Collective buckling of an elastic beam array on an elastic substrate for applications in soft lithography

We analyze the collective buckling of an array of vertical elastic beams with their lower ends built into an elastic substrate. The beams interact between themselves through the deformation of the elastic substrate. The present analysis is more sophisticated than previous ones on rigid beams on an elastic substrate in that the beams are regarded as elastic rather than rigid. From the linear theory for elastic beam buckling and the linear theory of elasticity, an eigenvalue problem is formulated and solved. Calculations show that the deformability of the beams lowers the critical height of the beams, but it does not affect the buckling pattern much. Our work also suggests that the collective buckling is dominated by the interaction of neighboring beams through the deformation of the substrate rather than whether the beams are rigid or elastic. The results are useful for the better understanding, design and application of the nanostructures produced by soft lithography.     

Collective buckling of nonuniform nanobeams interacting through an elastic substrate

We analyze the collective buckling of a row of vertical beams with their lower ends built into an elastic substrate. The beams interact among themselves through the deformation of the substrate. The present analysis is more sophisticated than a previous one in that the beams’ height and spacing are no longer uniform. This allows us to study the buckling of beams with specific height and spacing variation profiles. The effect of irregularity when the height of a particular beam or the distance between a particular pair of neighboring beams is different from the rest is also examined.     

Mechanical buckling instability of thin coatings deposited on soft polymer substrates

Deformation of rubber and poly(ethylene terephthalate) coated with a platinum or a gold film was studied. The thickness of the coating film was approximately ten nanometers. The polymer substrates were 10⁴ to 10⁵-fold softer than the coating. Folding of the coating leading to the appearance of a wave-like pattern on an originally smooth surface was observed both in tension and after shrinkage. In tension the wave crests are oriented along the elongation direction. After shrinkage the wave crests are perpendicular to the shrinkage direction. For rubber substrates, the appearance of the wave is explained by a mechanical buckling instability of the coating under compressive force. The length of the surface wave depends on the thickness of the coating layer and the rigidity of the polymer substrate. In addition to folding, regular fragmentation of the coating film on long and comparatively narrow bands is observed. The cracks are perpendicular to the wave crests both in tension and after shrinkage.     

Surface layer stiffness effects on fracture of polymer multilayers: a linear elastic model

A tough thermoplastic polymer may show a transition to brittle behaviour when a skin of different properties forms on, or is painted or bonded onto, its free surfaces. A small-scale yielding, linear elastic analysis of the core material, in combination with an axisymmetric plate analysis of the skin, is used here to explore the role in this phenomenon of skin-core modulus inequality. When applied to the homogeneous (equal modulus) case, this very simple constraint model appears to provide independent support for the ASTM thickness criterion for plane-strain LEFM test validity. When applied to previously published impact fracture data from inhomogeneous (polyethylene-polypropylene) sandwich plates, the model successfully explains the shift in brittle-tough transition temperature precipitated by bonding a polypropylene skin to a polyethylene core. The model offers specific predictions for the effect, on transition temperature shift, of variables such as skin thickness and core properties; these predictions remain to be verified.     

Two-dimensional stick-slip on a soft elastic polymer: pattern generation using atomic force microscopy

It has been demonstrated that it is possible to create laterally differentiated frictional patterning and three-dimensional structures using an atomic force microscope (AFM) probe on the surface of a soft elastic polymer, poly(dimethylsiloxane) (PDMS). The resulting effect of contact mode imaging at low loading forces (<100?nN), observed in the lateral force mode, revealed a homogeneous pattern on the PDMS surface exhibiting higher friction. With higher loading forces ([Formula: see text]?nN) the effect is non-uniform, resulting in structures with depths on the nanometre scale. The topographic and frictional data revealed stick-slip responses in both the fast (orthogonal to the long axis of the lever) and slow (parallel to the long axis of the lever) directions of probe travel from scanning in a raster pattern. The stick-slip events are manifested in the form of a series of shallow channels spaced evenly apart on the polymer surface. Detailed friction loop analysis acquired during the manipulation process showed that the lateral force changed according to the strength of trapping of the tip with the polymer surface exhibiting significant in-plane deformation due to lateral forces being imposed. An incremental increase in the initial loading force resulted in an increase in in-plane displacement and a greater spacing between the stick lines/channels in the slow-scan direction. A decrease in channel length in the fast-scan direction is also observed as a result of an increase in static friction with normal force, resulting in greater surface deformation and shorter track length for sliding friction.     

Investigation of aluminium thin layer microstructure on BOPP polymer substrate

In this work, 40 μm biaxially oriented polypropylene (BOPP) polymer substrate is coated in a roll coater system. The single- and double-coated aluminium thin layers are analyzed by XRD, SEM, TEM, AFM and optical light microscopy. The size and density of pinholes are investigated by using TEM, the size of the pinholes are in the range of 0.8–8 μm, it is shown that with increasing sample thickness, the dimension of pinholes decreases. SEM and AFM are applied to study the surface morphology. The results show that the surface roughness of double-coated film is better than the single-coated one and the size of pinholes is smaller. The transmittance through the samples is measured on the UV–Vis range. The results show that double-coated film has significantly low transmittance (almost zero transmittance) in UV–Vis region.     

Electromechanical analysis of a symmetric piezoelectric/elastic laminate structure: theory and experiment

The dynamic characteristics of a piezoelectric laminate cantilever structure treated as an actuator are analyzed by electroelasticity. General formulation of calculations for displacement sensitivity, electric current, electromechanical coupling coefficients, and results from parametric analyses are presented for axial expansion/contraction, transverse bending, and expansion/contraction-bending coupled motion. The frequency response of displacement and electrical current and the displacement sensitivity were experimentally measured. Close agreement between theoretical and experimental results confirms validity of the theory.     

Micromechanics as a basis of random elastic continuum approximations

The problem of the determination of stochastic constitutive laws for input to continuum-type boundary value problems is analyzed from the standpoint of the micromechanics of polycrystals and matrix-inclusion composites. Passage to a sought-for random continuum is based on a scale dependent window playing the role of a Representative Volume Element (RVE). It turns out that an elastic microstructure with piecewise continuous realizations of random tensor fields of stiffness cannot be uniquely approximated by a random field of stiffness with continuous realizations. Rather, two random continuum fields may be introduced to bound the material response from above and from below. As the size of the RVE relative to the crystal size increases to infinity, both fields converge to a deterministic continuum with a progressively decreasing strength of fluctuations. Since the RVE corresponds to a single finite element cell not infinitely larger than the crystal size, two random fields are to be used to bound the solution of a given boundary value problem at a given scale of resolution. The method applies to a number of other elastic microstructures, and provides the basis for stochastic finite differences and elements. The latter point is illustrated by an example of a stochastic boundary value problem of a heterogeneous membrane.     

On the dynamic behaviour of interfacial cracks between a piezoelectric layer and an elastic substrate

Surface-bonded piezoelectric layers can be used as actuators/sensors for advanced structural applications. The current paper provides a theoretical study of the dynamic behaviour of interacting cracks between a piezoelectric layer and an elastic medium under antiplane mechanical loads. The electromechanical field of a single interfacial crack is determined first using Fourier transform technique and solving the resulting integral equations. This fundamental solution is then imple- mented into a pseudo-incident wave method to account for the interaction between different cracks. The dynamic behaviour of the resulting stress field is studied with special attention being paid to the stress intensity factors at the crack tips. Typical examples are provided to show the effect of the size and position of the cracks, the material combination and the loading frequency upon the stress intensity factors.     

Double layer calculations for the attachment of a colloidal particle with a charged surface patch onto a substrate

The attachment of a particle onto a substrate with a like surface charge may be greatly facilitated in the presence of an oppositely charged surface patch on the particle. Calculations are presented for the effect of various parameters on particle attachment. These include the patch charge, patch size, particle size and the ionic strength of the medium.     

Delaminating buckling model based on nonlocal Timoshenko beam theory for microwedge indentation of a film/substrate system

A novel model built on the basis of nonlocal Timoshenko beam theory is presented for delaminating buckling in the microwedge indentation test of a thin film on an elastic substrate. Two size effects are accounted for in the proposed model. One is the delamination size effect, and the other is the film thickness effect. The influence of the elastic deformation in the substrate and the indentation-induced impression or notch on the buckling behaviors are taken into consideration by employing coupled line springs as the boundary conditions of the buckled film. The critical stress for buckling, the energy release rate and the phase angle of the interface delamination crack are calculated and compared with those by classical beam theories. Sensitivity of the two size effects is observed.     

Global buckling load of a nonlinearly elastic bar

Summary The nonlinear buckling of an elastic bar with softening characteristic is studied. It is found that, under large disturbances, the bar may buckle under loads well below the linear buckling load.     

Electromechanical analysis of an asymmetric piezoelectric/elastic laminate structure: theory and experiment

The electromechanical characteristics of an asymmetric piezoelectric/elastic laminated actuator are investigated by electroelasticity and experiments. The axial expansion-bending coupled motion of the system is separated into quasi-axial expansion and quasi-bending by its physical significance of vibration modes. General formulation of calculations for the mechanical, electrical, and electromechanical characteristics of the structure are presented via parametric analysis. Finally, the displacement sensitivity and the frequency response of displacement and electrical current are experimentally measured for this piezoelectric/elastic laminated specimen. Close agreement between theoretical and experimental results confirms the validity of the theory.     

Measuring mechanical properties of micro- and nano-fibers embedded in an elastic substrate: Theoretical framework and experiment

We propose to measure the elastoplastic properties of micro- and nano-fibers by a normal indentation technique in which the vertically aligned fibers are embedded in an elastic matrix. Measurements are taken at two different indentation depths, which represent different levels of the matrix effects and lead to the establishment of two independent equations that correlate the fiber/matrix properties with the indentation responses. Effective reverse analysis algorithms are proposed, and by following which the desired fiber properties can be determined from a sharp indentation test. Comprehensive analysis is also carried out to verify the effectiveness and error sensitivity of the presented method. The extracted material properties agree well with those measured from the parallel experiments on human hair and glass fibers.     

Analysis of the elastic buckling of a plywood column

Buckling tests were conducted on specimens of 5-ply lauan plywood for a range of slenderness ratios to measure its buckling stress. Three-dimensional finite element calculations of buckling stress were performed and their validity examined by comparison with experimental results. Both experimental and calculated results revealed that buckling stress is influenced by Young’s modulus values (a measure of stiffness) obtained not only under flexural loading but also under axial loading. When the axial Young’s modulus is larger than the flexural Young’s modulus, the buckling stress is measured as larger than that obtained using the flexural Young’s modulus alone. Inversely, when the axial Young’s modulus is smaller than the flexural Young’s modulus, the buckling stress is measured as smaller than that obtained using the flexural Young’s modulus alone. Therefore, both the Young’s modulus values should be taken into account for determining the buckling stress of a plywood column.     

基于弹性基础梁理论的复合材料薄壁圆柱壳屈曲承载力模型

提出一种复合材料薄壁圆柱壳轴压局部屈曲承载力计算模型。在梁弯曲变形平截面假定和小变形假定的基础上,提出复合材料层合梁抗弯刚度的计算方法;根据轴压下圆柱壳的几何对称性及受力对称性,将圆柱壳局部屈曲问题转化为轴向和环向壳带的弯曲变形问题。依据薄壳稳定理论,建立弹性基础上纵向壳带局部屈曲模型,得到了复合材料圆柱壳屈曲承载力解析公式。理论计算公式与经验工程计算公式相比,具有形式上的相似性,且得到的计算系数可直接求出,而非经验范围选取。对三种铺层的复合材料薄壁圆柱壳进行了轴压试验,结合文献试验数据对比,试验结果与理论预测值基本一致,满足工程精度要求,验证了模型的正确性。     

The effect of illumination on the parameters of the polymer layer deposited from solution onto a semiconductor substrate

The effect of illumination on the thickness and roughness of monolayers of polycationic molecules of polyethyleneimine deposited from solution onto a silicon substrate was discovered and investigated. The super-bandgap illumination of the substrate during polyethyleneimine adsorption causes a decrease in both the roughness and integral thickness of the organic layer on n- and p-Si substrates.     

Edge-wave buckling of rolled elastic strips: asymptotic results

The problem considered in this paper concerns the edge-wave buckling phenomenon commonly encountered in forming processes such as rolling and levelling. Due to the combined action of global tensile forces and residual stresses, the elastic strips involved in these scenarios experience a symmetric short-wave deformation pattern that tends to be confined near their long edges. We use boundary-layer techniques to provide simple estimates for the critical load and the wavelength of the buckling waves. A number of complementary asymptotic features of the marginal stability curves are also reported.