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This paper presents an overview of the theories and computer implementation aspects of phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches to fracture is that PFM can elegantly simulate complicated fracture processes including fracture initiation, propagation, coalescence, and branching by using only a scalar field, the phase field. In addition, fracture is a natural outcome of the simulation and obtained through the solution of an additional differential equation related to the phase field. No extra fracture criteria are needed and an explicit representation of a crack surface as well as complex track crack procedures are avoided in PFM for fracture, which in turn dramatically facilitates the implementation. The PFM is thermodynamically consistent and can be easily extended to multi-physics problem by 'changing' the energy functional accordingly. Besides an overview of different PFMs, we also present comparative numerical benchmark examples to show the capability of PFMs.

The recent experimental synthesis of the two-dimensional (2D)boron-graphdiyne (BGDY) nanosheet has motivated us to investigate its structural, electronic,and energy storage properties. BGDY is a particularly attractive candidate for this purpose due to uniformly distributed pores which can bind the light-metal atoms. Our DFTcalculations reveal that BGDY can accommodate multiple light-metal dopants (Li, Na, K, Ca)with significantly high binding energies. The stabilities of metal functionalized BGDY monolayers have been confirmed through ab initio molecular dynamics simulations. Furthermore, significant charge-transfer between the dopantsand BGDY sheet renders the metal with a significant positive charge, which is a prerequisite for adsorbing hydrogen (H2) molecules with appropriate binding energies.This results in exceptionally high H2 storage capacities of 14.29, 11.11, 9.10 and 8.99 wt% for the Li, Na, K and Ca dopants, respectively. These H2storage capacities are much higher than many 2D materials such as graphene, graphane, graphdiyne, graphyne, C2N, silicene, and phosphorene. Average H2 adsorption energies for all the studied systems fall within an ideal window of 0.17-0.40 eV/H2. We have also performed thermodynamic analysis to study the adsorption/desorption behavior of H2, which confirmsthat desorption of the H2molecules occurs at practical conditions of pressure and temperature.

Graphdiyne and graphyne are carbon-based two-dimensional (2D) porous atomic lattices, with outstanding physics and excellent application prospects for advanced technologies, like nanoelectronics and energy storage systems. During the last year, B- and N-graphdiyne nanomembranes were experimentally realized. Motivated by the latest experimental advances, in this work we predicted novel N-, B-, P-, Al-, As-, Ga-graphdiyne/graphyne 2D lattices. We then conducted density functional theory simulations to obtain the energy minimized structures and explore the mechanical, thermal stability, electronic and optical characteristics of these novel porous nanosheets. Acquired theoretical results reveal that the predicted carbon-based lattices are thermally stable. It was moreover found that these novel 2D nanostructures can exhibit remarkably high tensile strengths or stretchability. The electronic structure analysis reveals semiconducting electronic character for the predicted monolayers. Moreover, the optical results indicate that the first absorption peaks of the imaginary part of the dielectric function for these novel porous lattices along the in-plane directions are in the visible, IR and near-IR (NIR) range of light. This work highlights the outstanding properties of graphdiyne/graphyne lattices and recommends them as promising candidates to design stretchable energy storage and nanoelectronics systems.

We present a multiscale model bridging length and time scales from molecular to continuum levels with the objective of predicting the yield behavior of amorphous glassy polyethylene (PE). Constitutive parameters are obtained from molecular dynamics (MD) simulations, decreasing the requirement for ad-hoc experiments. Consequently, we achieve: (1) the identification of multisurface yield functions; (2) the high strain rate involved in MD simulations is upscaled to continuum via quasi-static simulations. Validation demonstrates that the entire multisurface yield functions can be scaled to quasi-static rates where the yield stresses are possibly predicted by a proposed scaling law; (3) a hierarchical multiscale model is constructed to predict temperature and strain rate dependent yield strength of the PE.

This article presents original work combining a NURBS-based inverse analysis with both kinematic and constitutive nonlinearities to recover the applied loads and deformations of thin shell structures. The inverse formulation is tackled by gradient-based optimization algorithms based on computed and measured displacements at a number of discrete locations. The proposed method allows accurately recovering the target shape of shell structures such that instabilities due to snapping and buckling are captured. The results obtained show good performance and applicability of the proposed algorithms to computer-aided manufacturing of shell structures.

We present a theoretical study of electronic and thermal transport in polycrystalline heterostructures combining graphene (G) and hexagonal boron nitride (hBN) grains of varying size and distribution. By increasing the hBN grain density from a few percents to $100\%$, the system evolves from a good conductor to an insulator, with the mobility dropping by orders of magnitude and the sheet resistance reaching the M$\Omega$ regime. The Seebeck coefficient is suppressed above $40\%$ mixing, while the thermal conductivity of polycrystalline hBN is found to be on the order of $30-120\,{\rm W}{\rm m}^{-1}{\rm K}^{-1}$. These results, agreeing with available experimental data, provide guidelines for tuning G-hBN properties in the context of two-dimensional materials engineering. In particular, while we proved that both electrical and thermal properties are largely affected by morphological features (like e.g. by the grain size and composition), we find in all cases that nm-sized polycrystalline G-hBN heterostructures are not good thermoelectric materials.

We developed a combined atomistic-continuum hierarchical multiscale approach to explore the effective thermal conductivity of graphene laminates. To this aim, we first performed molecular dynamics simulations in order to study the heat conduction at atomistic level. Using the non-equilibrium molecular dynamics method, we evaluated the length dependent thermal conductivity of graphene as well as the thermal contact conductance between two individual graphene sheets. In the next step, based on the results provided by the molecular dynamics simulations, we constructed finite element models of graphene laminates to probe the effective thermal conductivity at macroscopic level. A similar methodology was also developed to study the thermal conductivity of laminates made from hexagonal boron-nitride (h-BN) films. In agreement with recent experimental observations, our multiscale modeling confirms that the flake size is the main factor that affects the thermal conductivity of graphene and h-BN laminates. Provided information by the proposed multiscale approach could be used to guide experimental studies to fabricate laminates with tunable thermal conduction properties.

All-carbon heterostructures have been produced recently via focused ion beam patterning of single layer graphene. Amorphized graphene is similar to a graphene sheet in which some hexagons are replaced by a combination of pentagonal, heptagonal and octagonal rings. The present investigation provides a general view regarding phonon and load transfer along amorphous graphene. The developed models for the evaluation of mechanical and thermal conductivity properties yield accurate results for pristine graphene and acquired findings for amorphized graphene films are size independent. Our atomistic results show that amorphous graphene sheets could exhibit a remarkably high elastic modulus of ~500 GPa and tensile strengths of ~50 GPa at room temperature. However, our results show that mechanical properties of amorphous graphene decline at higher temperatures. Furthermore, we show that amorphized graphene present a low thermal conductivity ~15 W/mK which is two orders of magnitude smaller than pristine graphene, and we verify that its thermal conductivity is almost insensitive to temperature since it is dominated by phonon-defect scattering rather than phonon-phonon scattering. Finally, our results show that amorphized graphene structures present a remarkably high elastic modulus and mechanical strength, along with a low thermal conductivity, which is an unusual combination for carbon-based materials.

Graphitic carbon nitride nanosheets are among 2D attractive materials due to presenting unusual physicochemical properties.Nevertheless, no adequate information exists about their mechanical and thermal properties. Therefore, we used classical molecular dynamics simulations to explore the thermal conductivity and mechanical response of two main structures of single-layer triazine-basedg-C3N4 films.By performing uniaxial tensile modeling, we found remarkable elastic modulus of 320 and 210 GPa, and tensile strength of 47 GPa and 30 GPa for two different structures of g-C3N4sheets. Using equilibrium molecular dynamics simulations, the thermal conductivity of free-standing g-C3N4 structures were also predicted to be around 7.6 W/mK and 3.5 W/mK. Our study suggests the g-C3N4films as exciting candidate for reinforcement of polymeric materials mechanical properties.

Silicene, germanene and stanene likely to graphene are atomic thick material with interesting properties. We employed first-principles density functional theory (DFT) calculations to investigate and compare the interaction of Na or Li ions on these films. We first identified the most stable binding sites and their corresponding binding energies for a single Na or Li adatom on the considered membranes. Then we gradually increased the ions concentration until the full saturation of the surfaces is achieved. Our Bader charge analysis confirmed complete charge transfer between Li or Na ions with the studied 2D sheets. We then utilized nudged elastic band method to analyze and compare the energy barriers for Li or Na ions diffusions along the surface and through the films thicknesses. Our investigation findings can be useful for the potential application of silicene, germanene and stanene for Na or Li ion batteries.

Two dimensional allotropes of group IV substrates including silicene, germanene and stanene have recently attracted considerable attention in nanodevice fabrication industry. These materials involving the buckled structure have been experimentally fabricated lately. In this study, first principles density functional theory calculations were utilized to investigate the mechanical properties of single layer and free standing silicene, germanene and stanene. Uniaxial tensile and compressive simulations were carried out to probe and compare stress strain properties; such as the Young modulus, Poisson ratio and ultimate strength. We evaluated the chirality effect on the mechanical response and bond structure of the 2D substrates. Our first principles simulations suggest that in all studied samples application of uniaxial loading can alter the electronic nature of the buckled structures into the metallic character. Our investigation provides a general but also useful viewpoint with respect to the mechanical properties of silicene, germanene and stanene.

Recent experimental advances for the fabrication of various borophene sheets introduced new structures with a wide prospect of applications. Borophene is the boron atoms analogue of graphene. Borophene exhibits various structural polymorphs all of which are metallic. In this work, we employed first-principles density functional theory calculations to investigate the mechanical properties of five different single-layer borophene sheets. In particular, we analyzed the effect of loading direction and point vacancy on the mechanical response of borophene. Moreover, we compared the thermal stabilities of the considered borophene systems. Based on the results of our modelling, borophene films depending on the atomic configurations and the loading direction can yield remarkable elastic modulus in the range of 163-382 GPa.nm and high ultimate tensile strength from 13.5 GPa.nm to around 22.8 GPa.nm at the corresponding strain from 0.1 to 0.21. Our study reveals the remarkable mechanical characteristics of borophene films.

Borophene, the boron atom analogue to graphene, being atomic thick have been just recently experimentally fabricated. In this work, we employ first-principles density functional theory calculations to investigate the interaction of Ca, Mg, Na or Li atoms with single-layer and free-standing borophene. We first identified the most stable binding sites and their corresponding binding energies as well and then we gradually increased the ions concentration. Our calculations predict strong binding energies of around 4.03 eV, 2.09 eV, 2.92 eV and 3.28 eV between the borophene substrate and Ca, Mg, Na or Li ions, respectively. We found that the binding energy generally decreases by increasing the ions content. Using the Bader charge analysis, we evaluate the charge transfer between the adatoms and the borophene sheet. Our investigation proposes the borophene as a 2D material with a remarkably high capacity of around 800 mAh/g, 1960 mAh/g, 1380 mAh/g and 1720 mAh/g for Ca, Mg, Na or Li ions storage, respectively. This study can be useful for the possible application of borophene for the rechargeable ion batteries.

Molybdenum disulfide (MoS2) is a highly attractive 2D material due to its interesting electronic properties. Recent experimental advances confirm the possibility of further tuning the electronic properties of MoS2 through the fabrication of single-layer heterostructures consisting of semiconducting (2H) and metallic (1T) MoS2 phases. Nonetheless, despite significant technological and scientific interest, there is currently limited information concerning the mechanical properties of these heterostructure systems. This investigation aims to extend our understanding of the mechanical properties of all-MoS2 single-layer structures at room temperature. This goal was achieved by performing extensive classical molecular dynamics simulations using a recently developed RexFF forcefield. We first studied the direction dependent mechanical properties of defect-free 2H and 1T phases. Our modelling results for pristine 2H MoS2 were found to be in good agreement with the experimental tests and first-principles theoretical predictions. We also discuss the mechanical response of 2H/1T single layer heterostructures. Our reactive molecular dynamics results suggest all-MoS2 heterostructures as suitable candidates to provide a strong and flexible material with tuneable electronic properties.

Transition metal carbides include a wide variety of materials with attractive properties that are suitable for numerous and diverse applications. Most recent experimental advance could provide a path toward successful synthesis of large-area and high-quality ultrathin Mo2C membranes with superconducting properties. In the present study, we used first-principles density functional theory calculations to explore the mechanical and optical response of single-layer and free-standing Mo2C. Uniaxial tensile simulations along the armchair and zigzag directions were conducted and we found that while the elastic properties are close along various loading directions, nonlinear regimes in stress-strain curves are considerably different. We found that Mo2C sheets present negative Poisson's ratio and thus can be categorized as an auxetic material. Our simulations also reveal that Mo2C films retain their metallic electronic characteristic upon the uniaxial loading. We found that for Mo2C nanomembranes the dielectric function becomes anisotropic along in-plane and out-of plane directions. Our findings can be useful for the practical application of Mo2C sheets in nanodevices.

We perform classical molecular dynamics to investigate the effects of mechanical strain on single-layer black phosphorus nanoresonators at different temperatures. We find that the resonant frequency is highly anisotropic in black phosphorus due to its intrinsic puckered configuration, and that the quality factor in the armchair direction is higher than in the zigzag direction at room temperature. The quality factors are also found to be intrinsically larger than graphene and MoS2 nanoresonators. The quality factors can be increased by more than a factor of two by applying tensile strain, with uniaxial strain in the armchair direction being most effective. However, there is an upper bound for the quality factor increase due to nonlinear effects at large strains, after which the quality factor decreases. The tension induced nonlinear effect is stronger along the zigzag direction, resulting in a smaller maximum strain for quality factor enhancement.

In this paper, the axial vibration of cracked beams, the free flexural vibrations of nanobeams and plates based on Timoshenko beam theory and first-order shear deformable plate theory, respectively, using Eringen's nonlocal elasticity theory is numerically studied. The field variable is approximated by Lagrange polynomials and non-uniform rational B-splines. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the natural frequency is numerically studied. The influence of a crack on axial vibration is also studied. The results obtained from this study are found to be in good agreement with those reported in the literature., Comment: 29 pages, 6 tables, 10 figures

In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate bending element based on field and edge consistency requirement with 20 degrees of freedom per element is used for this study. The natural frequencies and mode shapes of simply supported and clamped square and rectangular plates are computed as a function of gradient index, crack length, crack orientation and crack location. The effect of thickness and influence of multiple cracks is also studied., Comment: 38 pages, 14 figures, 10 tables; Composite Structures, 2011