Fluctuation-based fracture mechanics of heterogeneous materials.

We present results of a hybrid analytical-simulation investigation of the fracture resistance of heterogeneous materials. We show that bond-energy fluctuations sampled by Monte Carlo simulations in the semigrand canonical ensemble provide a means to rationalize the complexity of heterogeneous fracture processes, encompassing probability and percolation theories of fracture. For a number of random and textured model materials, we derive upper and lower bounds of fracture resistance and link bond fracture fluctuations to statistical descriptors of heterogeneity, such as two-point correlation functions, to identify the origin of toughening mechanisms. This includes a shift from short- to long-range interactions of bond fracture processes in random systems to the transition from critical to subcritical bond fracture percolation in textured materials and the activation of toughness reserves at compliant interfaces. Induced by elastic mismatch, they connect to a number of disparate experimental observations, including toughening of brittle solids by deformable polymers or organics in, e.g., gas shale, nacre; stress-induced transformational toughening in ceramics; and toughening of sparse elastic networks in hydrogels, to name a few.

Phase diagram of brittle fracture in the semi-grand-canonical ensemble.

We present a simulation method to assess the quasistatic fracture resistance of materials. Set within a semi-grand-canonical Monte Carlo (SGCMC) simulation environment, an auxiliary field-the bond rupture potential-is introduced to generate a sufficiently large number of possible microstates in the semi-grand-canonical ensemble, and associated energy and bond fluctuations. The SGCMC approach permits identifying the full phase diagram of brittle fracture for harmonic and nonharmonic bond potentials, analogous to the gas-liquid phase diagram, with the equivalent of a liquidus line ending in a critical point. The phase diagram delineates a solid phase, a fractured phase, and a gas phase, and provides clear evidence of a first-order phase transition intrinsic to fracture. Moreover, energy and bond fluctuations generated with the SGCMC approach permit determination of the maximum energy dissipation associated with bond rupture, and hence of the fracture resistance of a widespread range of materials that can be described by bond potentials.

Mode Coarsening or Fracture: Energy Transfer Mechanisms in Dynamic Buckling of Rods.

We present results of a hybrid experimental, theoretical, and simulation-based investigation of the postbuckling behavior of thin elastic rods axially impacted by a projectile. We find a new postbuckling mechanism: mode coarsening. Much akin to inverse energy cascade phenomena in other nonlinear dynamic systems, energy is transferred during mode coarsening from higher to lower wave numbers-unless the rod breaks, abruptly dissipating in the course of fracture the rod's strain energy. We derive a model that provides a predictive means to capture mode coarsening in the form of a nondissipative, purely geometric force relaxation mechanism, and validate the model by means of molecular dynamics (MD) based structural dynamics simulations for rods of wood and pasta considering different thermodynamic ensembles. The scalability of theory and simulation for engineering applications opens new venues toward safe design of engineering structures subject to impact-induced risks of buckling, ranging from skyscrapers, to aerospace structures, to the crashworthiness of vehicles, for example.

Role of City Texture in Urban Heat Islands at Nighttime.

An urban heat island (UHI) is a climate phenomenon that results in an increased air temperature in cities when compared to their rural surroundings. In this Letter, the dependence of an UHI on urban geometry is studied. Multiyear urban-rural temperature differences and building footprints data combined with a heat radiation scaling model are used to demonstrate for more than 50 cities worldwide that city texture-measured by a building distribution function and the sky view factor-explains city-to-city variations in nocturnal UHIs. Our results show a strong correlation between nocturnal UHIs and the city texture.

Combinatorial molecular optimization of cement hydrates.

Despite its ubiquitous presence in the built environment, concrete's molecular-level properties are only recently being explored using experimental and simulation studies. Increasing societal concerns about concrete's environmental footprint have provided strong motivation to develop new concrete with greater specific stiffness or strength (for structures with less material). Herein, a combinatorial approach is described to optimize properties of cement hydrates. The method entails screening a computationally generated database of atomic structures of calcium-silicate-hydrate, the binding phase of concrete, against a set of three defect attributes: calcium-to-silicon ratio as compositional index and two correlation distances describing medium-range silicon-oxygen and calcium-oxygen environments. Although structural and mechanical properties correlate well with calcium-to-silicon ratio, the cross-correlation between all three defect attributes reveals an indentation modulus-to-hardness ratio extremum, analogous to identifying optimum network connectivity in glass rheology. We also comment on implications of the present findings for a novel route to optimize the nanoscale mechanical properties of cement hydrate.

Order and disorder in calcium-silicate-hydrate.

Despite advances in the characterization and modeling of cement hydrates, the atomic order in Calcium-Silicate-Hydrate (C-S-H), the binding phase of cement, remains an open question. Indeed, in contrast to the former crystalline model, recent molecular models suggest that the nanoscale structure of C-S-H is amorphous. To elucidate this issue, we analyzed the structure of a realistic simulated model of C-S-H, and compared the latter to crystalline tobermorite, a natural analogue of C-S-H, and to an artificial ideal glass. The results clearly indicate that C-S-H appears as amorphous, when averaged on all atoms. However, an analysis of the order around each atomic species reveals that its structure shows an intermediate degree of order, retaining some characteristics of the crystal while acquiring an overall glass-like disorder. Thanks to a detailed quantification of order and disorder, we show that, while C-S-H retains some signatures of a tobermorite-like layered structure, hydrated species are completely amorphous.

Nanostructure and nanomechanics of cement: polydisperse colloidal packing.

Cement setting and cohesion are governed by the precipitation and growth of calcium-silicate-hydrate, through a complex evolution of microstructure. A colloidal model to describe nucleation, packing, and rigidity of calcium-silicate-hydrate aggregates is proposed. Polydispersity and particle size dependent cohesion strength combine to produce a spectrum of packing fractions and of corresponding elastic properties that can be tested against nanoindentation experiments. Implications regarding plastic deformations and reconciling current structural characterizations are discussed.

Scratching as a fracture process: from butter to steel.

We present results of a hybrid experimental and theoretical investigation of the fracture scaling in scratch tests and show that scratching is a fracture dominated process. Validated for paraffin wax, cement paste, Jurassic limestone and steel, we derive a model that provides a quantitative means to relate quantities measured in scratch tests to fracture properties of materials at multiple scales. The scalability of scratching for different probes and depths opens new venues towards miniaturization of our technique, to extract fracture properties of materials at even smaller length scales.

Average hydroxyapatite concentration is uniform in the extracollagenous ultrastructure of mineralized tissues: evidence at the 1-10-microm scale.

At the ultrastructural observation scale of fully mineralized tissues (l=1-10 mum), transmission electron micrographs (TEM) reveal that hydroxyapatite (HA) is situated both within the fibrils and extrafibrillarly, and that the majority of HA lies outside the fibrils. The extrafibrillar amount of HA varies from tissue to tissue. By means of mathematical modeling, we here provide strong indications that there exists a physical quantity that is the same inside and outside the fibrils, for all different fully mineralized tissues. This quantity is the average mineral concentration in the non-collagenous space. This space is the sum of the extrafibrillar volume and of the volume of the fibrils that is not occupied by collagen molecules. Two independent sets of experimental observations covering a large range of tissue mass densities establish the relevance of our proposition: (i) mass density measurements and diffraction spacing measurements, re-analyzed through a dimensionally consistent packing model; (ii) optical density measurements of TEMs. The aforementioned average uniform HA-concentration in the extracollagenous space of the ultrastructure may emphasize the putative role played by a number of non-collagenous organic molecules in providing the chemical boundary conditions for mineralization of HA in the extracollagenous space. The probable existence of an average uniform extracollagenous HA concentration has far-reaching consequences for the mechanical behavior of mineralized tissues.

Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments.

Which of the elementary components (hydroxyapatite (HA) crystals, collagen, non-collagenous organic matter, water) do significantly contribute to the ultrastructural elastic stiffness magnitude and anisotropy of mineralized tissues; and how, i.e. through which shapes and assemblages (which micromechanical morphology)? We suggest answers to these questions by analyzing stiffness-volume fraction relationships of wet and dry tissue specimens in the framework of strain energy considerations. Radial stiffness values of both isotropic and anisotropic tissues are found to depend linearly to quadratically on only the mineral volume fraction. This suggests the isotropic contribution of HA to the ultrastructural stiffness. An energy-based analysis of the difference between the axial and radial stiffness values of anisotropic, collagen-rich tissues allows us to assess the collagen elasticity contribution, which is found to depend linearly on the extra-collagenous mineral concentration. These results suggest that collagen and hydroxyapatite are the elementary components governing the ultrastructural elastic stiffness magnitude and anisotropy of bone and mineralized tendons. The elastic stiffness of water and non-collagenous organic matter does not play a significant role. As for the morphological issue, we suggest that mineralized tissues are isotropic open crystal foams; and that these foams are reinforced unidirectionally by collagen molecules which are mechanically activated through tight links between these molecules and HA-crystals. The HA crystals are mechanically activated through stretching and bending in long bone tissues, they are predominantly stretched in mineralized tendons, and bent in hyperpycnotic tissues.