Accepted Manuscripts

Tao Wang, Zhanli Liu, Yue Gao, Qinglei Zeng and Zhuo Zhuang
J. Appl. Mech   doi: 10.1115/1.4038216
Shale is a typical layered and anisotropic material whose properties are characterized primarily by locally oriented anisotropic clay minerals and naturally formed bedding planes. The debonding of bedding planes will greatly influence the shale fracking to form a large-scale highly permeable fracture network, named stimulated reservoir volume (SRV). In this paper, both theoretical and numerical models are developed to quantitatively predict the growth of debonding zone in layered shale under fracking, and the good agreement is obtained between the theoretical and numerical prediction results. Two dimensionless parameters are proposed to characterize the corresponding conditions of tensile and shear debonding of bedding planes. It is found that debonding is mainly caused by the shear failure of bedding planes in the actual reservoir. Then the theoretical model is applied to design the perforation cluster spacing to optimize SRV, which is a critical issue in fracking. If the spacing is too small, there are overlapping areas of SRV and the fracking efficiency is much lower. If the spacing is too large, some stratums can't be stimulated. Simultaneously, another two dimensionless parameters, that are stimulating volume ratio and stimulating efficiency, are proposed. Through maximizing the values of these two parameters, the SRV and optimal perforation cluster spacing range can be quantitatively calculated to guide the fracking treatment design. These results are comparable with the data from field engineering.
TOPICS: Computer simulation, Hydraulic fracturing, Shales, Reservoirs, Anisotropy, Shear (Mechanics), Design, Fracture (Process), Failure, Minerals, Fracture (Materials)
Joseph J. Brown, Ryan C. Mettler, Omkar D. Supekar and V. M. Bright
J. Appl. Mech   doi: 10.1115/1.4038195
The use of large-deflection springs, tabs, and other compliant systems to provide integral attachment, joining, and retention is well established and may be found throughout nature and the designed world. Such systems present a challenge for mechanical analysis due to the interaction of contact mechanics with large-deflection analysis. Interlocking structures experience a variable reaction force that depends on the cantilever angle at the contact point. This paper develops the mathematical analysis of interlocking cantilevers and provides verification with finite-element analysis and physical measurements. Motivated by new opportunities for nanoscale compliant systems based on ultrathin films and 2D materials, we created a nondimensional analysis of retention tab systems. This analysis uses iterative and elliptic integral solutions to the moment-curvature elastica of a suspended cantilever, and can be scaled to large-deflection cantilevers of any size for which continuum mechanics applies. We find that when a compliant structure is bent backward during loading, overlap increases with load, until a force maximum is reached. In a force-limited scenario, surpassing this maximum would result in snap-through motion. By using angled cantilever restraint systems, the magnitude of insertion force relative to retention force can vary by 50× or more. The mathematical theory developed in this paper provides a basis for fast analysis and design of compliant retention systems, and expands the application of elliptic integrals for nonlinear problems.
TOPICS: Cantilevers, Deflection, Mathematical analysis, Springs, Restraint systems, Joining, Stress, Continuum mechanics, Contact mechanics, Design, Finite element analysis, Nanoscale phenomena
Alberto Garinei, Francesco Castellani, Davide Astolfi, Edvige Pucci and Lorenzo Scappaticci
J. Appl. Mech   doi: 10.1115/1.4038186
The analytic response for the Cauchy extra-stress in LAOS is computed from a constitutive model for isotropic incompressible materials, including viscoelastic contributions and relaxation time. Three cases of frame invariant derivatives are considered: lower, upper and Jaumann. In the first two cases, the shear stress at steady state includes the first and third harmonics and the difference of normal stresses includes the zeroth, second, fourth harmonics. In the Jaumann case, the stress components are obtained in integral form and are approximated with a Fouries series. The behavior of the coefficients is studied parametrically, as function of relaxation time and constitutive parameters. Further, the shear stress and the difference of normal stresses are studied as functions of shear strain and shear rate and are visualized by means of the elastic and viscous LB-plots. Sample results in the Pipkin plane are reported and the influence of the constitutive parameters in each case is discussed.
TOPICS: Relaxation (Physics), Stress, Shear (Mechanics), Shear stress, Constitutive equations, Steady state, Shear rate
Maoyi Zhang, Hao Liu, Peng Cao, Bin Chen, Jianqiao Hu, Yuli Chen, Bing Pan, Jonathan A. Fan, Rui Li, Lijuan Zhang and Yewang Su
J. Appl. Mech   doi: 10.1115/1.4038173
Stretchable electronics based on inorganic materials are an innovative technology with potential applications for many emerging electronic devices, due to their combination of stretchable mechanics and high electronic performance. The compliant elastomeric substrate, on which the brittle electronic components are mounted, plays a key role in achieving stretchability. However, conventional elastomeric substrates can undergo excessive mechanical deformation, which can lead to active component failure. Here, we introduce a simple and novel strategy to produce failure-resistant stretchable electronic platforms by bonding a thin film of stiff material, patterned into a serpentine network layout, to the elastomeric substrate. No prestraining of the substrate is required, and these systems offer sharp bilinear mechanical behavior and high ratio of tangent-to-elastic moduli. We perform comprehensive theoretical, numerical and experimental studies on the non-buckling based prestrain-free design, and we analyze the key parameters impacting the mechanical behavior of a strain-limiting substrate. As a device-level demonstration, we experimentally fabricate and characterize skin-mountable stretchable copper (Cu) electrodes for electrophysiological (EP) monitoring. This study paves the way to high performance stretchable electronics with failure-resistant designs.
TOPICS: Buckling, Electronics, Failure, Mechanical behavior, Skin, Thin films, Deformation, Copper, Bonding, Brittleness, Design, Electrodes, Electronic components
Hui Zhang, Yingxi Wang, Hareesh Godaba, Boo Cheong Khoo, Zhisheng Zhang and Jian Zhu
J. Appl. Mech   doi: 10.1115/1.4038174
It is an interesting open question how to achieve large actuation of a dielectric elastomer. In many previous works, in order to harness snap-through instability to achieve large deformation, a reservoir was employed to assist the dielectric elastomer actuator to optimize its loading condition/path, which makes the whole actuation system bulky and heavy. In this paper, we explore large actuation of a dielectric elastomer balloon with applications to a soft flight system. The balloon consists of two separate dielectric elastomer actuators. The inner one is stiffer, while the outer one softer. The whole actuation system has a small volume and a low weight, but can achieve large actuation by harnessing dielectric breakdown of the inner elastomer. The volume induced by dielectric breakdown is more than 20 times the voltage-induced volume change of dielectric elastomer actuators. The experiments demonstrate a soft flight system, which can move effectively in air by taking advantage of large actuation of this dielectric elastomer balloon. This project also shows that failure of materials can be harnessed to achieve useful functionalities.
TOPICS: Elastomers, Breakdown (Electricity), Actuators, Flight, Weight (Mass), Deformation, Reservoirs, Failure
Mattia Bacca, Costantino Creton and Robert M. McMeeking
J. Appl. Mech   doi: 10.1115/1.4037881
Double and triple network elastomers can be made by infusing monomers into a single network polymer, causing it to swell, and then polymerizing and cross-linking the monomers. The result is a double network elastomer in which one network is stretched and the other is in hydrostatic compression. Triple network systems are made by repeating the process starting with the double network material. The multi-network elastomers exhibit a Mullins effect in which softening occurs upon a first cycle of loading, with the elastomer stiffness recovered above the previous maximum strain. The Mullins effect is attributed to rupture of the stretched network, eliminating the constraint on the compressed network, thereby motivating straining at the lower stiffness of the remaining material. A model for this process is developed, based on previous work of Horgan, Ogden and Saccomandi (Proc. Roy. Soc. A, 460, 2004, 1737-1754). In the proposed model, a composite stiffness for the multi-network system is developed and a damage process introduced to degrade the contribution of the stretched network. The damage model is designed to account for the progressive elimination of chains that are most highly loaded in the stretched network, so that the undamaged stiffness is restored when the strain rises above levels previously experienced. The proposed model reproduces the behavior of the Mullins effect in the multi-network system.
TOPICS: Elastomers, Stiffness, Damage, Hydrostatics, Composite materials, Chain, Polymers, Compression, Cycles, Rupture

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