Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model

We study multi-fissuration and debonding phenomena of a thin film bonded to a stiff substrate using the variational approach to fracture mechanics. We consider a reduced one-dimensional membrane model where the loading is introduced through uniform inelastic (e.g., thermal) strains in the film or imposed displacements of the substrate. Fracture phenomena are accounted for by adopting a Griffith model for debonding and transverse fracture. On the basis of energy minimization arguments, we recover the key qualitative properties of the experimental evidences, like the periodicity of transverse cracks and the peripheral debonding of each regular segment. Phase diagrams relate the maximum number of transverse cracks that may be created before debonding takes place, as a function of the material properties and the sample’s geometry. The theoretical results are illustrated with numerical simulations obtained through a finite element discretization and a regularized variational formulation of the Ambrosio–Tortorelli type, which is suited to further extensions in two-dimensional settings.     

Structure dependent elastic properties of supergraphene

Complete replacement of aromatic carbon bonds in graphene by carbyne chains gives rise to supergraphene whose mechanical properties are expected to depend on its structure. However, this dependence is to date unclear. In this paper, explicit expressions for the in-plane stiffness and Poisson’s ratio of supergraphene are obtained using a mole-cular mechanics model. The theoretical results show that the in-plane stiffness of supergraphene is drastically (at least one order) smaller than that of graphene, whereas its Pois-son’s ratio is higher than 0.5. As the index number increases (i.e., the length of carbyne chains increases and the bond density decreases), the in-plane stiffness of supergraphene decreases while the Poisson’s ratio increases. By analyzing the relation among the layer modulus, in-plane stiffness and Poisson’s ratio, it is revealed that the mechanism of the faster decrease in the in-plane stiffness than the bond density is due to the increase of Poisson’s ratio. These findings are useful for future applications of supergraphene in nanomechanical systems.     

Nanoscale Broadband Viscoelastic Spectroscopy of Soft Materials Using Iterative Control

A novel approach to nanoscale broadband viscoelastic spectroscopy is presented. The proposed approach utilizes the recently developed modeling-free inversion-based iterative control (MIIC) technique to achieve accurate measurement of the material response to the applied excitation force over a broad frequency band. Scanning probe microscope (SPM) and nanoindenter have become enabling tools to quantitatively measure the mechanical properties of a wide variety of materials at nanoscale. Current nanomechanical measurement, however, is limited by the slow measurement speed: the nanomechanical measurement is slow and narrow-banded and thus not capable of measuring rate-dependent phenomena of materials. As a result, large measurement (temporal) errors are generated when material is undergoing dynamic evolution during the measurement. The low-speed operation of SPM is due to the inability of current approaches to (1) rapidly excite the broadband nanomechanical behavior of materials, and (2) compensate for the convolution of the hardware adverse effects with the material response during high-speed measurements. These adverse effects include the hysteresis of the piezo actuator (used to position the probe relative to the sample); the vibrational dynamics of the piezo actuator and the cantilever along with the related mechanical mounting; and the dynamics uncertainties caused by the probe variation and the operation condition. In the proposed approach, an input force signal with frequency characteristics of band-limited white-noise is utilized to rapidly excite the nanomechanical response of materials over a broad frequency range. The MIIC technique is used to compensate for the hardware adverse effects, thereby allowing the precise application of such an excitation force and measurement of the material response (to the applied force). The proposed approach is illustrated by implementing it to measure the frequency-dependent plane-strain modulus of poly(dimethylsiloxane) (PDMS) over a broad frequency range extending over 3 orders of magnitude (~1 Hz to 4.5 kHz).     

Probability distribution of fracture elongation,strength and toughness of notched rectangular blocks with lognormal Young's modulus

We find analytical approximations to the probability distribution of fracture properties of one-dimensional rods and thin two-dimensional plates when Young’s modulus varies spatially as an isotropic lognormal field. The properties considered are the elongation, strength, and toughness modulus at fracture initiation and at ultimate failure. This is an extension of a previous study that, under the same conditions, dealt with the distribution of the bulk elastic moduli (Dimas et al., 2015). For all quantities at fracture initiation our approach is analytical in 1D and semi-analytical in 2D. For ultimate failure, we quantify the random effects of fracture propagation and crack arrest by fitting regression models to simulation data and combine the regressions with the distributions at fracture initiation. The results are validated through a series of Monte Carlo simulations. Through parametric analysis, we gain insight into the strengthening/weakening roles of the Euclidean dimension and size of the specimen and the variance and correlation function of the log-modulus field.     

Nonlinear dynamic response of beam and its application in nanomechanical resonator

Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvature-dominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity can result in both hardening and softening effects. The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.     

Strength and fracture toughness of heterogeneous blocks with joint lognormal modulus and failure strain

We obtain analytical approximations to the probability distribution of the fracture strengths of notched one-dimensional rods and two-dimensional plates in which the stiffness (Young’s modulus) and strength (failure strain) of the material vary as jointly lognormal random fields. The fracture strength of the specimen is measured by the elongation, load, and toughness at two critical stages: when fracture initiates at the notch tip and, in the 2D case, when fracture propagates through the entire specimen. This is an extension of a previous study on the elastic and fracture properties of systems with random Young’s modulus and deterministic material strength (Dimas et al., 2015a). For 1D rods our approach is analytical and builds upon the ANOVA decomposition technique of (Dimas et al., 2015b). In 2D we use a semi-analytical model to derive the fracture initiation strengths and regressions fitted to simulation data for the effect of crack arrest during fracture propagation. Results are validated through Monte Carlo simulation. Randomness of the material strength affects in various ways the mean and median values of the initial strengths, their log-variances, and log-correlations. Under low spatial correlation, material strength variability can significantly increase the effect of crack arrest, causing ultimate failure to be a more predictable and less brittle failure mode than fracture initiation. These insights could be used to guide design of more fracture resistant composites, and add to the design features that enhance material performance.     

Mode I Fracture Characterization of Bituminous Paving Mixtures at Intermediate Service Temperatures

This study presents an integrated approach combining experimental tests and numerical modeling to characterize mode I fracture behavior of bituminous paving mixtures subjected to a wide range of loading rates at intermediate temperature conditions. A simple experimental protocol is developed using the semi-circular bending (SCB) test geometry. The local fracture behavior at the initial notch tip of the SCB specimens is monitored using high-speed cameras with a digital image correlation (DIC) system. The DIC results of the SCB fracture tests are then simulated using a finite element method that is incorporated with material viscoelasticity and cohesive zone fracture. Fracture properties are obtained locally at the notch tip by identifying two cohesive zone fracture parameters (cohesive strength and fracture energy) that result in a good agreement between test results and numerical simulations. The results clearly present significant rate-dependent fracture characteristics of bituminous paving mixtures at intermediate service temperatures. This study further demonstrates that fracture properties of viscoelastic materials need to be characterized at the local fracture process zone when they present ductile fracture behavior.     

Meso-scale approach to modelling the fracture process zone of concrete subjected to uniaxial tension

A meso-scale analysis is performed to determine the fracture process zone of concrete subjected to uniaxial tension. The meso-structure of concrete is idealised as stiff aggregates embedded in a soft matrix and separated by weak interfaces. The mechanical response of the matrix, the inclusions and the interface between the matrix and the inclusions is modelled by a discrete lattice approach. The inelastic response of the lattice elements is described by a damage approach, which corresponds to a continuous reduction of the stiffness of the springs. The fracture process in uniaxial tension is approximated by an analysis of a two-dimensional cell with periodic boundary conditions. The spatial distribution of dissipated energy density at the meso-scale of concrete is determined. The size and shape of the deterministic FPZ is obtained as the average of random meso-scale analyses. Additionally, periodicity of the discretisation is prescribed to avoid influences of the boundaries of the periodic cell on fracture patterns. The results of these analyses are then used to calibrate an integral-type nonlocal model.     

Computational and theoretical modeling of intermediate filament networks: Structure, mechanics and disease

Intermediate filaments,in addition to microtubules and actin microfilaments,are one of the three major components of the cytoskeleton in eukaryotic cells.It was discovered during the recent decades that in most cells,intermediate filament proteins play key roles to reinforce cells subjected to large-deformation,and that they participate in signal transduction,and it was proposed that their nanomechanical properties are critical to perform those functions.However,it is still poorly understood how the nanoscopic structure,as well as the combination of chemical composition,molecular structure and interfacial properties of these protein molecules contribute to the biomechanical properties of filaments and filament networks.Here we review recent progress in computational and theoretical studies of the intermediate filaments network at various levels in the protein’s structure.A multiple scale method is discussed,used to couple molecular modeling with atomistic detail to larger-scale material properties of the networked material.It is shown that a finer-trains-coarser methodology as discussed here provides a useful tool in understanding the biomechanical property and disease mechanism of intermediate filaments,coupling experiment and simulation.It further allows us to improve the understandingof associated disease mechanisms and lays the foundation for engineering the mechanical properties of biomaterials.     

An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes

An analytical molecular structural mechanics model for the prediction of mechanical properties of defect-free carbon nanotubes is developed by incorporating the modified Morse potential with an analytical molecular structural model. The developed model is capable of predicting Young’s moduli, Poisson’s ratios and stress–strain relationships of carbon nanotubes under tension and torsion loading conditions. Results on the mechanical properties of single-walled carbon nanotubes show that Young’s moduli of carbon nanotubes are sensitive to the tube diameter and the helicity. Young’s moduli of both armchair and zigzag carbon nanotubes increase monotonically and approach Young’s modulus of graphite when the tube diameter is increased. The nonlinear stress–strain relationships for defect-free nanotubes have been predicted, which gives a good approximation on the ultimate strength and strain to failure of nanotubes. Armchair nanotubes exhibit higher tensile strength than zigzag nanotubes but their torsion strengths are identical based on the present study. The present theoretical investigation provides a very simple approach to predict the mechanical properties of carbon nanotubes.     

Simulation of crack propagation in fiber-reinforced bulk metallic glasses

Based on a phase-field model for deformation in bulk metallic glasses (BMGs), shear band formation and crack propagation in the fiber-reinforced BMG are investigated. Ideal unbroken fibers embedded in the BMG matrix are found to significantly influence the shear banding and crack propagation in the matrix. The crack propagation affected by fibers’ length and orientation is quantitatively characterized and is described by micromechanics models for composite materials. Furthermore, fractures in some practical fiber-reinforced BMG composites such as tungsten-reinforced Zr-based BMG are simulated. The relation between the enhanced fracture toughness and the mechanical properties of fiber reinforcements is determined. Different fracture modes of BMG-matrix composites are identified from the systematic simulation studies, which are found to be consistent with experiments. The simulation results suggest that the phase-field modeling approach could be a useful tool to assist the fabrication and design of BMG composites with high fracture toughness and ductility.     

Investigation of nanomechanical properties of multilayered hybrid nanocomposites

Nanocomposites manufactured by combining two nano-structured phases are quite rare. While industry is seeking materials to meet difficult challenges with unique properties, there is no “rule of mixtures” to identify how to mix multiple nanomaterials in a composite structure and make available all required properties. Filler–matrix adhesion and its relation to materials’ properties have been the subject of continuing study due to composites advanced applications. Further on, studies at the interphase created in the area between the constituent materials can provide important information concerning materials interaction and composites behavior; this issue becomes even more interesting when discussing about nano-interphases. In the present investigation, a study of multi-layered nanocomposites is conducted. More precisely, the following four different types of multilayered hybrid nanocomposites were manufactured and tested: Pure titanium–carbon nanotubes–epoxy; pure titanium–epoxy–carbon nanotubes; titanium dioxide nanotubes–carbon nanotubes–epoxy and titanium dioxide nanotubes–epoxy–carbon nanotubes. The nano-mechanical properties of the above-mentioned nanocomposites were investigated using nanoindentation technique. The main conclusion of the present work is that in the case of multilayered nanocomposites, even if nanoindentation is executed on the surface of the same material, results greatly depend on the underlying substrates’ nature and their stacking sequence. Also, nano-interphases created at the contact surfaces between different layers affect the experimentally measured values of the nanomechanical properties (Young’s modulus and hardness) of multilayered nanocomposites.     

多模态原子力显微术研究进展

材料纳米尺度的各种性能中，纳米力学性能是纳米材料和器件服役所需要保证的最基本性能。因此，发展可靠的定量化纳米力学测试技术就显得尤为关键。原子力显微镜(Atomic Force Microscope，AFM)作为纳米力学测试的重要平台，目前广泛应用于材料纳米尺度形貌和力学性能成像。作为原子力显微术的前沿应用模式之一，多模态原子力显微术通过同时激励探针的两个或多个振动模态对样品进行测试或成像，可实现对被测样品高分辨率、高灵敏度、定量化和无损的纳米力学快速成像及检测，具有极其广泛的应用前景。围绕多模态原子力显微术，首先介绍了多模态原子力显微术的基本成像原理和力学模型基础。随后，综述了多模态原子力显微术探针动力学以及成像技术相关研究的主要进展。然后，对多模态原子力显微术的几类典型应用进行了总结和评述。最后，对多模态原子力显微术未来可能的研究方向进行了展望。     

Inverse determination of modeling parameters to consider inhomogeneities of semicrystalline thermoplastics in structure simulations

Two semicrystalline thermoplastics, an isotactic polypropylene (iPP, LynedllBasell Moplen HP501L) and a polyethylene-high-density (PE-HD, LynedllBasell Hostalen GC7260), were selected to approve a new approach. The developed approach allows the inverse determination of the amorphous and crystalline mechanical as well as the crystalline geometric constituents’ properties. Commonly, these properties are unknown in structure simulations, and hence, the application of micromechanical models to the inhomogeneous microstructure of semicrystalline thermoplastics is restricted. Rather, a homogenous microstructure is assumed, and only one Young’s modulus and Poisson’s ratio are used in calculations. Thus, the quality and reliability of simulations are limited. In the current study, a new approach was exemplarily conducted for the inverse determination of the required properties by combining a Mori–Tanaka mean field approach with a genetic optimization algorithm. Conclusive results were achieved for both polymers. According to the results, the attained geometric parameters for the crystalline constituents resemble the aspect ratio of the spherulite diameter and the long period of the real crystalline microstructure, and the mechanical properties of the amorphous and crystalline constituents are located within reasonable bounds.     

Size effect in quasibrittle failure: Analytical model and numerical simulations using cohesive zone model

The recent rewriting of the Ba?ant’s size effect law (Morel, 2008) which has suggested the existence of an additional asymptotic regime for intermediate structure sizes is now compared to numerical simulations of fracture of geometrically similar notched structures of different sizes extending over 2.4 decades. The quasibrittle fracture behavior is simulated through cohesive zone model (bilinear softening) using a constant set of cohesive parameters whatever the specimen size D is. The R-curves resulting from the load–displacement responses are estimated and appear as size-independent. On this basis, the different asymptotic regimes expected for the size effect on fracture properties at peak load such as the relative crack length, the resistance to crack growth and the nominal strength are shown in fair agreement with the size effect observed on the results obtained from numerical simulations.     

Dispersion of Surface Waves in a Periodically Laminated Piezoelectric Half-Space with Liquid Upper Layer

An approach is proposed to set up the dispersion equations for surface waves propagating through a periodically laminated piezoelectric medium, with the upper layer being a perfect compressible fluid. The approach is based on the formalism of Hamiltonian periodic systems. The dispersion equations derived are valid for an arbitrary law of variation in properties with periodicity coordinate. The influence of the liquid layer and inhomogeneity of the piezoelectric medium on the dispersion spectra of surface waves is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 55–61, March 2005.     

Surface Waves in a Stratified Periodic Medium with a Liquid Upper Layer

An approach is proposed to set up the dispersion equations for surface waves in a periodically stratified half-space contacting with a layer of a perfect compressible liquid. The approach is based on the formalism of periodic Hamiltonian systems. The dispersion equations derived are valid for an arbitrary law of variation in the properties with respect to the coordinate of periodicity. The effects of the liquid layer and the inhomogeneity of the elastic medium on the dispersion spectra of surface waves are studied     

Estimation of anisotropic elastic properties of nanocomposites using atomistic-continuum interphase model

We have revised classical micromechanics by accounting for the effect of interface to predict the effective anisotropic elastic properties of heterogeneous materials containing nano-inhomogeneities. In contrast to sharp interface between the matrix and inhomogeneity, we introduce the concept of interphase to account for the interfacial-stress effect at the nano-scale. The interphase’s constitutive properties are derived from atomistic simulations and then incorporated in a micromechanics-based interphase model to compute effective properties of nanocomposites. This scale transition approach bridges the gap between discrete atomic level interactions and continuum mechanics. An advantage of this approach is that it combines atomistic with continuum models that consider inhomogeneity and interphase morphology. It thereby enables us to account simultaneously for both the shape and the anisotropy of a nano-inhomogeneity and interphase at the continuum level when we compute material’s overall properties. In so doing, it frees us from making any assumptions about the interface characteristics between matrix and the nano-inhomogeneity.     

Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads

Mixed-mode fracture problems of orthotropic functionally graded materials (FGMs) are examined under mechanical and thermal loading conditions. In the case of mechanical loading, an embedded crack in an orthotropic FGM layer is considered. The crack is assumed to be loaded by arbitrary normal and shear tractions that are applied to its surfaces. An analytical solution based on the singular integral equations and a numerical approach based on the enriched finite elements are developed to evaluate the mixed-mode stress intensity factors and the energy release rate under the given mechanical loading conditions. The use of this dual approach methodology allowed the verifications of both methods leading to a highly accurate numerical predictive capability to assess the effects of material orthotropy and nonhomogeneity constants on the crack tip parameters. In the case of thermal loading, the response of periodic cracks in an orthotropic FGM layer subjected to transient thermal stresses is examined by means of the developed enriched finite element method. The results presented for the thermally loaded layer illustrate the influences of the material property gradation profiles and crack periodicity on the transient fracture mechanics parameters.     

Overall longitudinal shear elastic modulus of a 1–3 composite with anisotropic constituents

The overall properties of a binary elastic periodic fiber-reinforced composite, with transversely isotropic constituents in an anti-plane-strain deformation state, are studied here for a cell periodicity of square type. This analysis considers four different orientations of the axis of transverse isotropy of constituents with respect to the direction of fibers. Each case is characterized by very simple closed-form expressions for the effective coefficients, which were obtained using the asymptotic homogenization method. Local problems defined on a periodic square unit cell are solved using Weierstrassian and Natanzon’s functions and perturbation theory relative to small anisotropy. In the isotropic limit, comparison with rigorous bounds and some well-known mixing rules are made. Also, comparisons with finite element calculations show that the derived closed-form formulae provide excellent results even for large anisotropy.