A multiscale analysis of the mechanical behavior of bovine Haversian cortical bone is presented in the frame-work of linear elasticity. Cortical bone displays a complex microstructure that includes four phases: Haversian canals, osteons, cement lines, and interstitial bone. Based on close experimental observations, a Monte Carlo algorithm is implemented to build the natural bone composite microstructure. To represent the hierarchical nature of bone, the algorithm incorporates macroscopic morphological components, such as its porosity and osteonal volume fraction, as well as microscopic parameters, such as the characterized distributions of the osteons diameters. Bone local mechanical properties are measured by nanoindentation and microextensometry. The three-dimensional microstructures are discretized by a finite element method in order to evaluate the representative volume element of bovine cortical bone. The numerical model calculates the macroscopic bulk and material Young’s moduli and describes the local stress and strain. How geometrical or mechanical factors affect bone failure is investigated through a comparison of the macroscopic anisotropy and local strain to experimental data.

Presented are the experimental results of two light activated shape memory polymer (LASMP) formulations. The optical stimulus used to activate the materials is detailed including a mapping of the spatial optical intensity at the surface of the sample. From this, results of energy calculations are presented including the amount of energy available for transitioning from the glassy state to the rubbery state and from the rubbery state to the glassy state, highlighting one of the major advantages of LASMP as requiring less energy to transition than thermally activated shape memory polymers. The mechano-optical experimental setup and procedure is detailed and provides a consistent method for evaluating this relatively new class of shape memory polymer. A chemical kinetic model is used to predict both the theoretical glassy state modulus, as only the sample averaged modulus is experimentally attainable, as well as the through thickness distribution of Young’s modulus. The experimental and model results for these second generation LASMP formulations are then compared with earlier LASMP generations (detailed previously in Beblo and Mauck Weiland, 2009, “Light Activated Shape Memory Polymer Characterization,” ASME J. Appl. Mech., 76 , pp. 8) and typical thermally activated shape memory polymer.

A rigorous theoretical foundation for solving elastodynamic inverse problem of multilayered media under an impulse load is established in this paper. The inversion is built upon the forward dynamic analysis of multilayered elastic media using transfer matrix approach, with which displacement continuity is assumed at the interfaces of upper and lower adjacent layers. Formulations for inverse analysis are derived in both the time domain and the complex frequency domain. Least square estimates and nonlinear optimization algorithms are used to implement parameter identification. The proposed theory and formulae can be utilized to develop a computer software for nondestructive evaluation of laminated civil and aerospace structure (highway and airport pavements, bridge decks, soil foundations, aircraft wing, etc.), exploration and dynamic source detection and identification, and petroleum exploration in geophysics.

Chandraseker et al. (2009, “An Atomistic-Continuum Cosserat Rod Model of Carbon Nanotubes,” J. Mech. Phys. Solids, 57, pp. 932–958 ), in a 2009 JMPS paper, proposed an atomistic-continuum model, based on Cosserat rod theory, for deformation of a single-walled carbon nanotube (SWNT). This model allows extension and twist, as well as shear and bending (in two directions) of a SWNT. This present paper proposes a finite element method (FEM) implementation of the above mentioned Cosserat rod model for a SWNT, subjected, in general, to axial and transverse loads, as well as bending moments and torques. The resulting FEM implementation includes both geometric and material nonlinearities. Numerical results for several examples are presented in this paper. Finally, a recent experimental paper on SWNTs ( Xu, Y-.Q., et al., 2009, “Bending and Twisting of Suspended Single-Walled Carbon Nanotubes in Solution,” ASAP Nano Lett., 9, pp. 1609–1614 ) is revisited herein. It is pointed out in the present paper that Xu et al. attempted to determine the bending stiffness of a SWNT from an experiment in which the dominant mode of deformation is stretching, not bending. (Their model, Euler–Bernoulli beam bending, should perhaps have been extended to include stretching.) As a result, their measured deflection is nearly insensitive to the bending modulus.

The mechanical system considered is a bilayer cantilever plate. The substrate and the film are linear elastic. The film is subjected to isotropic uniform prestresses due for instance to volume variation associated with cooling, heating, or drying. This loading yields deflection of the plate. We recall Stoney’s analytical formula linking the total mechanical stresses to this deflection. We also derive a relationship between the prestresses and the deflection. We relax Stoney’s assumption of very thin films. The analytical formulas are derived by assuming that the stress and curvature states are uniform and biaxial. To quantify the validity of these assumptions, finite element calculations of the three-dimensional elasticity problem are performed for a wide range of plate geometries, Young’s and Poisson’s moduli. One purpose is to help any user of the formulas to estimate their accuracy. In particular, we show that for very thin films, both formulas written either on the total mechanical stresses or on the prestresses, are equivalent and accurate. The error associated with the misfit between our theorical study and numerical results are also presented. For thicker films, the observed deflection is satisfactorily reproduced by the expression involving the prestresses and not the total mechanical stresses.

The two small parameters that appear in the final equations developed in Part I ( Simmonds and Hosseinbor, 2010, “The Free and Forced Vibrations of a Closed Elastic Spherical Shell Fixed to an Equatorial Beam—Part I: The Governing Equations and Special Solutions,” ASME J. Appl. Mech., 77, p. 021017 ), namely, h / R , the ratio of the constant shell thickness to the radius of curvature of the shell’s reference surface and H / R , where H is the depth (or width) of the equatorial beam, are exploited using perturbation techniques (including the WKB method). The natural frequencies depend not only on these parameters, but also on the ratio of the mass densities of the shell and beam, the ratio of the Young’s moduli of the shell and beam, Poisson’s ratio, and the circumferential wave number m . Short tables for typical parameter values are given for those cases where the frequency equation is not explicit.

In the present work we propose a particle approach, which is designed to treat complex mechanics and dynamics of the open-draw sections that are still present in many of today’s paper machines. First, known steady-state continuous solutions are successfully reproduced. However, it is shown that since the boundary conditions depend on the solution itself, the solutions for web strain and web path in the open-draw section are generally time-dependent. With a certain set of system parameters, the nonsteady solutions are common. A temporal fluctuation of Young’s modulus, for example, destabilizes the system irreversibly, resulting in the continuous growth of web strain, i.e., break. Finally we exemplify with some strategic draw countermeasures how to prevent a dangerous evolution in the web strain.

Ceramic materials applied by air plasma spray are used as components of thermal barrier coatings. As it has been found that such coatings also dissipate significant amounts of energy during vibration, they can also contribute to reducing the amplitude of resonant vibrations. In order to select a coating material for this purpose, or to adjust application parameters for increased dissipation, it is important that the specific mechanism, by which such dissipation occurs, be known and understood. It has been suggested that the dissipative mechanism in air plasma sprayed coatings is friction, along interfaces arising from defects between and within the “splats” created during application. An analysis, similar to that for the dissipation in a lap joint, is developed for an idealized microstructure characteristic of such coatings. A measure of damping (loss modulus) is extracted, and the amplitude dependence is found to be similar to that observed with actual coating materials. A critical combination of parameters is identified, and variations within the microstructure are accounted for by representing values through a distribution. The effective or average value of the storage (Young’s) modulus is also developed, and expressed in terms of the parameters of the microstructure. The model appears to provide a satisfactory analytical representation of the damping and stiffness of these materials.

A new approach to measure the elastic modulus of nanowires is presented in this paper using a nanowire and a microcantilever beam composite system. The mechanical behavior of a nanowire-microcantilever beam structure under electrostatic actuation was studied using the finite element method, and a comparison of the resonance frequencies for a nanowire-microcantilever composite beam structure and a microcantilever beam only is presented. The test system can be optimized by introducing arrays of nanowires to increase the resonance frequency difference between the microcantilever beams and the nanowire array microbeam structures.

The Föppl–Hencky nonlinear membrane theory is employed to study the axisymmetric deformation of annular elastic membranes. The general solutions for displacements and stresses are established for arbitrary edge boundary conditions. New exact solution results are developed for central loading and edge forcing conditions. Both positive and negative radial stress solutions are found. Comparisons are made for special cases to previously known solutions with excellent agreement.

Since their development, shape memory polymers (SMPs) have been of increasing interest in active materials and structures design. In particular, there has been a growing interest in SMPs for use in adaptive structures because of their ability to switch between low and high stiffness moduli in a relatively short temperature range. However, because a thermal stimulus is inappropriate for many morphing applications, a new light activated shape memory polymer (LASMP) is under development. Among the challenges associated with the development of a new class of material is establishing viable characterization methods. For the case of LASMP both the sample response to light stimulus and the stimulus itself vary in both space and time. Typical laser light is both periodic and Gaussian in nature. Furthermore, LASMP response to the light stimulus is dependent on the intensity of the incident light and the time varying through the thickness penetration of the light as the transition progresses. Therefore both in-plane and through-thickness stimulation of the LASMP are nonuniform and time dependent. Thus, the development of a standardized method that accommodates spatial and temporal variations associated with mechanical property transition under a light stimulus is required. First generation thick film formulations are found to have a transition time on the order of 60 min. The characterization method proposed addresses optical stimulus irregularities. A chemical kinetic model is also presented capable of predicting the through-thickness evolution of Young’s modulus of the polymer. This work discusses in situ characterization strategies currently being implemented as well as the current and projected performance of LASMPs.

We postulate that an equivalent continuum structure (ECS) of a single-walled carbon nanotube (SWCNT) is a hollow cylinder with mean radius and length equal to that of the SWCNT, and find the thickness of the ECS so that its mechanical response in free vibrations is the same as that of the SWCNT. That is, for mechanical deformations, the ECS is energetically equivalent to the SWCNT. We use MM3 potential to study axial, torsional, radial breathing and bending vibrations of several traction free–traction free SWCNTs of different helicities and diameters and compare them with the corresponding vibrational modes and frequencies of traction free–traction free ECSs obtained by using the three-dimensional linear elasticity theory and the finite element analysis (3D-FEA). The consideration of free ends eliminates the effects of boundary conditions and avoids resolving equivalence between boundary conditions in the analyses of SWCNTs and their ECSs. It is found that the wall thickness of the ECS (and hence of a SWCNT) is ∼ 1 Å and Young’s modulus of the material of the ECS (and hence of the SWCNT) is ∼ 3.3 TPa . Both quantities are independent of the helicity and the diameter of the SWCNT. We also study radial breathing mode (RBM) vibrations with the molecular dynamics and the 3D-FEA simulations, and compare them with experimental findings. Accuracy in the assignment of spectral lines for RBMs in the Raman spectroscopy is discussed.

Strong single-wall carbon nanotubes (SWNTs) possess very high stiffness and strength. They have potential for use to tailor the material design to reach desired mechanical properties through SWNT nanocomposites. Layer-by-layer (LBL) assembly technique is an effective method to fabricate SWNT/polyelectrolyte nanocomposite films. To determine the relationship between the constituents of the SWNT/polymer nanocomposites made by LBL technique, a method has been developed to extend the recent work by Liu and Chen (Mech. Mater., 35, pp. 69–81, 2003 ) for the calculation of the effective Young’s modulus. The work by Liu and Chen on the mixture model is evaluated by finite element analysis of nanocomposites with SWNT volume fraction between 0% and 5%. An equivalent length coefficient is introduced and determined from finite element analysis. A formula is presented using this coefficient to determine the effective Young’s modulus. It is identified that the current work can be applied to SWNT loadings between 0% and 5%, while Liu and Chen’s approach is appropriate for relatively high SWNT volume fractions, close to 5%, but is not appropriate for relatively low SWNT volume fractions. The results obtained from this method are used to determine the effective Young’s modulus of SWNT/polyelectrolyte nanocomposite with 4.7% SWNT loading. The material properties are characterized using both nanoindentation and tensile tests. Nanoindentation results indicate that both the in-plane relaxation modulus and the through-thickness relaxation modulus of SWNT nanocomposites are very close to each other, despite the orientation preference of the SWNTs in the nanocomposites. The steady state in-plane Young’s relaxation modulus compares well with the tensile modulus, and measurement results are compared with Young’s modulus determined from the method presented.

Inaccuracies in the modeling assumptions about the distributional characteristics of the monitored signatures have been shown to cause frequent false positives in vehicle monitoring systems for high-risk aerospace applications. To enable the development of robust fault detection methods, this work explores the deterministic as well as variational characteristics of failure signatures. Specifically, we explore the combined impact of crack damage and manufacturing variation on the vibrational characteristics of beams. The transverse vibration and associated eigenfrequencies of the beams are considered. Two different approaches are used to model beam vibrations with and without crack damage. The first approach uses a finite difference approach to enable the inclusion of both cracks and manufacturing variation. The crack model used with both approaches is based on a localized decrease in the Young’s modulus. The second approach uses Myklestad’s method to evaluate the effects of cracks and manufacturing variation. Using both beam models, Monte Carlo simulations are used to explore the impacts of manufacturing variation on damaged and undamaged beams. Derivations are presented for both models. Conclusions are presented on the choice of modeling techniques to define crack damage, and its impact on the monitored signal, followed by conclusions about the distributional characteristics of the monitored signatures when exposed to random manufacturing variations.

We present a numerical simulation of heat treatment of cast metallic alloys by the finite element method, to predict strains and stresses produced during the said process. From a computational point of view, this problem involves a coupled thermal-metallurgical-mechanical analysis modeled as a non-stationary and non-linear process. The calculation of metallurgical properties is coupled directly with thermal analysis. Material properties, which are dependent on temperature and microstructural composition, are rewritten for the purpose of the analysis as functions of temperature and time. Results of thermo-metallurgical analysis are taken as data for the subsequent mechanical analysis. The simulation was successful and proved the causes of failure during heat treatment of a centrifugally cast three-layered Hi-Chrome work roll.

The design of reliable micro electro-mechanical systems (MEMS) requires understanding of material properties of devices, especially for free-standing thin structures such as membranes, bridges, and cantilevers. The desired characterization system for obtaining mechanical properties of active materials often requires load control. However, there is no such device among the currently available tools for mechanical characterization of thin films. In this paper, a new technique, which is load-controlled and especially suitable for testing highly fragile free-standing structures, is presented. The instrument developed for this purpose has the capability of measuring both the static and dynamic mechanical response and can be used for electro∕magneto∕thermo mechanical characterization of actuators or active materials. The capabilities of the technique are demonstrated by studying the behavior of 75 nm thick amorphous silicon nitride ( Si 3 N 4 ) membranes. Loading up to very large deflections shows excellent repeatability and complete elastic behavior without significant cracking or mechanical damage. These results indicate the stability of the developed instrument and its ability to avoid local or temporal stress concentration during the entire experimental process. Finite element simulations are used to extract the material properties such as Young’s modulus and residual stress of the membranes. These values for Si 3 N 4 are in close agreement with values obtained using a different technique, as well as those found in the literature. Potential applications of this technique in studying functional thin film materials, such as shape memory alloys, are also discussed.

This paper deals with the derivation of exact solutions for the static analysis of functionally graded (FG) plates integrated with a layer of piezoelectric fiber reinforced composite (PFRC) material. The layer of the PFRC material acts as the distributed actuator of the FG plates. The Young’s modulus of the FG plate is assumed to vary exponentially along the thickness of the plate while the Poisson’s ratio is assumed to be constant over the domain of the plate. The numerical values of the exact solutions are presented for both thick and thin smart FG plates and indicate that the activated PFRC layer potentially counteracts the deformations of the FG plates due to mechanical load. The through-thickness behavior of the plates revealed that the coupling of bending and extension takes place in the FG plates even if the PFRC layer is not subjected to the applied voltage. The solutions also revealed that the activated PFRC layer is more effective in controlling the deformations of the FG plates when the layer is attached to the surface of the FG plate with minimum stiffness than when it is attached to the surface of the same with maximum stiffness. The solutions of this benchmark problem may be useful for verifying the other approximate and numerical models of the smart functionally graded plates for which exact solutions cannot be derived.

The virtual internal bond (VIB) method was developed for the numerical simulation of fracture processes. In contrast to the traditional approach of fracture mechanics where stress analysis is separated from a description of the actual process of material failure, the VIB method naturally allows for crack nucleation, branching, kinking, and arrest. The idea of the method is to use atomic-like bond potentials in combination with the Cauchy-Born rule for establishing continuum constitutive equations which allow for the material separation–strain localization. While the conventional VIB formulation stimulated successful computational studies with applications to structural and biological materials, it suffers from the following theoretical inconsistency. When the constitutive relations of the VIB model are linearized for an isotropic homogeneous material, the Poisson ratio is found equal to 1 ∕ 4 so that there is only one independent elastic constant—Young’s modulus. Such restriction is not suitable for many materials. In this paper, we propose a modified VIB (MVIB) formulation, which allows for two independent linear elastic constants. It is also argued that the discrepancy of the conventional formulation is a result of using only two-body interaction potentials in the microstructural setting of the VIB method. When many-body interactions in “bond bending” are accounted for, as in the MVIB approach, the resulting formulation becomes consistent with the classical theory of isotropic linear elasticity.

This paper presents the development of a theoretical damage mechanics model applicable to random short glass fiber reinforced composites. This model is based on a macroscopic approach using internal variables together with a thermodynamic potential expressed in the stress space. Induced anisotropic damage, nonsymmetric tensile/compressive behavior (unilateral effect) and residual effects (permanent strain) are taken into account. The anisotropic damage is represented with second-order tensorial internal variables D . The unilateral effect due to microcrack closure in compression is introduced by generalizing the hypothesis of the complementary elastic energy equivalence. In the case of the permanent strain, a new term related to frozen energy, which is a function of the damage variable, the stress tensor, and some materials constants to be identified, is added to the basic thermodynamic potential. Using laboratory test results, parameter identification has been performed to illustrate the applicability of the proposed model.

A new boundary element method (BEM) is developed for three-dimensional analysis of fiber-reinforced composites based on a rigid-inclusion model. Elasticity equations are solved in an elastic domain containing inclusions which can be assumed much stiffer than the host elastic medium. Therefore the inclusions can be treated as rigid ones with only six rigid-body displacements. It is shown that the boundary integral equation (BIE) in this case can be simplified and only the integral with the weakly-singular displacement kernel is present. The BEM accelerated with the fast multipole method is used to solve the established BIE. The developed BEM code is validated with the analytical solution for a rigid sphere in an infinite elastic domain and excellent agreement is achieved. Numerical examples of fiber-reinforced composites, with the number of fibers considered reaching above 5800 and total degrees of freedom above 10 millions, are solved successfully by the developed BEM. Effective Young’s moduli of fiber-reinforced composites are evaluated for uniformly and “randomly” distributed fibers with two different aspect ratios and volume fractions. The developed fast multipole BEM is demonstrated to be very promising for large-scale analysis of fiber-reinforced composites, when the fibers can be assumed rigid relative to the matrix materials.