We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m(-1)) and -690 Nm(-1), respectively. The breaking strength is 42 N m(-1) and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = -2.0 terapascals, and intrinsic strength of sigma(int) = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.

The nonlinear in-plane elastic properties of graphene are calculated using density-functional theory. A thermodynamically rigorous continuum description of the elastic response is formulated by expanding the elastic strain energy density in a Taylor series in strain truncated after the fifth-order term. Upon accounting for the symmetries of graphene, a total of fourteen nonzero independent elastic constants are determined by least-squares fit to the ab initio calculations. The nonlinear continuum description is valid for infinitesimal and finite strains under arbitrary in-plane tensile loading in circumstance for which the bending stiffness can be neglected. The continuum formulation is suitable for incorporation into the finite element method.

This research explores the non-linear elastic properties of two-dimensional molybdenum disulfide. , where E is the Young's modulus. This study reveals the predictive power of first-principles density functional theory, in the derivation of non-linear elastic properties of two-dimensional MoS 2 . Furthermore, the study bridges three main gaps that hinder understanding of material properties: DFT to finite element analysis (FEA), experimental results to DFT, and the nanoscale to the microscale. In bridging these three gaps the experimental results validate the DFT calculations and the multiscale constitutive model.

We describe studies of the elastic properties and frictional characteristics of graphene samples of varying thickness using an atomic force microscope. For tensile testing, graphene is suspended over micron-sized circular holes and indented by atomic force microscope (AFM) tips. Fitting of the forcedisplacement curves yields the prestress and elastic stiffness, while comparison of the breaking force to simulation gives the ultimate strength, which is the highest measured for any material. Experiments on samples with 1-3 atomic layers yield similar values for the intrinsic stiffness and strength of a single sheet, but also reveal differences in mechanical behavior with thickness. The frictional force between an AFM tip and graphene decreases with thickness for samples from 1 to 4 layers, and does not depend on the presence of a substrate. Highresolution friction force imaging in stick-slip mode shows the same trend, and allows direct imaging of the crystal lattice.

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Numerous theoretical and experimental studies on various species of natural composites, such as nacre in abalone shells, collagen fibrils in tendon, and spider silk fibers, have been pursued to provide insight into the synthesis of novel bioinspired high-performance composites. However, a direct link between the mechanical properties of the constituents and the various geometric features and hierarchies remains to be fully established. In this paper, we explore a common denominator leading to the outstanding balance between strength and toughness in natural composite materials. We present an analytical model to link the mechanical properties of constituents, their geometric arrangement, and the chemistries used in their lateral interactions. Key critical overlap length scales between adjacent reinforcement constituents, which directly control strength and toughness of composite materials, emerge from the analysis. When these length scales are computed for three natural materials-nacre, collagen molecules, and spider silk fibers-very good agreement is found as compared with experimental measurements. The model was then used to interpret load transfer capabilities in synthetic carbon-based materials through parametrization of in situ SEM shear experiments on overlapping multiwall carbon nanotubes.

Advanced ceramic sponge materials with temperature-invariant high compressibility are urgently needed as thermal insulators, energy absorbers, catalyst carriers, and high temperature air filters. However, the application of ceramic sponge materials is severely limited due to their complex preparation process. Here, we present a facile method for large-scale fabrication of highly compressible, temperature resistant SiO 2-Al 2 O 3 composite ceramic sponges by blow spinning and subsequent calcination. We successfully produce anisotropic lamellar ceramic sponges with numerous stacked microfiber layers and density as low as 10 mg cm −3. The anisotropic lamellar ceramic sponges exhibit high compression fatigue resistance, strain-independent zero Poisson's ratio, robust fire resistance, temperatureinvariant compression resilience from −196 to 1000°C, and excellent thermal insulation with a thermal conductivity as low as 0.034 W m −1 K −1. In addition, the lamellar structure also endows the ceramic sponges with excellent sound absorption properties, representing a promising alternative to existing thermal insulation and acoustic absorption materials.

The ability to bias chemical reaction pathways is a fundamental goal for chemists and material scientists to produce innovative materials. Recently, two-dimensional materials have emerged as potential platforms for exploring novel mechanically activated chemical reactions. Here we report a mechanochemical phenomenon in graphene oxide membranes, covalent epoxide-to-ether functional group transformations that deviate from epoxide ring-opening reactions, discovered through nanomechanical experiments and density functional-based tight binding calculations. These mechanochemical transformations in a two-dimensional system are directionally dependent, and confer pronounced plasticity and damage tolerance to graphene oxide monolayers. Additional experiments on chemically modified graphene oxide membranes, with ring-opened epoxide groups, verify this unique deformation mechanism. These studies establish graphene oxide as a two-dimensional building block with highly tuneable mechanical properties for the design of high-performance nanocomposites, and stimulate the discovery of new bond-selective chemical transformations in two-dimensional materials.