Journal of Nanomechanics and Micromechanics

Statistical mechanics has provided powerful techniques to measure mechanical properties of materials at the nanoscale and paved the way for bottom-up computational materials design. The introduction of such techniques in civil engineering applications, namely construction and geotechnical materials, remains limited to the elastic and fracture properties. This paper presents an atomistic approach to calculate the nanoscale cohesion, friction angle, and hardness. This method is based on the application of biaxial external deformation, or stress, in the weakest crystallographic direction in the material. The onset of the failure is characterized by investigating the unloading paths from several points on the stress-strain curve. Such calculations of the failure stress along different deformation paths provide multiple failure Mohr circles in the normal-shear stress space, which is found to provide a failure envelope akin to the Mohr–Coulomb failure criterion that is widely used for the plastic analysis of granular geomaterials. The failure envelope characterizes the nanoscale cohesion and friction angle, which in conjunction with continuum mechanics can be utilized to estimate the nanoscale hardness of layered materials. Application of this method to tobermorite and Na-montmorillonite crystals yields values that are close to the experimental measurements obtained using nanoindentation and atomic force microscopy techniques.

On the basis of Reissner’s mixed variational theorem (RMVT), rather than the principle of virtual displacement (PVD), the authors presented a nonlocal Timoshenko beam theory (TBT) for the geometrically nonlinear static analysis of multiwalled carbon nanotubes (MWCNT) embedded in an elastic medium. The embedded MWCNT was subjected to mechanical loads on its outer-most surface, with combinations of free, simply supported, and clamped edge conditions. The van der Waals interaction between any pair of walls constituting the MWCNT was considered, and the interaction between the MWCNT and its surrounding medium was simulated using the Pasternak-type foundation model. In the formulation, the governing equations of a typical wall and the associated boundary conditions were derived, in which von Kármán geometrical nonlinearity was considered. Eringen’s nonlocal elasticity theory was used to account for the small-length scale effect. The deformations induced in the embedded MWCNT were obtained using the differential quadrature method and a direct iteration approach. In the numerical examples, solutions of the RMVT-based nonlocal TBT converged rapidly, and the convergent solutions of its linear counterpart closely agreed with the analytical and numerical solutions of the PVD-based nonlocal beam theories available in the literature.

In this work, the effect of surface elasticity on the effective elastic properties of nanoporous gold is studied. To this end, a theoretical framework for surface elasticity effects in submicron-sized solids is implemented as a user-defined finite element subroutine. This allows the use of the theory in large-scale engineering problems. The theory suggests a zero-thickness surface accommodating unique energetic properties and surface tension. For the example of ball-and-stick diamond cubic unit cell structures for nanoporous gold, it is shown that incorporation of surface excess elasticity and surface tension allows prediction of the size effect associated with the change of the surface area-to-volume ratio by capturing, e.g., the increase in the effective Young’s modulus and decrease in the effective Poisson’s ratio with decreasing ligament diameter, a phenomenon that is not accessible to classical continuum elasticity approaches.

Metal-nanocomposites are drawing attention of the composites community due to improvements in stiffness, strength, crack-bridging ability, and resistance to creep and fracture. The analysis of nanocomposites involves studies at multiple length scales due to the small length of the reinforcement. This paper conducts a detailed study on the mechanical behavior of a metal nanocomposite (Al-BNNT)—made of an aluminum (Al) matrix reinforced with boron nitride nanotubes (BNNTs)—under compressive and shear loadings. First a representative volume element (RVE) is modeled and analyzed using molecular dynamics (MD) simulation. Then the elastic properties are derived for a specially orthotropic lamina using a hierarchical multiscale scheme in conjunction. This result is further extended to derive elastic and shear moduli of bulk nanocomposites with aligned and randomly oriented reinforcement. The result shows excellent agreement with previous experimental observations. The bounds of elastic moduli using Voigt and Reuss formulations diverge with an increase in volume fraction of reinforcement—unlike typical composites, in which these two bounds first diverge and then eventually converge. This anomaly is attributed to the weakness of nanotubes in the radial direction. However, most elastic properties are found to be improved by the reinforcement, especially by double-walled nanotubes. Depending on the type of loading, nanocomposite exhibits failure at the matrix, interface, or nanotubes. This reveals the importance of considering all three loading cases when modeling a nanocomposite.

Biomaterials selection and design, and mechanical properties evolution during degradation and tissue regeneration play a critical role in the successful design of nanocomposite scaffolds for bone tissue regeneration. A new multiscale mechanics-based in silico approach is developed to provide a robust predictive methodology for nanocomposite scaffolds. Scaffolds are fabricated using amino acid–modified nanoclay with biomineralized hydroxyapatite (in situ HAPclay) and polycaprolactone (PCL). Steered molecular dynamics (SMD) simulations of the molecular models of HAPclay and the PCL composite provide a mechanical response of the material and the nature of the molecular interactions among constituents. The mechanical responses obtained from SMD are incorporated into a finite element (FE) model of a PCL/in situ HAPclay scaffold with its microstructure obtained from microcomputed tomography images. The model is validated using experimental results. The stress–strain response from multiscale models and experiments shows good agreement with the consideration of wall porosity correction. The multiscale models incorporate damage mechanics–based degradation and healing behavior to capture the evolution of the mechanical properties as the scaffolds degrade and human osteoblasts grow and proliferate inside the scaffolds. The novel multiscale models provide a robust prediction of the mechanical properties evolution in the scaffolds over the time evolution of cell growth proliferation and tissue formation.

The poromechanics of heterogeneous media is reformulated in a discrete framework using the lattice element method (LEM) that accounts for the presence of interfaces as well as local microtextural and elastic variations. The exchange of mechanical information between pore and solid(s) is captured by means of force field potentials for these domains, which eliminate the requirement of scale separability of continuum-based poromechanics approaches. In congruence with $\mu VT$ and $NPT$ ensembles of statistical mechanics, discrete expressions for Biot poroelastic coefficients are derived. Considering harmonic-type interaction potentials for each link, analytical expressions for both isotropic and transversely isotropic effective elasticity are presented. The theory is validated against continuum-based expressions of Biot poroelastic coefficients for porous media with isotropic and transversely isotropic elastic solid behavior.

Recent studies have showed that microindentation techniques allow assessing the logarithmic creep rate of a cement paste in good correlation with the long-term creep rates measured by compressive tests at macroscopic scale. After having applied microindentation techniques to characterize the effect of relative humidity (RH) on both the creep and relaxation behavior of a cement paste, the objective of this work is to analyze the duality between creep and relaxation curves by means of the analytical models which are currently employed in open literature. First, large grids of creep and relaxation microindentation tests were carried out on a cement paste sample in hygral equilibrium at different levels of RH. Thus, the results were modeled by a viscoelastic model by considering different creep functions (logarithmic and power-law) and corrective terms for initial plasticity under loading. The presented results provide new insights to understand the duality between creep and relaxation rates of a cement paste measured at micrometer scale, especially considering the possible plastic effect.

Temperature and moisture impacts on unoxidized and oxidized asphalts’ thermodynamic and rheological properties were studied using molecular dynamics (MD) simulations. Changes in asphalt property under different degrees of oxidation, temperature, and moisture content were investigated regarding density, isothermal compressibility, bulk modulus, and zero-shear viscosity. MD simulation results show that the density of asphalt before and after oxidation decreases at a similar rate with an increase in temperature. Bulk modulus (inverse of isothermal compressibility) of asphalt before and after oxidation also decreases with an increase in temperature but with different trends. Because of oxidative hardening, oxidized asphalt shows lower isothermal compressibility, but higher bulk modulus and zero-shear viscosity compared with unoxidized asphalt. When moisture is added, such trends become opposite. Specifically, the zero-shear viscosity of the oxidized asphalt becomes lower than that of the unoxidized asphalt above 5% moisture inclusion. This is true in the case of the density of asphalt with moisture as well, but this finding is not significant.

Customary micromechanics models for the poroelasticity, creep, and strength of concrete restrict the domain affected by the hydration reaction to the cement paste volume, considering the latter as a thermodynamically closed system with respect to the (chemically inert) aggregate. Accordingly, the famous Powers hydration model appears to be a natural choice for the determination of clinker, cement, water, and aggregate volume fractions entering such micromechanical models. The situation changes once internal curing occurs, i.e., once part of the water present is absorbed initially by the aggregate, and then is sucked back to the cement paste during the hydration reaction. This paper develops an extended hydration model for this case, introducing water uptake capacity of the aggregate and paste void-filling extent as additional quantities. Based on constant values for just these two new quantities, and on previously determined creep properties of cement pastes as functions of an effective water:cement mass ratio (i.e., that associated with the cement paste domain rather than with the entire concrete volume), a series of ultrashort-term creep tests on different mortars and concretes can be very satisfactorily predicted by a standard microviscoelastic mathematical model. This further extends the applicability range of micromechanics modeling in cement and concrete research.

A new methodology is proposed for investigating compressive failure behavior of cement paste at the micrometer scale. Micropillar geometries are fabricated by focused ion-beam milling on potential calcium-silicate-hydrate (C-S-H) locations identified through energy dispersive spectroscopy (EDS) spot analysis. Uniaxial compression testing of these pillars is performed using nanoindentation equipment. The compressive strength of C-S-H aggregates (225–606 MPa) measured from microcompression tests is found to be consistent with values from multiscale damage and molecular dynamic models. From posttest images, two primary deformation mechanisms at failure were identified; axial splitting and plastic collapse of the entire sample were observed.