27 research outputs found

    Finite bending and pattern evolution of the associated instability for a dielectric elastomer slab

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    We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental version. We first study the static finite bending deformation of the slab. We then derive the three-dimensional equations for the onset of small-amplitude wrinkles superimposed upon the finite bending. We use the surface impedance matrix method to build a robust numerical procedure for solving the resulting dispersion equations and determining the wrinkled shape of the slab at the onset of buckling. Our analysis is valid for dielectrics modeled by a general free energy function. We then present illustrative numerical calculations for ideal neo-Hookean dielectrics. In that case, we provide an explicit treatment of the boundary value problem of the finite bending and derive closed-form expressions for the stresses and electric field in the body. For the incremental deformations, we validate our analysis by recovering existing results in more specialized contexts. We show that the applied voltage has a destabilizing effect on the bending instability of the slab, while the effect of the axial load is more complex: when the voltage is applied, changing the axial loading will influence the true electric field in the body, and induce competitive effects between the circumferential instability due to the voltage and the axial instability due to the axial compression. We even find circumstances where both instabilities cohabit to create two-dimensional patterns on the inner face of the bent sector

    Pattern evolution in bending dielectric-elastomeric bilayers

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    We propose theoretical and numerical analyses of smart bending deformation of a dielectric-elastic bilayer in response to a voltage, based on the nonlinear theory of electro-elasticity and the associated linearized incremental field theory. We reveal that the mechanism allowing the bending angle of the bilayer can be tuned by adjusting the applied voltage. Furthermore, we investigate how much can the bilayer be bent before it loses its stability by buckling when one of its faces is under too much compression. We find that the physical properties of the two layers must be selected to be of the same order of magnitude to obtain a consequent bending without encountering buckling. If required, the wrinkles can be designed to appear on either the inner or the outer bent surface of the buckled bilayer. We validate the results through comparison with those of the classical elastic problem

    Silver-Indium Solid Solution on Copper as Passivation and Study of its Reaction with Tin Solder

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    As the most commonly used electrode, leadframe, and package material in electronic packaging, copper (Cu) has severe oxidation problem, preventing wetting during soldering processes and prohibiting successful wire bonding. Thus leads and bond pads of leadframes and packages are often coated with a passivation layers such as palladium, silver, or tin, which suppresses the growth of copper oxides. In this research, I investigated the use of silver-indium ((Ag)In) solid solution as a new alternative coating material for passivation. First, a reaction study of bulk (Ag)-9.5In solid solution disks with Sn was conducted to evaluate possible intermetallic compounds in the Ag-In-Sn system. Next, (Ag)-9.5In solid solution layer was coated on copper substrates by E-beam evaporation. The (Ag)9.5In-passivated Cu substrates and bare Cu substrates were aged at 150°C for up to 1000 hours in air. No oxide was detectable on (Ag)9.5In-passsivated Cu substrates while thick Cu2O3 was grown on bare Cu. This result illustrates that (Ag)9.5In solid solution is an excellent passivation coating material. Then, (Ag)9.5In-passivated Cu substrates were electroplated with tin. As a reference, bare Cu substrates were also plated with tin. These two different types of samples were reflowed and aged for different amount of time. No flux was used. The reaction results were examined by scanning electron microscope/energy dispersive X-ray spectroscopy (SEM/EDX) and compared. The experimental results show that tin wetted and reacted well with (Ag)9.5In-passivated Cu substrates. The growth of intermetallic compound (Cu6Sn5, Cu3Sn) on (Ag)9.5In-passivated Cu substrates is also suppressed compared to the growth on bare Cu substrates. The design of (Ag)In solid solution passivation is an invention and its superior performance is a discovery. It provides an economical, environmentally friendly, and valuable passivation alternative on copper electrodes, leadframes, and packages

    Pattern evolution in bending dielectric-elastomeric bilayers

    No full text
    We propose theoretical and numerical analyses of smart bending deformation of a dielectric-elastic bilayer in response to a voltage, based on the nonlinear theory of electro-elasticity and the associated linearized incremental field theory. We reveal that the mechanism allowing the bending angle of the bilayer can be tuned by adjusting the applied voltage. Furthermore, we investigate how much the bilayer can be bent before it loses its stability by buckling when one of its faces is under too much compression. We find that the physical properties of the two layers must be selected to be of the same order of magnitude to obtain a consequent bending without encountering buckling. If required, the wrinkles can be designed to appear on either the inner or the outer bent surface of the buckled bilayer. We validate the results through comparison with those of the classical elastic problem. (C) 2019 Elsevier Ltd. All rights reserved.This work was supported by a Government of Ireland Postdoctoral Fellowship from the Irish Research Council (No. GOIPD/2017/1208) and by the National Natural Science Foundation of China (No. 11621062). WQC and YPS acknowledge the support from the Shenzhen Scientific and Technological Fund for R&D (No. JCYJ20170816172316775). BW acknowledges the awarding of Research Fellow at Politecnico di Torino. MD thanks Zhejiang University for funding research visits to Hangzhou. YPS is also grateful to Chengjun Wang and Renwei Mao at Zhejiang University for fruitful discussions.peer-reviewed2021-07-2

    Pattern evolution in bending dielectric-elastomeric bilayers

    No full text
    We propose theoretical and numerical analyses of smart bending deformation of a dielectric-elastic bilayer in response to a voltage, based on the nonlinear theory of electro-elasticity and the associated linearized incremental field theory. We reveal that the mechanism allowing the bending angle of the bilayer can be tuned by adjusting the applied voltage. Furthermore, we investigate how much the bilayer can be bent before it loses its stability by buckling when one of its faces is under too much compression. We find that the physical properties of the two layers must be selected to be of the same order of magnitude to obtain a consequent bending without encountering buckling. If required, the wrinkles can be designed to appear on either the inner or the outer bent surface of the buckled bilayer. We validate the results through comparison with those of the classical elastic problem. (C) 2019 Elsevier Ltd. All rights reserved.This work was supported by a Government of Ireland Postdoctoral Fellowship from the Irish Research Council (No. GOIPD/2017/1208) and by the National Natural Science Foundation of China (No. 11621062). WQC and YPS acknowledge the support from the Shenzhen Scientific and Technological Fund for R&D (No. JCYJ20170816172316775). BW acknowledges the awarding of Research Fellow at Politecnico di Torino. MD thanks Zhejiang University for funding research visits to Hangzhou. YPS is also grateful to Chengjun Wang and Renwei Mao at Zhejiang University for fruitful discussions.2021-07-2

    Finite bending and pattern evolution of the associated instability for a dielectric elastomer slab

    No full text
    We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental version. We first study the static finite bending deformation of the slab. We then derive the three-dimensional equations for the onset of small-amplitude wrinkles superimposed upon the finite bending. We use the surface impedance matrix method to build a robust numerical procedure for solving the resulting dispersion equations and determining the wrinkled shape of the slab at the onset of buckling. Our analysis is valid for dielectrics modeled by a general free energy function. We then present illustrative numerical calculations for ideal neo-Hookean dielectrics. In that case, we provide an explicit treatment of the boundary value problem of the finite bending and derive closed-form expressions for the stresses and electric field in the body. For the incremental deformations, we validate our analysis by recovering existing results in more specialized contexts. We show that the applied voltage has a destabilizing effect on the bending instability of the slab, while the effect of the axial load is more complex: when the voltage is applied, changing the axial loading will influence the true electric field in the body, and induce competitive effects between the circumferential instability due to the voltage and the axial instability due to the axial compression. We even find circumstances where both instabilities cohabit to create two-dimensional patterns on the inner face of the bent sector. (C) 2018 Elsevier Ltd. All rights reserved.This work was supported by a Government of Ireland Postdoctoral Fellowship from the Irish Research Council (no. GOIPG/2016/712) and by the National Natural Science Foundation of China (no. 11621062). MD thanks Zhejiang University for funding a research visit to Hangzhou. WQC and YPS also acknowledge the support from the Shenzhen Scientific and Technological Fund for R&D (no. JCYJ20170816172316775).2020-09-2
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