases in which the fiber Weibull modulus is high, the failure strain lies in the softening portion of the curve. Here a linear-softening model is found to yield accurate results. A preliminary assessment of the model has been made by comparing predicted and measured bending/tension strength and failure strain ratios for one specific composite. The correlations appear good, though additional experiments are required in order to critically assess the model predictions over a range of loading scenarios.     

Macroscopic response of particle-reinforced elastomers subjected to prescribed torques or rotations on the particles

Particle-reinforced rubbers are composite materials consisting of randomly distributed, stiff fibers/particles in a soft elastomeric material. Since the particles are stiff compared to the embedding rubber, their deformation can be ignored for all practical purposes. However, due to the softness of the rubber, they can undergo rigid body translations and rotations. Constitutive models accounting for the effect of such particle motions on the macroscopic response under prescribed deformations on the boundary have been developed recently. But, in some applications (e.g., magneto-active elastomers), the particles may experience additional torques as a consequence of an externally applied (magnetic) field, which, in turn, can affect the overall rotation of the particles in the rubber, and therefore also the macroscopic response of the composite. This paper is concerned with the development of constitutive models for particle-reinforced elastomers, which are designed to account for externally applied torques on the internally distributed particles, in addition to the externally applied deformation on the boundary of the composite. For this purpose, we propose a new variational framework involving suitably prescribed eigenstresses on the particles. For simplicity, the framework is applied to an elastomer reinforced by aligned, rigid, cylindrical fibers of elliptical cross section, which can undergo finite rotations in the context of a finite-deformation, plane strain problem for the composite. In particular, expressions are derived for the average in-plane rotation of the fibers as a function of the torques that are applied on them, both under vanishing and prescribed strain on the boundary. The results of this work will make possible the development of improved constitutive models for magneto-active elastomers, and other types of smart composite materials that are susceptible to externally applied torques.     

Mechanics of nonbuckling interconnects with prestrain for stretchable electronics

The performance of the flexibility and stretchability of flexible electronics depends on the mechanical structure design, for which a great progress has been made in past years. The use of prestrain in the substrate, causing the compression of the transferred interconnects, can provide high elastic stretchability. Recently, the nonbuckling interconnects have been designed, where thick bar replaces thin ribbon layout to yield scissor-like in-plane deformation instead of in-or out-of-plane buckling modes. The nonbuckling interconnect design achieves significantly enhanced stretchability. However,combined use of prestrain and nonbuckling interconnects has not been explored. This paper aims to study the mechanical behavior of nonbuckling interconnects bonded to the prestrained substrate analytically and numerically. It is found that larger prestrain,longer straight segment, and smaller arc radius yield smaller strain in the interconnects.On the other hand, larger prestrain can also cause larger strain in the interconnects after releasing the prestrain. Therefore, the optimization of the prestrain needs to be found to achieve favorable stretchability.     

多孔PI/MSNT复合含油润滑薄膜的设计制备及其摩擦学性能研究

以聚苯乙烯(PS)微球为致孔剂、介孔二氧化硅纳米管(MSNT)为填充剂来改性多孔聚酰亚胺(PI),设计制备了多孔PI/MSNT复合薄膜,并对其孔结构和形貌进行了表征;在此基础上,以液体石蜡油为存储介质制备了多孔PI/MSNT复合含油润滑薄膜,系统考察了MSNT的添加对多孔PI薄膜的热稳定性、储油性能、力学性能和摩擦学性能的影响. 结果表明:与单组分PI含油薄膜相比,MSNT的加入不仅改善了多孔PI基体的热稳定性和力学性能,而且使得复合薄膜的储油性能和摩擦磨损性能均得到了显著提高,证实多孔PI/MSNT复合含油薄膜更适用于高载荷下的摩擦工况.      

Bounds and estimates for the effect of strain gradients upon the effective plastic properties of an isotropic two-phase composite

Predictions are made for the size effect on strength of a random, isotropic two-phase composite. Each phase is treated as an isotropic, elastic-plastic solid, with a response described by a modified deformation theory version of the Fleck-Hutchinson strain gradient plasticity formulation (Fleck and Hutchinson, J. Mech. Phys. Solids 49 (2001) 2245). The essential feature of the new theory is that the plastic strain tensor is treated as a primary unknown on the same footing as the displacement. Minimum principles for the energy and for the complementary energy are stated for a composite, and these lead directly to elementary bounds analogous to those of Reuss and Voigt. For the case of a linear hardening solid, Hashin-Shtrikman bounds and self-consistent estimates are derived. A non-linear variational principle is constructed by generalising that of Ponte Castañeda (J. Mech. Phys. Solids 40 (1992) 1757). The minimum principle is used to derive an upper bound, a lower estimate and a self-consistent estimate for the overall plastic response of a statistically homogeneous and isotropic strain gradient composite. Sample numerical calculations are performed to explore the dependence of the macroscopic uniaxial response upon the size scale of the microstructure, and upon the relative volume fraction of the two phases.     

Microstructural effects in non linear stratified composites

In this paper, we analyze the microstructural effects on non linear elastic and periodic composites within the framework of asymptotic homogenization. We assume that the constitutive laws of the individual constituents derive from strain potentials. The microstructural effects are incorporated by considering the higher order terms, which come from the asymptotic series expansion. The complete solution at any order requires the resolution of a chain of cell problems in which the source terms depend on the solution at the lower order. The influence of these terms on the macroscopic response of the non linear composite is evaluated in the particular case of a stratified microstructure. The analytic solutions of the cell problems at the first and second order are provided for arbitrary local strain–stress laws which derive from potentials. As classically, the non-linear dependence on the applied macroscopic strain is retrieved for the solution at the first order. It is proved that the second order term in the expansion series also exhibits a non linear dependence with the macroscopic strain but linearly depends on the gradient of macroscopic strain. As a consequence, the macroscopic potential obtained by homogenization is a quadratic function of the macroscopic strain gradient when the expansion series is truncated at the second order. This model generalizes the well known first strain gradient elasticity theory to the case of non linear elastic material. The influence of the non local correctors on the macroscopic potential is investigated in the case of power law elasticity under macroscopic plane strain or antiplane conditions.     

二硫化钼/硫化锌纳米粉体的制备及其改性聚酰亚胺复合材料的摩擦学性能研究

采用一步水热法设计制备了二硫化钼/硫化锌(MoS₂/ZnS)纳米杂化体,并利用热压成型技术得到聚酰亚胺/二硫化钼/硫化锌(PI/MoS₂/ZnS)复合材料. 采用扫描电子显微镜、透射电子显微镜、X射线衍射仪以及光电子能谱仪对所制备材料的形貌和化学组成进行表征,结果表明MoS₂纳米薄片均匀致密地包覆在ZnS纳米颗粒表面. 热重分析和差示扫描量热曲线结果表明,MoS₂/ZnS纳米杂化体的引入显著地提升了PI基体的热稳定性能. 摩擦磨损测试结果表明,三种填料(MoS₂,ZnS和MoS₂/ZnS)均能有效改善PI基体的摩擦学性能,其中MoS₂/ZnS纳米杂化体的增强效应最为显著,这主要归因于MoS₂纳米片和ZnS纳米粒子之间的协同增强效应. 当MoS₂/ZnS纳米杂化体的质量分数为1.5%时, PI/MoS₂/ZnS复合材料的摩擦学性能达到最优,相较于纯的PI,复合材料的摩擦系数和磨损率分别下降了15. 9%和34. 3%.      

The uniaxial tension of particulate composite materials with nonlinear interface debonding

Debonding of particle/matrix interfaces can significantly affect the macroscopic behavior of composite material. We have used a nonlinear cohesive law for particle/matrix interfaces to study interface debonding and its effect on particulate composite materials subject to uniaxial tension. The dilute solution shows that, at a fixed particle volume fraction, small particles lead to hardening behavior of the composite while large particles yield softening behavior. Interface debonding of large particles is unstable since the interface opening (and sliding) displacement(s) may have a sudden jump as the applied strain increases, which is called the catastrophic debonding. A simple estimate is given for the critical particle radius that separates the hardening and softening behavior of the composite.