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Research Papers

# Design and Analysis of Magnetic-Assisted Transfer PrintingPUBLIC ACCESS

[+] Author and Article Information
Qinming Yu

Department of Engineering Mechanics,
School of Mechanics, Civil Engineering
and Architecture,
Northwestern Polytechnical University,
Xi'an 710129, China;
State Key Laboratory for Strength and
Vibration of Mechanical Structures,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: qingminyu@163.com

Furong Chen, Honglei Zhou, Xudong Yu

Department of Engineering Mechanics,
School of Mechanics, Civil Engineering
and Architecture,
Northwestern Polytechnical University,
Xi'an 710129, China

Huanyu Cheng

Department of Engineering
Science and Mechanics,
The Pennsylvania State University,
University Park, PA 16802
e-mail: Huanyu.Cheng@psu.edu

Huaping Wu

Key Laboratory of E&M
(Zhejiang University of Technology),
Ministry of Education and Zhejiang Province,
Hangzhou 310014, China

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 14, 2018; final manuscript received June 15, 2018; published online July 5, 2018. Editor: Yonggang Huang.

J. Appl. Mech 85(10), 101009 (Jul 05, 2018) (7 pages) Paper No: JAM-18-1283; doi: 10.1115/1.4040599 History: Received May 14, 2018; Revised June 15, 2018

## Abstract

As a versatile yet simple technique, transfer printing has been widely explored for the heterogeneous integration of materials/structures, particularly important for the application in stretchable and transient electronics. The key steps of transfer printing involve pickup of the materials/structures from a donor and printing of them onto a receiver substrate. The modulation of the interfacial adhesion is critically important to control the adhesion/delamination at different material–structural interfaces. Here, we present a magnetic-assisted transfer printing technique that exploits a unique structural design, where a liquid chamber filled with incompressible liquid is stacked on top of a compressible gas chamber. The top liquid chamber wall uses a magnetic-responsive thin film that can be actuated by the external magnetic field. Due to the incompressible liquid, the actuation of the magnetic-responsive thin film induces the pressure change in the bottom gas chamber that is in contact with the material/structure to be transfer printed, leading to effective modulation of the interfacial adhesion. The decreased (increased) pressure in the bottom gas chamber facilitates the pickup (printing) step. An analytical model is also established to study the displacement profile of the top thin film of the gas chamber and the pressure change in the gas chamber upon magnetic actuation. The analytical model, validated by finite element analysis, provides a comprehensive design guideline for the magnetic-assisted transfer printing.

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## Introduction

The recent advance in stretchable electronics allows direct integration of sensing devices on the biological tissues for continuous monitoring of vital signals for clinical diagnostics [13]. The application of such device inside the human body, i.e., implantable devices, has also spurred the development of transient devices that stably function for a programmed timeframe and then disintegrate completely inside the human body [46]. The fabrication of these two type of devices typically involves the pickup of the fabricated device from a conventional growth substrate (donor) by an elastomeric stamp, followed by a printing step to deliver the device onto a target substrate (receiver) (e.g., soft elastomer in stretchable electronics or a biodegradable substrate in transient devices). Such process consisting of pickup and printing steps is typically termed as transfer printing [7]. Transfer printing is also a very important technique for the heterogeneous integration of different materials to form functional components with two-dimensional or three-dimensional (3D) structures in a device [8]. This technique enables high throughput, large-scale, yet simple, device integration from various discrete components for applications in bio-integrated electronics [1,9,10], platforms for the study of two-dimensional materials and cells [1114], and beyond [3,1517].

The transfer printing process involves the competing fracture between the stamp/device and device–receiver interfaces [18]. To ensure a successful transfer printing, the adhesion at the stamp–device interface needs to be larger than that at the device–donor interface in the pickup step but smaller than that at the device–receiver interface in the printing step. Therefore, it is of great interest to explore a strategy to modulate interfacial adhesion strength at the stamp–device interface and a variety of techniques has been developed. For instance, modifying the surface chemistry is a simple strategy to tune the interfacial adhesion [19,20]. As the mechanical strategies are reversible in the transfer printing process, they present a promising alternative. Exploiting mechanics in the transfer printing process, advanced techniques have been extensively studied, including (1) kinetically controlled transfer printing [18,21,22], (2) surface relief structure-assisted transfer printing [23,24], (3) force-assisted transfer printing [2527], (4) laser-assisted transfer printing [28,29], and many others with the use of smart materials [30].

However, each technique mentioned earlier is associated with its limitation. For instance, the kinetically controlled transfer printing that uses the retraction velocity of the stamp to tune the adhesion at the stamp–device interface is limited by the range of retraction velocity of the stamp. It becomes challenging when the receiver substrate is also viscoelastic. Although the contact area at the stamp–device interface can be changed through the design of the surface relief structures in the stamp, the operation of the surface relief structure-assisted transfer printing is limited to a certain timeframe due to the use of viscoelastic restoration effect. Alternatively, shape memory polymer has been explored in the design of the stamp, where the change in the geometry of the surface relief structure made from the shape memory polymer is modulated by the external temperature change [31,32]. The process requires relatively precise temperature control that takes time and it also involves programming of the stamp after each use. In the force-assisted transfer printing, the delivery of the force can be challenging. As for the laser-assisted transfer printing, the power and duration of the pulsed laser have to be precisely controlled to avoid damage to the device. The thermoresponsive hydrogel can be used to control the cavity pressure for switchable adhesion, but the response is slow [30].

Therefore, it is vitally important to develop a high-precision, high-yield, and high-throughput, yet simple to use, transfer printing technique for the heterogeneous integration that has broad impact in the applications of stretchable and transient electronics. In this study, we present an alternative design of the stamp that can be controlled by the external magnetic field to retrieve device components from the growth substrate and then deliver them onto the target substrate.

## Design of Magnetic-Responsive Stamp

Figure 1 presents the design of the magnetic-responsive stamp for transfer printing. The stamp consists of a closed soft chamber and incompressible liquid in this sealed chamber. The top layer of the chamber wall is a magnetic-responsive soft polymer and the rest of the chamber walls are all made of soft elastomers, such as polydimethylsiloxane (PDMS). One possible choice of the magnetic-responsive polymer is to disperse Fe3O4 nanoparticles in the PDMS matrix. Upon application of the external magnetic field, the magnetic-responsive top thin film would be actuated to deform. The realization of the proposed transfer printing technique requires the complete seal of the gas chamber, which has been demonstrated in the experiment from several literature studies [30,33,34], with the gas chamber ranging from millimeter scale to micrometer scale. Thus, the complete seal of the gas chamber is assumed in this study.

Assuming a negligible magnetization along the radial direction in the magnetic-responsive thin film, the total magnetic force F applied to the magnetic-responsive thin film in the z-direction is given by [3537] Display Formula

(1)$F=μ0VtopΔHhtopMz$

where $μ0=4π×10−7 Tm/A$ is the permeability of free space, $Vtop=πRtop2htop$ is the volume of the top magnetic-responsive thin film, $ΔH=Hz1−Hz2$ is the difference in the magnetic field strength between the top $Hz1$ and bottom $Hz2$ thin film surfaces along the z-direction, $htop=z1−z2$ is the thickness of the magnetic-responsive thin film, and $Mz$ is the magnetization along the z-direction. For a magnetic-responsive film in a circular geometry with a radius of $Rtop$, it is then subject to a pressure resulting from the electromagnetic field in addition to the atmospherical pressure Display Formula

(2)$Δp=FπRtop2=μ0ΔHMz$

For a relatively uniform pressure $Δp$ that deforms the top magnetic-responsive polymer, the displacement of the top layer can be assumed to take the following form [38]: Display Formula

(3)$wtop(r)=wtopmax(1−r2Rtop2)2$

where r is the radial distance from a point on the film to its center and $wtopmax$ is the maximum displacement in the magnetic-responsive thin film.

When the magnetic-responsive thin film moves in the positive (negative) z-direction, the soft, elastomeric thin film at the bottom of the chamber also moves in the positive (negative) z-direction due to the existence of the incompressible liquid in the sealed chamber. The increased (decreased) volume of the gas chamber above the device component leads to a decreased (increased) pressure to facilitate the device component retrieval (delivery). Taking the same assumption as in Eq. (3), the displacement in the bottom PDMS thin film can be written as Display Formula

(4)$wbot(r)=wbotmax(1−r2Rbot2)2$

where $wbotmax$ is the maximum displacement in the PDMS film. As the liquid sealed in the top chamber is incompressible, the volume change $ΔVbot$ from the deformation of the bottom thin film should be the same of that $ΔVtop$ from the top magnetic-responsive thin film, i.e., ΔVtop = ΔVbot, leading to Display Formula

(5)$∫02πdφ∫0Rtopwtop(r)dr=∫02πdφ∫0Rbotwbot(r)dr$

Substituting Eqs. (3) and (4) into Eq. (5) leads to $wtopmax=k2wbotmax$, where $k=Rbot/Rtop$ is the radii ratio of the bottom PDMS film to the top magnetic-responsive film.

For the displacement fields given in Eqs. (3) and (4), the elastic energies of the top (Young's modulus of $Etop$, and Poisson's ratio of $vtop$) and bottom (Young's modulus of $Ebot$, and Poisson's ratio of $vbot$) thin films can be expressed as [38] Display Formula

(6)$Ui=∫02πdφ∫0Ri{E¯ih324[∂2wi(r)∂r2+1r2∂2wi(r)∂φ2+1r∂wi(r)∂r]2+h2[σri(∂wi(r)∂r)2+σrir2(∂wi(r)∂φ)2]+hE¯i8(∂wi(r)∂r)4}dr$

where $E¯i=Ei/(1−νi2)$ and $σri$ (i = top, bot) are the plane-strain Young's modulus and residual stress of the top magnetic-responsive and bottom PDMS thin films, respectively. Assuming negligible residual stresses, the residual stress in each thin film is taken to be 0. The work done by the external force $UΔP$ is expressed as $UΔP=∫0ΔVcΔpcdΔVc−∫02πdφ∫0Rtopwtop(r)Δpdr$, where $ΔVc=|Vc−Vc0|$ is the volume change in the bottom gas chamber and $Δpc$ = $|pc−pc0|$ is the volume-induced pressure change in the bottom gas chamber. While the volume Vc in the gas chamber increases (or decrease) in the pickup (or printing) process, the pressure $pc$ decreases (increases) in the pickup (or printing) process. Denoting $α=1$ (or $α=−1$) for the pickup (or printing) step, the volume and pressure changes in the bottom gas chamber can be rewritten as $ΔVc=|Vc−Vc0|=α(Vc−Vc0)$ and $Δpc=|pc−pc0|=α(pc0−pc)$. In the bottom gas chamber, the Clausius–Clapeyron relation dictates its pressure $pc$ to be related to its volume $Vc$ as $pc=pc0Vc0/Vc$, where $pc0≈0.1MPa$ is the sea level standard atmospheric pressure and $Vc0=πRbot2hc$ is the initial volume of the bottom gas chamber prior to deformation. Thus, the volume-induced pressure change in the bottom gas chamber is determined to be $Δpc=ΔVcpc0/(Vc0+αΔVc)$. Realizing the volume change is obtained as $ΔVc=∫02πdφ∫0Rbotwbot(r)rdr=πwbotmaxRbot2/3$, the volume-induced pressure change in the bottom gas chamber can then be determined to be Display Formula

(7)$Δpc=ΔVcpc0Vc0+αΔVc=wbotmax3hc+αwbotmaxpc0$

Substituting Eq. (7) into $Δpc=α(pc0−pc)$ leads to the pressure in the bottom gas chamber as Display Formula

(8)$pc=[1−wbotmaxα(3hc+αwbotmax)]pc0=(1−αwbotmax3hc+αwbotmax)pc0$

The total energy of the stamp upon deformation in the magnetic field is given by Display Formula

(9)$Utot=Utop+UΔP+Ubot$

Minimization of the total energy $∂Utot/∂wbot=0$ leads to Display Formula

(10)$Δp=4hwbotmaxRbot2[4E¯both23Rbot2(1+λk6)+64E¯bot(wbotmax)2105Rbot2(1+λk10)]+wbotmaxpc03hc+αwbotmax$

where $λ=E¯top/E¯bot$ is the plane-strain Young's moduli ratio of the top to the bottom film.

In order to validate the analytical model, finite element analysis was carried out to model the coupled liquid–solid problem. In the simulation, Smoothed Particle Hydrodynamics was used in the commercial software abaqus [39] to model the liquid in the sealed chamber by particles and the liquid–solid interaction was modeled by the general contact property. Because of the negligible motion, rigid body with a fixed constraint was applied to the chamber sidewall. As for the bottom gas chamber, fluid cavity constraint with an initial fluid cavity pressure of 0.1 MPa was applied. For a representative liquid such as water in the sealed chamber, the corresponding material parameters were used (sound velocity of c0 = 1483 m/s, viscosity of 0.001 kg/ms, and density of 1000 kg/m3). The Young's modulus of PDMS typically ranges from 0.65 MPa to 2 MPa. The incorporation of the magnetic nanoparticles in PDMS could either increase or decrease its Young's modulus, depending on the type and concentration of the nanoparticle [40]. In the finite element simulation, both the top and bottom thin films are modeled by the eight-node brick elements with reduced integration (C3D8R). The gas in the gas chamber is modeled by the ideal gas (i.e., molecular weight of 3.2 g/mol) in a fluid cavity model (absolute zero temperature of −273 °C, universal gas constant of 8.314 J/mol K). In order to simplify the analysis and focus on the working principle of the design, the Young's moduli of the top magnetic-responsive and bottom PDMS thin films are taken to be the same, with Poisson's ratio fixed at 0.45 for both thin films. In addition, the pressure resulting from the electromagnetic field is assumed to uniform on the magnetic film [36] in the current study. The simulation that considers the electromagnetic-mechanical coupling can be done in comsol [4143], which will be presented in the future work.

As shown in Fig. 2, the normalized maximum displacement $wbotmax/hc$ of the bottom PDMS thin film during the pickup step increases with the increasing normalized electromagnetic driving pressure $Δp/pc0$ but decreases with increasing thickness hbot of the bottom PDMS thin film (or k, Ebot), consisting with theoretical prediction from Eq. (9). For a normalized electromagnetic driving pressure $Δp/pc0=0.2$, the maximum displacement of the bottom PDMS thin film is 0.328, 0.280, and 0.248 mm for a normalized thin film thickness $h/hc$ of 0.11, 0.16, and 0.19, respectively (Fig. 2(a)). For the same normalized electromagnetic driving pressure $Δp/pc0=0.2$, the maximum displacement of the bottom PDMS thin film is 0.342, 0.296, and 0.228 for a normalized modulus of the thin film $Ebot/pc0$ of 6.5, 10, and 20, respectively (Fig. 2(b)). When the radii ratio k increases from 0.75 to 1 and to 1.2, the maximum displacement of the bottom PDMS thin film decreases from 0.340, to 0.282 and to 0.190 (Fig. 2(c)). The decrease becomes more evident for an increased normalized electromagnetic driving pressure. Therefore, a large maximum displacement of the bottom PDMS thin film is associated with a small radii ratio k and a soft and thin bottom PDMS layer. In particular, in order to achieve the same $wbotmax$, smaller k value is associated with a smaller actuation force from the magnetic field, leading to easier operation in both retrieval and printing steps (Fig. 3).

As shown in Eq. (9), the volume-induced pressure change in the bottom gas chamber is directly related to the maximum displacement of the bottom PDMS thin film and the height of the bottom gas chamber, i.e., $Δpc∼(wbotmax,hc)$. The larger pressure change in the bottom gas chamber is desired for both pickup and printing steps. The normalized volume-induced pressure change in the bottom gas chamber $Δpc/pc0$ increases with the increasing maximum displacement of the bottom PDMS thin film. Thus, it increases as the normalized electromagnetic driving pressure $Δp/pc0$ increases but decreases as the thickness hbot (or k, Ebot) of the bottom PDMS thin film increases (Fig. 4).

The maximum displacement of the bottom PDMS thin film can be determined from Eqs. (8) and (2) as Display Formula

(11)$μ0ΔHMz=4hwbotmaxRbot2[4E¯both23Rbot2(1+λk6)+64E¯bot(wbotmax)2105Rbot2(1+λk10)]+wbotmaxpc03hc+αwbotmax$

where the difference in the magnetic field strength $ΔH$ depends on the magnetic field strength distribution and the thickness of the magnetic thin film, and the magnetization along the z-direction $Mz$ depends on the type of the nanoparticle in the magnetic thin film [44]. Equation (11) indicates that an increased magnetization along the z-direction leads to increased maximum displacement of the bottom PDMS thin film. For a given type of magnetic nanoparticle in the magnetic thin film, the maximum displacement of the bottom PDMS thin film increases with increased PDMS film thickness. According to the experimental measurement [36], the magnetization of the magnetic-responsive thin film with EMG1200 iron oxide is 30,000 A/m, and the difference in the magnetic field strength between the top and bottom surface of the film is ∼$294.6 kA/m$ when the film is within 5 mm from the permanent magnet for $h/hc=0.16$. Taking the plane-strain Young's moduli ratio of 1 ($λ=1$) and the normalized Young's modulus of the bottom PDMS thin film $Ebot/pc0$ of 10, the normalized maximum displacement $wbotmax/hc$ of the bottom PDMS substrate during the pickup (printing) step is obtained as 0.0371, 0.0316, and 0.0234 (0.0322, 0.0266, and 0.0184) for the radii ratio k = 0.75, 1, and 1.2, respectively. In addition, the normalized maximum displacement $wbotmax/hc$ of the bottom PDMS substrate during the pickup (printing) step decreases from 0.0408 to 0.0322 and to 0.0268 (from 0.0432 to 0.0328 and to 0.0270), as the normalized thickness $h/hc$ increases from 0.11 to 0.16 and to 0.19 ($λ=1$, $Ebot=1MPa$ and $k=0.75$). The dependence of the normalized volume-induced pressure in the bottom gas chamber $pc/pc0$ on the normalized magnetization of the magnetic-responsive thin film $Mz/M̃z$ and the normalized difference in the magnetic field strength $ΔH/ΔH̃$ for different radii ratios is also studied ($M̃z=30 kA/m$, $ΔH̃=294.6 kA/m$). As shown in Fig. 5(a), the normalized volume-induced pressure in the bottom gas chamber $pc/pc0$ increases with the increased normalized magnetization the magnetic responsive thin film $Mz/M̃z$ for the same $ΔH/ΔH̃$ and this increase becomes more evident for a small radii ratio. The same trend is observed for the dependence of $pc/pc0$ on $ΔH/ΔH̃$ (Fig. 5(b)).

This study demonstrates the working principle of the magnetic-assisted transfer printing that the magnetic field induced pressure change in the gas chamber modulates the interfacial adhesion, representing an alternative approach for fast response and easy control. Although the current result only shows a small pressure change of (∼20%), it is possible to further increase the value through the change in magnetic field strength and stamp geometric parameters. For instance, the pressure change doubles (i.e., 42%) the value in the current study for $Rbot=10 mm$, $Ebot=0.65 MPa$, $νbot=0.45$, $k=1/3$, $λ=1/2$, $h=0.04 mm$, $h/hc=1/200$, and an electromagnetic driving pressure of 0.04 MPa. Therefore, the rational design of the stamp structure, as well as the proper choice of the magnetic nanoparticle in the thin film (e.g., structural designed top magnetic-responsive and bottom PDMS thin films [4549]) and the external magnetic field with high field strength (e.g., electromagnets with a sufficient number of turns and large applied current), would allow optimization of the pressure change and thus the modulation of the interfacial adhesion in the magnetic assisted transfer printing process for active control and high precision, which will be a subject of the future study.

## Conclusions

This paper presents one type of stamp with a unique structural design that uses an incompressible liquid chamber stacked on top of a gas chamber for magnetic-assisted transfer printing. The top magnetic-responsive chamber wall of the liquid chamber can be actuated by the magnetic field and its deformation can be transmitted to the bottom chamber wall through the incompressible liquid. The resulting deformation changes the pressure in the bottom gas chamber, which modulates the interfacial adhesion between the stamp and target material/structure. Minimization of the total energy of the system establishes the analytic relationship between the pressure change in the bottom gas chamber and the electromagnetic driving pressure. Validated by the finite element analysis, the analytic result indicates that the pressure change in the bottom gas chamber increase with the increasing electromagnetic driving pressure but decreases with increasing radii ratio, thickness, and modulus of the thin film.

## Funding Data

• National Natural Science Foundation of China (Grant No.11272260).

• Fundamental Research Funds for the Central Universities (Grant Nos. 3102017JC01003 and 3102017JC11001).

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Cheng, H. Y. , Wu, J. , Yu, Q. M. , Kim-Lee, H. J. , Carlson, A. , Turner, K. T. , Hwang, K. C. , Huang, Y. G. , and Rogers, J. A. , 2012, “ An Analytical Model for Shear-Enhanced Adhesiveless Transfer Printing,” Mech. Res. Commun., 43, pp. 46–49.
Carlson, A. , Kim-Lee, H. J. , Wu, J. , Elvikis, P. , Cheng, H. Y. , Kovalsky, A. , Elgan, S. , Yu, Q. M. , Ferreira, P. M. , Huang, Y. G. , Turner, K. T. , and Rogers, J. A. , 2011, “ Shear-Enhanced Adhesiveless Transfer Printing for Use in Deterministic Materials Assembly,” Appl. Phys. Lett., 98(26), p. 264104.
Carlson, A. , Wang, S. D. , Elvikis, P. , Ferreira, P. M. , Huang, Y. G. , and Rogers, J. A. , 2012, “ Active, Programmable Elastomeric Surfaces With Tunable Adhesion for Deterministic Assembly by Transfer Printing,” Adv. Funct. Mater., 22(21), pp. 4476–4484.
Li, R. , Li, Y. H. , Lu, C. F. , Song, J. Z. , Saeidpouraza, R. , Fang, B. , Zhong, Y. , Ferreira, P. M. , Rogers, J. A. , and Huang, Y. G. , 2012, “ Thermo-Mechanical Modeling of Laser-Driven Non-Contact Transfer Printing: Two-Dimensional Analysis,” Soft Matter, 8(27), pp. 7122–7127.
Gao, Y. , Li, Y. , Li, R. , and Song, J. , 2017, “ An Accurate Thermomechanical Model for Laser-Driven Microtransfer Printing,” ASME J. Appl. Mech., 84(6), p. 064501.
Lee, H. , Um, D. S. , Lee, Y. , Lim, S. , Kim, H. J. , and Ko, H. , 2016, “ Octopus-Inspired Smart Adhesive Pads for Transfer Printing of Semiconducting Nanomembranes,” Adv. Mater., 28(34), pp. 7457–7465. [PubMed]
Xue, Y. G. , Zhang, Y. H. , Feng, X. , Kim, S. , Rogers, J. A. , and Huang, Y. G. , 2015, “ A Theoretical Model of Reversible Adhesion in Shape Memory Surface Relief Structures and Its Application in Transfer Printing,” J. Mech. Phys. Solids, 77, pp. 27–42.
Eisenhaure, J. D. , Xie, T. , Varghese, S. , and Kim, S. , 2013, “ Microstructured Shape Memory Polymer Surfaces With Reversible Dry Adhesion,” ACS Appl. Mater. Interfaces, 5(16), p. 7714. [PubMed]
Baik, S. , Kim, D. W. , Park, Y. , Lee, T.-J. , Bhang, S. H. , and Pang, C. , 2017, “ A Wet-Tolerant Adhesive Patch Inspired by Protuberances in Suction Cups of Octopi,” Nature, 546(7658), pp. 396–400. [PubMed]
Hu, B.-S. , Wang, L.-W. , Fu, Z. , and Zhao, Y.-Z. , 2009, “ Bio-Inspired Miniature Suction Cups Actuated by Shape Memory Alloy,” Int. J. Adv. Rob. Syst., 6(3), pp. 151–160.
Abbott, J. J. , Ergeneman, O. , Kummer, M. P. , Hirt, A. M. , and Nelson, B. J. , 2007, “ Modeling Magnetic Torque and Force for Controlled Manipulation of Soft-Magnetic Bodies,” IEEE Trans. Rob., 23(6), pp. 1247–1252.
Pirmoradi, F. , Jackson, J. , Burt, H. , and Chiao, M. , 2011, “ A Magnetically Controlled MEMS Device for Drug Delivery: Design, Fabrication, and Testing,” Lab Chip, 11(18), pp. 3072–3080. [PubMed]
Huang, L.-B. , Bai, G. , Wong, M.-C. , Yang, Z. , Xu, W. , and Hao, J. , 2016, “ Magnetic-Assisted Noncontact Triboelectric Nanogenerator Converting Mechanical Energy Into Electricity and Light Emissions,” Adv. Mater., 28(14), pp. 2744–2751. [PubMed]
Schomburg, W. K. , 2011, Introduction to Microsystem Design, Springer, Berlin. [PubMed] [PubMed]
Khan, S. , Lorenzelli, L. , and Dahiya, R. , 2016, “ Flexible MISFET Devices From Transfer Printed Si Microwires and Spray Coating,” IEEE J. Electron Devices Soc., 4(4), pp. 189–196.
Fatemeh, P. , Luna, C. , and Mu, C. , 2010, “ A Magnetic Poly(Dimethylesiloxane) Composite Membrane Incorporated With Uniformly Dispersed, Coated Iron Oxide Nanoparticles,” J. Micromech. Microeng., 20(1), p. 015032.
Kevin, M. , Saad, A. , Mary, F. , and Zoubeida, O. , 2014, “ Finite Element Analysis and Validation of Dielectric Elastomer Actuators Used for Active Origami,” Smart Mater. Struct., 23(9), p. 094002.
Jürgen, M. , and Dominik, U. , 2016, “ Experimental and Theoretical Analysis of the Actuation Behavior of Magnetoactive Elastomers,” Smart Mater. Struct., 25(10), p. 104002.
Robert, S. , Juan, R. , Samuel, E. L. , and Paris, R. V. , 2014, “ Numerical Simulation and Experimental Validation of the Large Deformation Bending and Folding Behavior of Magneto-Active Elastomer Composites,” Smart Mater. Struct., 23(9), p. 094004.
Weisong, W. , Zhongmei, Y. , Jackie, C. C. , and Ji, F. , 2004, “ Composite Elastic Magnet Films With Hard Magnetic Feature,” J. Micromech. Microeng., 14(10), p. 1321.
Zhang, E. , Liu, Y. , and Zhang, Y. , 2018, “ A Computational Model of Bio-Inspired Soft Network Materials for Analyzing Their Anisotropic Mechanical Properties,” ASME J. Appl. Mech., 85(5), p. 071002.
Ma, Q. , and Zhang, Y. , 2016, “ Mechanics of Fractal-Inspired Horseshoe Microstructures for Applications in Stretchable Electronics,” ASME J. Appl. Mech., 83(11), p. 111008.
Che, K. , Yuan, C. , Wu, J. , Jerry Qi, H. , and Meaud, J. , 2016, “ Three-Dimensional-Printed Multistable Mechanical Metamaterials With a Deterministic Deformation Sequence,” ASME J. Appl. Mech., 84(1), p. 011004.
Li, H. , Ma, Y. , Wen, W. , Wu, W. , Lei, H. , and Fang, D. , 2017, “ In Plane Mechanical Properties of Tetrachiral and Antitetrachiral Hybrid Metastructures,” ASME J. Appl. Mech., 84(8), p. 081006.
Liu, J. , and Zhang, Y. , 2018, “ A Mechanics Model of Soft Network Materials With Periodic Lattices of Arbitrarily Shaped Filamentary Microstructures for Tunable Poisson's Ratios,” ASME J. Appl. Mech., 85(5), p. 051003.
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Kim, R. H. , Kim, D. H. , Xiao, J. L. , Kim, B. H. , Park, S. I. , Panilaitis, B. , Ghaffari, R. , Yao, J. M. , Li, M. , Liu, Z. J. , Malyarchuk, V. , Kim, D. G. , Le, A. P. , Nuzzo, R. G. , Kaplan, D. L. , Omenetto, F. G. , Huang, Y. G. , Kang, Z. , and Rogers, J. A. , 2010, “ Waterproof AlInGaP Optoelectronics on Stretchable Substrates With Applications in Biomedicine and Robotics,” Nat. Mater., 9(11), pp. 929–937. [PubMed]
Wu, J. , Kim, S. , Chen, W. , Carlson, A. , Hwang, K.-C. , Huang, Y. , and Rogers, J. A. , 2011, “ Mechanics of Reversible Adhesion,” Soft Matter, 7(18), pp. 8657–8662.
Cheng, H. Y. , Wu, J. , Yu, Q. M. , Kim-Lee, H. J. , Carlson, A. , Turner, K. T. , Hwang, K. C. , Huang, Y. G. , and Rogers, J. A. , 2012, “ An Analytical Model for Shear-Enhanced Adhesiveless Transfer Printing,” Mech. Res. Commun., 43, pp. 46–49.
Carlson, A. , Kim-Lee, H. J. , Wu, J. , Elvikis, P. , Cheng, H. Y. , Kovalsky, A. , Elgan, S. , Yu, Q. M. , Ferreira, P. M. , Huang, Y. G. , Turner, K. T. , and Rogers, J. A. , 2011, “ Shear-Enhanced Adhesiveless Transfer Printing for Use in Deterministic Materials Assembly,” Appl. Phys. Lett., 98(26), p. 264104.
Carlson, A. , Wang, S. D. , Elvikis, P. , Ferreira, P. M. , Huang, Y. G. , and Rogers, J. A. , 2012, “ Active, Programmable Elastomeric Surfaces With Tunable Adhesion for Deterministic Assembly by Transfer Printing,” Adv. Funct. Mater., 22(21), pp. 4476–4484.
Li, R. , Li, Y. H. , Lu, C. F. , Song, J. Z. , Saeidpouraza, R. , Fang, B. , Zhong, Y. , Ferreira, P. M. , Rogers, J. A. , and Huang, Y. G. , 2012, “ Thermo-Mechanical Modeling of Laser-Driven Non-Contact Transfer Printing: Two-Dimensional Analysis,” Soft Matter, 8(27), pp. 7122–7127.
Gao, Y. , Li, Y. , Li, R. , and Song, J. , 2017, “ An Accurate Thermomechanical Model for Laser-Driven Microtransfer Printing,” ASME J. Appl. Mech., 84(6), p. 064501.
Lee, H. , Um, D. S. , Lee, Y. , Lim, S. , Kim, H. J. , and Ko, H. , 2016, “ Octopus-Inspired Smart Adhesive Pads for Transfer Printing of Semiconducting Nanomembranes,” Adv. Mater., 28(34), pp. 7457–7465. [PubMed]
Xue, Y. G. , Zhang, Y. H. , Feng, X. , Kim, S. , Rogers, J. A. , and Huang, Y. G. , 2015, “ A Theoretical Model of Reversible Adhesion in Shape Memory Surface Relief Structures and Its Application in Transfer Printing,” J. Mech. Phys. Solids, 77, pp. 27–42.
Eisenhaure, J. D. , Xie, T. , Varghese, S. , and Kim, S. , 2013, “ Microstructured Shape Memory Polymer Surfaces With Reversible Dry Adhesion,” ACS Appl. Mater. Interfaces, 5(16), p. 7714. [PubMed]
Baik, S. , Kim, D. W. , Park, Y. , Lee, T.-J. , Bhang, S. H. , and Pang, C. , 2017, “ A Wet-Tolerant Adhesive Patch Inspired by Protuberances in Suction Cups of Octopi,” Nature, 546(7658), pp. 396–400. [PubMed]
Hu, B.-S. , Wang, L.-W. , Fu, Z. , and Zhao, Y.-Z. , 2009, “ Bio-Inspired Miniature Suction Cups Actuated by Shape Memory Alloy,” Int. J. Adv. Rob. Syst., 6(3), pp. 151–160.
Abbott, J. J. , Ergeneman, O. , Kummer, M. P. , Hirt, A. M. , and Nelson, B. J. , 2007, “ Modeling Magnetic Torque and Force for Controlled Manipulation of Soft-Magnetic Bodies,” IEEE Trans. Rob., 23(6), pp. 1247–1252.
Pirmoradi, F. , Jackson, J. , Burt, H. , and Chiao, M. , 2011, “ A Magnetically Controlled MEMS Device for Drug Delivery: Design, Fabrication, and Testing,” Lab Chip, 11(18), pp. 3072–3080. [PubMed]
Huang, L.-B. , Bai, G. , Wong, M.-C. , Yang, Z. , Xu, W. , and Hao, J. , 2016, “ Magnetic-Assisted Noncontact Triboelectric Nanogenerator Converting Mechanical Energy Into Electricity and Light Emissions,” Adv. Mater., 28(14), pp. 2744–2751. [PubMed]
Schomburg, W. K. , 2011, Introduction to Microsystem Design, Springer, Berlin. [PubMed] [PubMed]
Khan, S. , Lorenzelli, L. , and Dahiya, R. , 2016, “ Flexible MISFET Devices From Transfer Printed Si Microwires and Spray Coating,” IEEE J. Electron Devices Soc., 4(4), pp. 189–196.
Fatemeh, P. , Luna, C. , and Mu, C. , 2010, “ A Magnetic Poly(Dimethylesiloxane) Composite Membrane Incorporated With Uniformly Dispersed, Coated Iron Oxide Nanoparticles,” J. Micromech. Microeng., 20(1), p. 015032.
Kevin, M. , Saad, A. , Mary, F. , and Zoubeida, O. , 2014, “ Finite Element Analysis and Validation of Dielectric Elastomer Actuators Used for Active Origami,” Smart Mater. Struct., 23(9), p. 094002.
Jürgen, M. , and Dominik, U. , 2016, “ Experimental and Theoretical Analysis of the Actuation Behavior of Magnetoactive Elastomers,” Smart Mater. Struct., 25(10), p. 104002.
Robert, S. , Juan, R. , Samuel, E. L. , and Paris, R. V. , 2014, “ Numerical Simulation and Experimental Validation of the Large Deformation Bending and Folding Behavior of Magneto-Active Elastomer Composites,” Smart Mater. Struct., 23(9), p. 094004.
Weisong, W. , Zhongmei, Y. , Jackie, C. C. , and Ji, F. , 2004, “ Composite Elastic Magnet Films With Hard Magnetic Feature,” J. Micromech. Microeng., 14(10), p. 1321.
Zhang, E. , Liu, Y. , and Zhang, Y. , 2018, “ A Computational Model of Bio-Inspired Soft Network Materials for Analyzing Their Anisotropic Mechanical Properties,” ASME J. Appl. Mech., 85(5), p. 071002.
Ma, Q. , and Zhang, Y. , 2016, “ Mechanics of Fractal-Inspired Horseshoe Microstructures for Applications in Stretchable Electronics,” ASME J. Appl. Mech., 83(11), p. 111008.
Che, K. , Yuan, C. , Wu, J. , Jerry Qi, H. , and Meaud, J. , 2016, “ Three-Dimensional-Printed Multistable Mechanical Metamaterials With a Deterministic Deformation Sequence,” ASME J. Appl. Mech., 84(1), p. 011004.
Li, H. , Ma, Y. , Wen, W. , Wu, W. , Lei, H. , and Fang, D. , 2017, “ In Plane Mechanical Properties of Tetrachiral and Antitetrachiral Hybrid Metastructures,” ASME J. Appl. Mech., 84(8), p. 081006.
Liu, J. , and Zhang, Y. , 2018, “ A Mechanics Model of Soft Network Materials With Periodic Lattices of Arbitrarily Shaped Filamentary Microstructures for Tunable Poisson's Ratios,” ASME J. Appl. Mech., 85(5), p. 051003.

## Figures

Fig. 1

Schematic illustration of the stamp with a structural design that uses an incompressible liquid chamber stacked on top of a gas chamber for magnetic-assisted transfer printing. (a) The 3D representation and cross-sectional views of the design. The stamp is deformed upon the external magnetic actuation in the (b) pickup and (c) printing step.

Fig. 2

The normalized maximum displacement wbotmax/hc of thebottom PDMS thin film as a function of the normalized electromagnetic driving pressure Δp/pc0 during the pickup step (λ=1, Rbot/hc=1.2). (a) The effect from the thickness (Etop/Ebot=1,νtop/vbot=1, k=0.75, Ebot/pc0=10); (b) the effect from the modulus (νtop/vbot=1, h/hc=0.16, k=0.75); and (c) the effect from the radii ratio (Etop/Ebot=1, νtop/vbot=1, h/hc=0.16, Ebot/pc0=10).

Fig. 3

The dependence of the volume-induced pressure in thebottom gas chamber on the normalized electromagnetic driving pressure Δp/pc0 for different radii ratios (Ebot/Etop=1, νbot/vtop=1, λ=1, Rbot/hc=1.2, h/hc=0.16, Ebot/pc0=10)

Fig. 4

The normalized volume-induced pressure change in thebottom gas chamber during (a) pickup step and (b) printingstep for different radii ratios (Etop/Ebot=1, νtop/vbot=1,h/hc=0.16, Rbot/hc=1.2, Ebot/pc0=10)

Fig. 5

The dependence of the volume-induced pressure in the bottom gas chamber as a function of (a) the normalized magnetization of the magnetic-responsive thin film Mz/M̃z (for ΔH/ΔH̃=1) and (b) the normalized difference in the magnetic field strength ΔH/ΔH̃ (for Mz/M̃z=1) for different radii ratios. (Ebot/Etop=1, νbot/vtop=1, λ=1, Rbot/hc=1.2, h/hc=0.16, Ebot/pc0=10).

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