Continuum Mechanics Analysis Research Articles

Damping of the acoustic vibrations of a suspended gold nanowire in air and water environments

The lifetimes of the acoustic vibrations of metal nanostructures depend sensitively on the properties of the environment, such as the acoustic impedance and viscosity. In order to accurately study these effects, they have to be separated from the damping processes that are inherent to the nanostructure. Here we show that this can be done experimentally by investigating individual gold nanowires suspended over a trench in air and liquid environments. The experiments were done by ultrafast pump-probe microscopy, recording transient absorption traces at the same point on the nanowire in both environments. These first experiments were performed with water, and the measured vibrational quality factors due to the presence of water were compared to continuum mechanics calculations for a cylinder in a homogeneous environment. Good agreement was found between the experimental quality factors and the calculated values. The continuum mechanics analysis shows that damping is dominated by the acoustic impedance of the solvent rather than by its viscosity for the nanowires in the present experiments. This experimental technique opens up the possibility of studying the effect of viscosity on the high frequency vibrational motions of nanostructures for a variety of liquids.

Spontaneous formation of double helical structure due to interfacial adhesion

Many quasi-one-dimensional micro/nanomaterials assume double or multi-stranded helical conformations, but the reasons are still unclear. On the basis of continuum mechanics analysis, we demonstrate that interfacial adhesion is a significant physical mechanism responsible for the formation of some double helices, especially at micro and nano scales and for soft materials. With the formation of a double helical structure by two nanowires, surface energy decreases while elastic strain energy increases. Their competition dictates the global morphology of adhered micro/nanowires or tubes. The theoretical model agrees well with relevant experiments.

Continuum Mechanical Analysis of Collective Motion of Robots

Continuum Mechanical Analysis of Collective Motion of Robots

Maximum asymmetry in strain induced mechanical instability of graphene: Compression versus tension

We demonstrate that graphene, as the thinnest possible solid membrane of only one atomic layer thick, exhibits the maximum asymmetry in tensile versus compressive strain induced mechanical instability. Using continuum mechanics analysis and molecular dynamics simulations, we show that for graphene nanoribbons (sheets) with a typical length (size) of ∼100 nm, the critical compressive strain for buckling instability is only ∼10−4%, while the critical tensile strain for fracture is ∼2%, a four orders of magnitude difference. Such a large asymmetry implies that practically, strain engineering of graphene devices is only viable with application of tensile strain but difficult with compressive strain.

Crack resistance in two-dimensional periodic materials of medium and low porosity

The plane problem of crack resistance in elastic materials with doubly periodic system of voids is investigated. The relatively high fractional density (medium and low porosity) of above 0.6 which is typical for the partially-sintered materials is addressed. The stress field in the voided plane with embedded Mode I crack of arbitrary length bridging the voids is evaluated. In the framework of stress criterion of fracture this field allows the determination of the fracture toughness of the considered material with periodic microstructure in terms of the solid (parent) material tensile strength. The mathematical modeling of this problem is complicated due to the fact that the “ligaments” between the voids are so thick that they cannot be treated as beams. As a result, theoretical methods used to evaluate the fracture toughness of low-density cellular materials are not applicable. Accordingly, the present problem is solved by means of a novel analysis which is based on the combined use of the representative cell method, based on the discrete Fourier transform, in conjunction with a higher-order theory and a micromechanical model. These combined three approaches allow the performance of an accurate continuum mechanics analysis of the highly non-uniform stress field in the voided material with a crack. The analysis of this field for different crack lengths has shown which length must be employed in the fracture toughness evaluation. The dependence of the fracture toughness upon the relative density is examined and found to vary linearly in the majority of the considered density range. This result agrees with the known experimental observations and other theoretical predictions.

Formation of hydrogenated graphene nanoripples by strain engineering and directed surface self-assembly

We propose a new class of semiconducting graphene-based nanostructures: hydrogenated graphene nanoripples (HGNRs), based on continuum-mechanics analysis and first principles calculations. They are formed via a two-step combinatorial approach: first by strain engineered pattern formation of graphene nanoripples, followed by a curvature-directed self-assembly of H adsorption. It offers a high level of control of the structure and morphology of the HGNRs, and hence their band gaps which share common features with graphene nanoribbons. A cycle of H adsorption/desorption at/from the same surface locations completes a reversible metal-semiconductor-metal transition with the same band gap.

Hierarchical computational approaches of the effects of interstitial and vacancy loops on plastic deformation

ABSTRACTHierarchical modeling based on atomistic and continuum simulations were established to describe the fundamental characteristics of plastic deformation in irradiated materials. Typical irradiation defects of a self-interstitial atom (SIA) loop and vacancy loop are considered. At first atomic models, including a SIA loop and a vacancy as well as a straight dislocation loop in single crystals were constructed. Constant strain is applied to each model and the equilibrium configuration under deformation is calculated by a molecular statics simulation. Maximum shear stresses in various radii of irradiated defects are stored in a database for the continuum mechanics analysis. Then local interaction events between glide dislocation and irradiation defects were introduced through crystal plasticity finite element analysis. In this model the effect of radiation hardening was considered by referring to the experiment. We found that softening after the first yield event is caused by annihilation of irradiation defects resulting from unfaulting of the radiation defects.

Modeling and Simulation of Wave Propagation Based on Atomistic Field Theory

Abstract Motivated by the need for a more efficient simulation of material behavior at both larger length scale and longer time scale than direct molecular dynamics simulation, an atomistic field theory (AFT) for modeling and simulation of multiphase material systems has been developed. Atomistic formulation of the multiscale field theory and its corresponding finite element implementation are briefly introduced. By virtue of finite element analysis of classical continuum mechanics, we show the existing phenomena of spurious wave reflections at the interfaces between regions with different mesh sizes. AFT is employed to investigate the wave propagation in magnesium oxide from the atomistic region to the continuum region without any special numerical treatment. Unlike some other atomistic/continuum computational methods, AFT has demonstrated the capability to display both acoustic and optic types of wave motion. Numerical results show that AFT has the capability to significantly reduce the wave reflections at the interface. This work provides a more fundamental understanding of wave reflections at the atomistic/continuum interface.

Statistical continuum mechanics analysis of effective elastic properties in solid oxide fuel cell glass–ceramic seal material

A full statistical analysis of the microstructure of glass–ceramic solid oxide fuel cell (SOFC) seal material, G18, is performed to calculate elastic properties. Predictions are made for samples aged for 4 h and 1000 h, giving different crystallinity levels. Microstructure of the glass–ceramic G18 is characterized by correlation function for each individual phase. Predicted results are compared with the Voigt and Reuss bounds in this study. The weak contrast analysis results in elastic modulus predictions between the upper and lower bounds but closer to the upper bound.

Numerical Analysis of Continuum Mechanics and Multi-phase Flow Using Particle Methods

Numerical Analysis of Continuum Mechanics and Multi-phase Flow Using Particle Methods

Deformation gradients for continuum mechanical analysis of atomistic simulations

We present an expression developed for calculating an atomic-scale deformation gradient within atomistic simulations. This expression is used to analyze the deformation fields for a one-dimensional atomic chain, a biaxially stretched thin film containing a surface ledge, and a FCC metal subject to indentation loading from a nanometer-scale indenter. The analyses presented show that the metric established here is consistent with the continuum mechanical concept of deformation gradient (which is known to have a zero curl for compatible deformations) in most instances. However, our metric does yield non-zero values of curl for atoms near loaded geometric inhomogeneities, such as those that form the ledges themselves and those beneath or adjacent to the indentation contact region. Also, we present expressions for higher order gradients of the deformation field and discuss the requirements for their calculation. These expressions are necessary for linking atomistic simulation results with advanced continuum mechanics theories such as strain gradient plasticity, thereby enabling fundamental, atomic-scale information to contribute to the formulation and parameterization of such theories.

Micromechanical Viscoelastic Characterization of Fibrous Composites

An efficient computational algorithm is proposed to evaluate the viscoelastic properties of fibrous composites. A repeating unit cell (RUC) based on a pre-determined fiber packing is assumed to represent the microstructure of the composite. Finite element analysis of this unit cell under six specified loading conditions is carried out to study and quantify the time-dependent composite viscoelastic property of the unit cell. Volume averaging scheme is implemented to determine the averaged response as function of time in terms of stresses and strains. This time history analysis constitutes the data for characterization of the composite and determination of the viscoelastic parameters and coefficients. The individual viscoelastic properties of the constituents' materials as well as the composite are assumed to follow the Prony series definitions. To verify the algorithm certain examples are included. In these examples, the constituting fiber materials are assumed to be elastic and the matrix is assumed viscoelastic. Three different types of fiber packings; hexagonal (HEX), square (SQR) and bidirectional crossed fibers (BCF), will be used and each packing will be examined for different fiber volume (V f/V) fractions. The accuracy and verification of the results have been examined with known circumstances. The methodology is to be accurate and efficient so far the periodicity of the composite material rules. This micromechanics tool could make a powerful viable algorithm for determination of many linear as well as nonlinear properties in continuum mechanics material characterization and analysis.

A micromechanical characterization of angular bidirectional fibrous composites

A micromechanical numerical algorithm to efficiently determine the homogenized elastic properties of bidirectional fibrous composites is presented. A repeating unit cell (RUC) based on a pre-determined bidirectional fiber packing is assumed to represent the microstructure of the composite. For angular bidirectional fiber distribution, the symmetry lines define a parallelepiped unit cell, representing the periodic microstructure of an angular bidirectional fiber composite. The lines of symmetry extrude a volume to capture a three dimensional unit cell. Finite element analysis of this unit cell under six possible independent loading conditions is carried out to study and quantify the homogenized mechanical property of the cell. A volume averaging scheme is implemented to determine the average response as a function of loading in terms of stresses and strains. The individual elastic properties of the constituents’ materials, as well as, the composite can be assumed to be completely isotropic to completely anisotropic. The output of the analysis can determine this degree. The logic behind the selection of the unit cell and the implementation of the periodic boundary conditions as well as the constraints are presented. To verify this micromechanics algorithm, the results for four composites are presented. The results in this paper are mainly focused on the impact of the fiber cross angles on the stiffness properties of the composites chosen. The accuracy of the results from this micromechanics modeling procedure has been compared with the stiffness/compliance solutions from lamination theory. The methodology is to be accurate and efficient to the extent that periodicity of the composite material is maintained. In addition, the results will show the impact of fiber volume fraction on the material properties of the composite. This micromechanics tool could make a powerful viable algorithm for determination of many linear as well as nonlinear properties in continuum mechanics material characterization and analysis.

Fracture formation in vitrified thin films of cryoprotectants

As a part of an ongoing effort to study the continuum mechanics effects associated with cryopreservation, the current report focuses on fracture formation in vitrified thin films of cryoprotective agents. The current study combines experimental observations with continuum mechanics analysis. Experimental results have been developed using a new imaging device, termed a “cryomacroscope”, which has been recently presented by the current research team. A newly developed liquid nitrogen-based cooling stage is presented in this paper. The samples under investigation are 0.5 ml droplets of cryoprotective agents, having a characteristic diameter of 20 mm and a characteristic thickness of 1.5 mm. Tested samples included dimethyl sulfoxide (DMSO) in a concentration range from 6 to 8.4 M, and the cryoprotectant cocktails VS55 and DP6. Some samples contained small bovine muscle segments, having a characteristic dimension of 1 mm, in order to study stress concentration effects. Experimental results show that the onset of fracturing in vitrified films of cryoprotectants is very consistent, occurring over a small temperature range. Fracture pattern, however, was affected by the cooling rate. The presence of tissue segments did not affect the onset temperature of fracture, but affected the fracture pattern. The continuum mechanics analysis solidified the hypothesis that fracture is driven by thermal stress, not by temperature per se, and allowed fracture strain to be inferred from observed fracture temperature. In conjunction with the current report, additional photos of fracture formation in thin films are available at http://www.me.cmu.edu/faculty1/rabin/CryomacroscopyImages02.html.

A probabilistic model for the pearlite-induced cleavage of a plain carbon structural steel

The cleavage fracture of a carbon structural steel is shown to deviate from what is typical of a ferritic matrix. This occurs at temperatures ranging from −150 to 20 °C and affects the scatter of fracture toughness, and fractographic features. To explain the observed discrepancies a probabilistic model is developed by linking physical mechanisms of cleavage with continuum mechanics analysis applied to fracture. The model assumes that cleavage is nucleated and triggered in pearlite within the blunting zone of the crack tip by the mechanism of Miller and Smith. Once the model is calibrated for the steel, its predictions are shown to agree with the experimental results.

Computational design of carbon nanotube electromechanical pressure sensors

We investigate electronic transport properties of single-walled carbon nanotubes (SWNT's) under hydrostatic pressure, using first-principles quantum transport calculations aided by molecular-dynamics simulation and continuum mechanics analysis. We demonstrate a pressure-induced metal-to-semiconductor transition in armchair SWNT's, which provides a basis for designing nanoscale tunable pressure sensors.

Energy formulations of head cut dynamics

This study employs the principles of energy conservation to establish the framework for the development of the dynamical equations of head cut as a part of a continuum mechanical analysis of soil erosion induced by surface flow. The dynamics of head cut are controlled by several physically distinct processes, notable among which are surface seal formation, its failure and the redistribution of flow energy into kinetic and dissipation energies of water and soil. Thus, an erosive energy release rate function is introduced in the global energy equation, which is shown to depend on physical parameters governing the dynamics of the process region. The energy release rates are decomposed into line integrals representing motions associated with the translation, rotation, self-similar expansion and the distortion of the head cut cavity. From these considerations, approximate analytical expressions are derived which establish criteria for the initiation and the steady state head cut velocity. The results at this stage of development are preliminary and need testing and validation with data under controlled experimental conditions.

Measurement of apparent extensional viscosities of polyolefin melts from process contraction flows

The extensional characteristics of branched and linear polyolefin melts have been evaluated in slit die flow cells with abrupt contraction ratios of 4:1 and 15:1 on a single screw extruder. Apparent extensional viscosities of the melts in planar flows have been obtained by two routes, the first employing extensional strain rate data measured from particle velocimetry, the second using a continuum mechanics analysis based on the entry flow profile. The influence of flow geometry on apparent extensional viscosity of the polymer melts has been investigated. The measured in-process apparent extensional viscosities of the branched and linear polyolefin melts are found to be in good agreement, despite differences in the strain histories imposed by two contraction geometries (centre line extensional stress and corresponding average axial strain rates differ). Particle velocimetry was found to be better than the continuum mechanics approach in obtaining extensional strain rates due to a lower susceptibility to experimental errors. It appears that the in-process methods of assessing apparent extensional viscosity, with an abrupt 180° entry slit die, are geometry independent for the range of materials, strain and strain rates covered and provide a useful technique for ranking process-typical extensional behaviour of melts.

Statistical continuum mechanics analysis of an elastic two-isotropic-phase composite material

A statistical mechanics theory is formulated to capture the effect of microstructure distribution on the effective elastic moduli of a composite material. Two point probability functions are used as a major component of the statistical theory. The statistical correlation functions represent the morphology and the distribution (random, periodic,…) of phases. The theory can benefit from simple mathematical representation of distribution or the shape of the second phase (circular, elliptical,…). A two-point probability function is used to approximate the correlation functions for a general class of geometries with isotropic and random distributions. The simulations are also provided and compared to other (periodic) distributions. The results show that the theory is capable of capturing the microstructural featuring in addition to the statistical distributions.

Continuum mechanics characterization of plastic deformation-induced oxide film rupture

Abstract The film rupture behaviour of dynamically strained metastable Ti-15wt% Mo-3wt% Nb-3wt% Al in the solution-treated and aged (STA) (β + α) condition that is prone to coplanar slip was examined. Film rupture was detected by rapid data acquisition (10 000 Hz, 40 nA resolution) of repassivation current transients on fatigue precracked, circumferentially notched, and smooth tensile specimens. Finite element modelling of notch stress and strain fields was conducted to correlate the onset of film rupture with continuum mechanics analysis of notch stress and strain fields. Discrete film rupture repassivation transients were only observed in notched and smooth specimens when local notch stresses exceeded the uniaxial tensile yield strength of the STA alloy over a depth of about four grain diameters, and upon necking, respectively. Such extensive plastic deformation was a necessary but not sufficient criterion for observation of discrete current transients. Local plastic strain rates exceeding 1.4 × 10−5s−1...