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Using a blister test, we measured the work of separation between MoS$_2$ membranes from metal, semiconductor, and graphite substrates. We found a work of separation ranging from 0.11 +- 0.05 J/m^2 for chromium to 0.39 +- 0.1 J/m^2 for graphite substrates. In addition, we measured the work of adhesion of MoS$_2$ membranes over these substrates and observed a dramatic difference between the work of separation and adhesion which we attribute to adhesion hysteresis. Due to the prominent role that adhesive forces play in the fabrication and functionality of devices made from 2D materials, an experimental determination of the work of separation and adhesion as provided here will help guide their development.

Advancement of additive manufacturing is driving a need for design tools that exploit the increasing fabrication freedom. Multimaterial, three-dimensional (3D) printing allows for the fabrication of components from multiple materials with different thermal, mechanical, and “active” behavior that can be spatially arranged in 3D with a resolution on the order of tens of microns. This can be exploited to incorporate shape changing features into additively manufactured structures. 3D printing with a downstream shape change in response to an external stimulus such as temperature, humidity, or light is referred to as four-dimensional (4D) printing. In this paper, a design methodology to determine the material layout of 4D printed materials with internal, programmable strains is introduced to create active structures that undergo large deformation and assume a desired target displacement upon heat activation. A level set (LS) approach together with the extended finite element method (XFEM) is combined with density-based topology optimization to describe the evolving multimaterial design problem in the optimization process. A finite deformation hyperelastic thermomechanical model is used together with an higher-order XFEM scheme to accurately predict the behavior of nonlinear slender structures during the design evolution. Examples are presented to demonstrate the unique capabilities of the proposed framework. Numerical predictions of optimized shape-changing structures are compared to 4D printed physical specimen and good agreement is achieved. Overall, a systematic design approach for creating 4D printed active structures with geometrically nonlinear behavior is presented which yields nonintuitive material layouts and geometries to achieve target deformations of various complexities.

Regularization of the level-set (LS) field is a critical part of LS-based topology optimization (TO) approaches. Traditionally this is achieved by advancing the LS field through the solution of a Hamilton-Jacobi equation combined with a reinitialization scheme. This approach, however, may limit the maximum step size and introduces discontinuities in the design process. Alternatively, energy functionals and intermediate LS value penalizations have been proposed. This paper introduces a novel LS regularization approach based on a signed distance field (SDF) which is applicable to explicit LS-based TO. The SDF is obtained using the heat method (HM) and is reconstructed for every design in the optimization process. The governing equations of the HM, as well as the ones describing the physical response of the system of interest, are discretized by the extended finite element method (XFEM). Numerical examples for problems modeled by linear elasticity, nonlinear hyperelasticity and the incompressible Navier-Stokes equations in two and three dimensions are presented to show the applicability of the proposed scheme to a broad range of design optimization problems.

Lattice structures are frequently found in nature and engineering due to their myriad attractive properties, with applications ranging from molecular to architectural scales. Lattices have also become a key concept in additive manufacturing, which enables precise fabrication of complex lattices that would not be possible otherwise. While design and simulation tools for stiff lattices are common, here we present a digital design and nonlinear simulation approach for additive manufacturing of soft lattices structures subject to large deformations and instabilities, for which applications in soft robotics, healthcare, personal protection, energy absorption, fashion and design are rapidly emerging. Our framework enables design of soft lattices with curved members conforming to freeform geometries, and with variable, gradually changing member thickness and material, allowing the local control of stiffness. We model the lattice members as 3D curved rods and using a spline-based isogeometric method that allows the efficient simulation of nonlinear, large deformation behavior of these structures directly from the CAD geometries. Furthermore, we enhance the formulation with a new joint stiffening approach, which is based on parameters derived from the actual node geometries. Simulation results are verified against experiments with soft lattices realized by PolyJet multi-material polymer 3D printing, highlighting the potential for simulation-driven, digital design and application of non-uniform and curved soft lattice structures.

Advanced manufacturing methods like multi-material additive manufacturing are enabling realization of multiscale materials with intricate spatially varying microstructures and thus, material properties. This blurs the boundary between material and structure, paving the way to lighter, stiffer, and stronger structures. Taking advantage of these tunable multiscale materials warrants development of novel design methods that effectively marry the concepts of material and structure. We propose such a design to manufacture workflow and demonstrate it with laminated continuous fiber-reinforced composites that possess variable stiffness enabled by spatially varying microstructure. This contrasts with traditional fiber-reinforced composites which typically have a fixed, homogenous microstructure and thus constant stiffness. The proposed workflow includes three steps: (1) Design automation—efficient synthesis of an optimized multiscale design with microstructure homogenization enabling efficiency, (2) Material compilation—interpretation of the homogenized design lacking specificity in microstructural detail to a manufacturable structure, and (3) Digital manufacturing—automated manufacture of the compiled structure. We adapted multiscale topology optimization, a mesh parametrization-based algorithm and voxel-based multimaterial jetting for these three steps, respectively. We demonstrated that our workflow can be applied to arbitrary 2D or 3D surfaces. We validated the complete workflow with experiments on two simple planar structures; the results agree reasonably well with simulations.

Voxel-based multimaterial jetting additive manufacturing allows fabrication of digital materials (DMs) at the meso-scale (∼1 mm) by controlling the deposition patterns of soft elastomeric and rigid glassy polymers at the voxel-scale (∼90 μm). The digital materials can then be used to create heterogeneous functionally graded material (FGM) structures at the macro-scale (∼10 mm) programmed to behave in a predefined manner. This offers huge potential for design and fabrication of novel and complex bespoke mechanical structures.\ud \ud This paper presents a complete design and manufacturing workflow that simultaneously integrates material design, structural design, and product fabrication of FGM structures based on digital materials. This is enabled by a regression analysis of the experimental data on mechanical performance of the DMs i.e., Young’s modulus, tensile strength and elongation at break. This allows us to express the material behavior simply as a function of the microstructural descriptors (in this case, just volume fraction) without having to understand the underlying microstructural mechanics while simultaneously connecting it to the process parameters.\ud \ud Our proposed design and manufacturing approach is then demonstrated and validated in two series of design exercises to devise complex FGM structures. First, we design, computationally predict and experimentally validate the behavior of prescribed designs of FGM tensile structures with different material gradients. Second, we present a design automation approach for optimal FGM structures. The comparison between the simulations and the experiments with the FGM structures shows that the presented design and fabrication workflow based on our modeling approach for DMs at meso-scale can be effectively used to design and predict the performance of FGMs at macro-scale.

Graphene, the 2D form of carbon, has excellent mechanical, electrical and thermal properties and a variety of potential applications including NEMS, protective coatings, transparent electrodes in display devices and biological applications. Adhesion plays a key role in many of these applications. In addition, it has been proposed that the electronic properties of graphene can be affected by elastic deformation caused by adhesion of graphene to its substrate. In light of this, we present here a continuum mechanics based theoretical framework to understand the effect of nanoscale morphology of substrates on adhesion and mechanics of graphene. In the first part, we analyze the adhesion mechanics of graphene on 1 and 2D periodic corrugations. We carried out molecular statics simulations and found the results to be in good agreement with our theory. We modeled adhesive interactions surface forces described by Lennard-Jones 6-12 potential in both our analysis and simulations and in principle can be extended to any other interaction potential. The results show that graphene adheres conformally to substrates with large curvatures. We showed in principal that the theory developed here can be extended to substrates of arbitrary shapes that can be represented by a Fourier series. In the second part, we study the mechanics of peeling of graphene ribbons from 1D sinusoidally textured substrates. In the molecular statics simulations, we observed two key features in the peel mechanics of the ribbons: the ribbons slide over the substrate and undergo adhesion and peeling near the crack front in an oscillatory manner, the frequency of which reveals the wavelength of the underlying substrate. Our theory qualitatively captures these features of the peel mechanics and is general enough that it can be extended to other 2D materials like MoS2, BN etc and different kinds of interaction potentials., Comment: 45 pages, 21 figures, published in IJSS, 2016

Soft lattice structures and beam-metamaterials made of hyperelastic, rubbery materials undergo large elastic deformations and exhibit structural instabilities in the form of micro-buckling of struts under both compression and tension. In this work, the large-deformation nonlinear elastic behaviour of beam-lattice metamaterials is investigated by micromechanical nonlinear buckling analysis. The micromechanical 3D beam finite element model uses a primary linear buckling analysis to incorporate the effect of geometric imperfections into a subsequent nonlinear post-buckling analysis. The micromechanical computational model is validated against tensile and compressive experiments on a 3D-printed sample lattice structure manufactured via multi-material jetting. For the development and calibration of macroscale continuum constitutive models for nonlinear elastic deformation of soft lattice structures at finite strains, virtual characterization tests are conducted to quantify the effective nonlinear response of representative unit cells under periodic boundary conditions. These standard tests, commonly used for hyperelastic material characterization, include uniaxial, biaxial, planar and volumetric tension and compression, as well as simple shear. It is observed that besides the well-known stretch- and bending-dominated behaviour of cellular structures, some lattice types are dominated by buckling and post-buckling response. For multiscale simulation based on nonlinear homogenization, the uniaxial standard test results are used to derive parametric hyperelastic constitutive relations for the effective constitutive behaviour of representative unit cells in terms of lattice aspect ratio. Finally, a comparative study for compressive deformation of a sample sandwich lattice structure simulated by both full-scale beam and continuum finite element models shows the feasibility and computational efficiency of the effective continuum model.

We measured the work of separation of single and few-layer MoS

We present a general framework that digitally integrates the workflow for optimal design and fabrication of novel multiscale laminated fiber-based composites with spatially varying microstructure in each lamina of a flat or curved laminate. Given a design problem, our framework consists of three key components: 1) Design automation, 2) Material compilation, and 3) Digital fabrication. Design automation involves efficient simultaneous synthesis of optimal macroscale topology and spatially varying fibrous microstructure in a laminated composite, whereas digital fabrication comprises manufacture of the optimal structure. Material compilation is an intermediate process that translates the multiscale results of the design automation step to a digitally manufacturable arrangement of matrix and fibers within each layer of a laminate. These components constitute a digital thread and can be initialized by any method or process of choice. In this paper, we develop a multiscale topology optimization approach for design automation, new computational geometry algorithms for material compilation, and voxel-based material jetting for digital fabrication. We demonstrate and experimentally validate the extensive capabilities of our framework with various plate and shell structures that have potential applications in architecture, aerospace and soft robotics.

As mechanical structures enter the nanoscale regime, the influence of van der Waals forces increases. Graphene is attractive for nanomechanical systems because its Young's modulus and strength are both intrinsically high, but the mechanical behavior of graphene is also strongly influenced by the van der Waals force. For example, this force clamps graphene samples to substrates, and also holds together the individual graphene sheets in multilayer samples. Here we use a pressurized blister test to directly measure the adhesion energy of graphene sheets with a silicon oxide substrate. We find an adhesion energy of 0.45 \pm 0.02 J/m2 for monolayer graphene and 0.31 \pm 0.03 J/m2 for samples containing 2-5 graphene sheets. These values are larger than the adhesion energies measured in typical micromechanical structures and are comparable to solid/liquid adhesion energies. We attribute this to the extreme flexibility of graphene, which allows it to conform to the topography of even the smoothest substrates, thus making its interaction with the substrate more liquid-like than solid-like., to appear in Nature Nanotechnology

We created graphene blisters that cover and seal an annular cylinder-shaped microcavity in a SiO2 substrate filled with a gas. By controlling the pressure difference between the gas inside and outside of the microcavity, we switch the graphene membrane between multiple stable equilibrium configurations. We carried out experiments starting from the situation where the pressure of the gas inside and outside of the microcavity is set equal to a prescribed charging pressure, p0 and the graphene membrane covers the cavity like an annular drum, adhered to the central post and the surrounding substrate due to van der Waals forces. We decrease the outside pressure to a value, pe which causes it to bulge into an annular blister. We systematically increase the charging pressure by repeating this procedure causing the annular blister to continue to bulge until a critical charging pressure pc(i) is reached. At this point the graphene membrane delaminates from the post in an unstable manner, resulting in a switch of graphene membrane shape from an annular to a spherical blister. Continued increase of the charging pressure results in the spherical blister growing with its height increasing, but maintaining a constant radius until a second critical charging pressure pc(o) is reached at which point the blister begins to delaminate from the periphery of the cavity in a stable manner. Here, we report a series of experiments as well as a mechanics and thermodynamic model that demonstrate how the interplay among system parameters (geometry, graphene stiffness (number of layers), pressure, and adhesion energy) results in the ability to controllably switch graphene blisters among different shapes. Arrays of these blisters can be envisioned to create pressure-switchable surface properties where the difference between patterns of annular versus spherical blisters will impact functionalities such as wettability, friction, adhesion, and surface wave characteristics.

Large arrays of 3-terminal nanoelectromechanical graphene switches are fabricated. The switch is designed with a novel geometry that leads to low actuation voltages and improved mechanical integrity, while reducing adhesion forces, which improves the reliability of the switch. A finite element model including non-linear electromechanics is used to simulate the switching behavior and to deduce a scaling relation between the switching voltage and device dimensions.

We present a unique experimental configuration that allows us to determine the interfacial forces on nearly parallel plates made from the thinnest possible mechanical structures, single and few layer graphene membranes. Our approach consists of using a pressure difference across a graphene membrane to bring the membrane to within ~ 10-20 nm above a circular post covered with SiOx or Au until a critical point is reached whereby the membrane snaps into adhesive contact with the post. Continuous measurements of the deforming membrane with an AFM coupled with a theoretical model allow us to deduce the magnitude of the interfacial forces between graphene and SiOx and graphene and Au. The nature of the interfacial forces at ~ 10 - 20 nm separations is consistent with an inverse fourth power distance dependence, implying that the interfacial forces are dominated by van der Waals interactions. Furthermore, the strength of the interactions is found to increase linearly with the number of graphene layers. The experimental approach can be used to measure the strength of the interfacial forces for other atomically thin two-dimensional materials, and help guide the development of nanomechanical devices such as switches, resonators, and sensors., Comment: To appear in Nano Letters

We study the mechanics of pressurized graphene membranes using an experimental configuration that allows the determination of the elasticity of graphene and the adhesion energy between a substrate and a graphene (or other two-dimensional solid) membrane. The test consists of a monolayer graphene membrane adhered to a substrate by surface forces. The substrate is patterned with etched microcavities of a prescribed volume and when they are covered with the graphene monolayer it traps a fixed number (N) of gas molecules in the microchamber. By lowering the ambient pressure, and thus changing the pressure difference across the graphene membrane, the membrane can be made to bulge and delaminate in a stable manner from the substrate. Here we describe the analysis of the membrane/substrate as a thermodynamic system and explore the behavior of the system over representative experimentally-accessible geometry and loading parameters. We carry out companion experiments and compare them to the theoretical predictions and then use the theory and experiments together to determine the adhesion energy of graphene/SiO2 interfaces. We find an average adhesion energy of 0.24 J/m2 which is lower, but in line with our previously reported values. We assert that this test, which we call the constant N blister test, is a valuable approach to determine the adhesion energy between two-dimensional solid membranes and a substrate, which is an important, but not well-understood aspect of behavior. The test also provides valuable information that can serve as the basis for subsequent research to understand the mechanisms contributing to the observed adhesion energy. Finally, we show how in the limit of a large microcavity, the constant N test approaches the behavior observed in a constant pressure blister test and we provide an experimental observation that suggests this behavior., Comment: To appear in Journal of Applied Mechanics