Mechanical boundary conditions

Maximum strength sets the limit of a material's intrinsic resistance to permanent deformation. Its significance, however, lies not in the highest strength value that a solid can possibly achieve, but rather in how this quantity is degraded, from which one could decipher the underlying mechanisms of yielding in a real material. A wide range of maximum strength values have been measured experimentally for metallic glasses. However, the true maximum strength remains unknown to date. Here, using finite deformation theory, we give the first theoretical estimate of the ultimate strength of metallic glasses. Our theoretical results, along with those from experiment and simulation, lead us to several mechanisms of degradation of the theoretical strength that are closely connected to correlated atomic motion with varying characteristic length in real metallic glasses.

Basic Science Symposium III: Animal Models for Orthopaedic Matthew J. Allen, Anthony Simon Turner, Koichi Sairyo and Lisa Ferrara http://ijssurgery.com/content/2/4/195 https://doi.org/10.1016/SASJ-2008-Symposium4 doi: 2008, 2 (4) 195-200 Int J Spine Surg This information is current as of August 4, 2019. Email Alerts http://ijssurgery.com/alerts Receive free email-alerts when new articles cite this article. Sign up at:

The degenerative disc disease is among the promoters of low back pain, being normally associated with sciatica and disc herniation. Several experimental works have studied the intervertebral disc and proven that it presents poroelastic, osmotic, viscoelastic and anisotropic characteristics. However, the information about the mechanical loading on the IVD and its relation with the degenerative disc disease remains unclear. This work aimed to provide new insights about the mechanical properties of the intervertebral disc, as well as to contribute for selection and characterization of a new implant,

This study deals with the vibration and stability analysis of double-graphene nanoribbonsystem (DGNRS) based on different nonlocal elasticity theories such as Eringen's nonlocal, strain gradient, and modified couple stress withinthe framework of Rayleigh beam theory. In this system, two graphene nanoribbons (GNRs) are bonded by Pasternak medium which characterized by Winkler modulus and shear modulus. An analytical approach is utilized to determine the frequency and critical buckling load of the coupled system. The three vibrational states including out-of-phase vibration, in-phase vibration and one GNR being stationary are discussed. A detailed parametric study is conducted to elucidate the influences of the small scale coefficients, stiffness of the internal elastic medium, mode number and axial load on the vibration of the DGNRS. The results reveal that the dimensionless frequency and critical buckling load obtained by the strain gradient theory is higher than the Eringen&#39...

Samir Y Marzouk Comparative Biomechanical Analysis of Lumbar Disc Arthroplasty using Finite Element Modeling Lumbar total disc replacement (LTDR) is a surgical procedure for the treatment of degenerative disc disease (DDD) and lumbar spinal distortion to preserve range of motion (ROM). The SB Charité™ is the first device for LTDR but it produces more complications and long-term issues, causing a shortage of SB Charité™ disc. Currently, the evolution of lumbar disc arthroplasty based on some criteria like prosthetics structure, biomechanical model, tissue engineering and biomaterials approach. The optimal biomechanical model is based on kinematic and kinetic parameters together to ensure a long-term implantation with a lower rate of damage from disc implant in the spinal column. The finite element method (FEE) of human lumbar spinal is advanced to support biomechanical modeling techniques which are related to biomaterials guideline for choosing better material for implantation. Therefore, this paper presented a 3D biomechanical FEM model of L1 to L3 lumbar spines by different types of discs and materials. We applied a compressive force, and compressive force plus extension moment to this model to calculate Tresca stress of annulus fibers, strain and von Mises stress on the vertebral endplate at each intervertebral level under COMSOL Multiphysics® software.

Spinal manipulative therapy (SMT) creates health benefits for some while for others, no benefit or even adverse events. Understanding these differential responses is important to optimize patient care and safety. Toward this, characterizing how loads created by SMT relate to those created by typical motions is fundamental. Using robotic testing, it is now possible to make these comparisons to determine if SMT generates unique loading scenarios. In 12 porcine cadavers, SMT and passive motions were applied to the L3/L4 segment and the resulting kinematics tracked. The L3/L4 segment was removed, mounted in a parallel robot and kinematics of SMT and passive movements replayed robotically. The resulting forces experienced by L3/L4 were collected. Overall, SMT created both significantly greater and smaller loads compared to passive motions, with SMT generating greater anterioposterior peak force (the direction of force application) compared to all passive motions. In some comparisons, SMT...

Background: High primary stability is the fundamental prerequisite for safe osseointegration of cementless intervertebral disc prosthesis. The aim of our study was to determine the primary stability of intervertebral disc prosthesis with two different anchoring concepts – keel and spike anchoring. Methods: 10 human cadaveric lumbar spine specimens with an ActivL intervertebral disc prosthesis (5 x keel anchoring, 5 x spike anchoring) were tested on a spine simulator. Under axial load, moments of flexion, extension, left and right bending and axial rotation were applied on the lumbar spine specimens through a defined three-dimensional movement program as per ISO 2631 and ISO/CD 18192-1.3 standards. Micro-motion of the implant was measured in every axis for both anchor types and compared using statistical test for significance after calculating 95% confidence intervals. Results: In the transverse axis, the keel anchoring concept showed lower mean values of micro-motion , which was sta...

and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

The choice of boundary conditions used in multiscale analysis of heterogeneous materials affects the numerical results, including the macroscopic constitutive response, the type and extent of damage taking place at the microscale and the required size of the Representative Volume Element (RVE). We compare the performance of periodic boundary conditions and minimal kinematic boundary conditions applied to the unit cell of a particulate composite material, both in the absence and presence of damage at the particle–matrix interfaces. In particular, we investigate the response of the RVE under inherently non-periodic loading conditions, and the ability of both boundary conditions to capture localization events that are not aligned with the RVE boundaries. We observe that, although there are some variations in the evolution of the microscale damage between the two methods, there is no significant difference in homogenized responses even when localization is not aligned with the cell boun...

Background Mechanically replacing one or more pain generating articulations in the functional spinal unit (FSU) may be a motion preservation alternative to arthrodesis at the affected level. Baseline biomechanical data elucidating the quantity and quality of motion in such arthroplasty constructs is non-existent. Purpose The purpose of the study was to quantify the motion-preserving effect of a posterior total disc replacement (PDR) combined with a unilateral facet replacement (FR) system at a single lumbar level (L4-L5). We hypothesized that reinforcement of the FSU with unilateral FR to replace the resected, native facet joint following PDR implantation would restore quality and quantity of motion and additionally not change biomechanics at the adjacent levels. Study Design In-vitro study using human cadaveric lumbar spines. Methods Six (n=6) cadaveric lumbar spines (L1-S1) were evaluated using a pure-moment stability testing protocol (±7.5 Nm) in flexion-extension (F/E), lateral bending (LB) and axial rotation (AR). Each specimen was tested in: (1) intact; (2) unilateral FR; and (3) unilateral FR + PDR conditions. Index and adjacent level ROM (using hybrid protocol) were determined opto-electronically. Interpedicular travel (IPT) and instantaneous center of rotation (ICR) at the index level were radiographically determined for each condition. ROM, ICR, and IPT measurements were compared (repeated measures ANOVA) between the three conditions. Results Compared to the intact spine, no significant changes in F/E, LB or AR ROM were identified as a result of unilateral FR or unilateral FR + PDR. No significant changes in adjacent L3-L4 or L5-S1 ROM were identified in any loading mode. No significant differences in IPT were identified between the three test conditions in F/E, LB or AR at the L4-L5 level. The ICRs qualitatively were similar for the intact and unilateral FR conditions and appeared to follow placement (along the anterior-posterior (AP) direction) of the PDR in the disc space Conclusion Biomechanically, quantity and quality of motion are maintained with combined unilateral FR + PDR at a single lumbar spinal level.

Object The center (axis) of rotation (COR) in the lumbar spine has been studied well. However, there is limited information on the kinetic and kinematic consequences of imposed shift in the location of the COR, although this type of shift can be seen after surgeries using motion preservation or dynamic stabilization devices. The objective of this study was to assess the kinetic and kinematic changes in the lumbar spinal segment due to various imposed CORs. Methods A 3D finite element model of the L4–5 segment was constructed and validated. The segment was loaded under a 7.5-Nm bending moment while constrained to rotate about various imposed CORs in the sagittal and axial motion planes. Range of motion, ligament forces, facet loads, and disc stresses were measured. Results The present model showed an agreement with previous in vitro and finite element studies under the same load and boundary conditions. Range of motion, facet forces, disc stresses, and ligament loads showed a strong ...

Extremely few in-vitro biomechanical studies have incorporated shear loads leaving a gap for investigation, especially when applied in combination with compression and bending under dynamic conditions. The objective of this study was to biomechanically compare sagittal plane application of two standard protocols, pure moment (PM) and follower load (FL), with a novel trunk weight (TW) loading protocol designed to induce shear in combination with compression and dynamic bending in a neutrally potted human cadaveric L4-L5 motion segment unit (MSU) model. A secondary objective and novelty of the current study was the application of all three protocols within the same testing system serving to reduce artifacts due to testing system variability. Six L4-L5 segments were tested in a Cartesian load controlled system in flexion-extension to 8Nm under PM, simulated ideal 400N FL, and vertically oriented 400N TW loading protocols. Comparison metrics used were rotational range of motion (RROM), ...

and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

The role of grain size on the overall behaviour of polycrystals is investigated by using a strain gradient constitutive law for each slip system for a reference single crystal. Variational principles of Hashin-Shtrikman type are formulated for the case where the strain energy density is a convex function of both strain and strain gradient. The variational principles are specialized to polycrystals with a general multislip strain gradient constitutive law. An extension of the Hashin-Shtrikman bounding methodology to general strain gradient composites is discussed in detail and then applied to derive bounds for arbitrary linear strain gradient composites or polycrystals. This is achieved by an extensive study of kernel operators related to the Green's function for a general "strain-gradient" linear isotropic incompressible comparison medium. As a simple illustrative example, upper and lower bounds are computed for linear face-centred cubic polycrystals: a size effect is noted whereby smaller grains are stiffer than large grains. The relation between the assumed form of the constitutive law for each slip system and the overall response is explored.

We present a micro-macro method for the simulation of large elastic deformations of plant tissue. At the microscopic level we use a discrete element model to describe the geometrical structure and basic properties of individual plant cells. The macroscopic domain is ...

In this study, static resonance that occurs in rotating nanobars is addressed. The analysis is based on Eringen's nonlocal elasticity theory and is performed in Lagrangian coordinates. Explicit solutions are given for both clamped-free and clamped-clamped boundary conditions. The present study shows that the static resonance phenomenon is largely a critical case requiring attention for rotating nanobars with small lengths.

Although both computational and analytical homogenization are well-established today, a thorough and systematic study to compare them is missing in the literature. This manuscript aims to provide an exhaustive comparison of numerical computations and analytical estimates, such as Voigt, Reuss, Hashin–Shtrikman, and composite cylinder assemblage. The numerical computations are associated with canonical boundary conditions imposed on either tetragonal, hexagonal, or circular representative volume elements using the finite-element method. The circular representative volume element is employed to capture an effective isotropic material response suitable for comparison with associated analytical estimates. The analytical results from composite cylinder assemblage are in excellent agreement with the numerical results obtained from a circular representative volume element. We observe that the circular representative volume element renders identical responses for both linear displacement an...

Finite element (FE) models driven by medical image data can be used to estimate subject-specific spinal biomechanics. This study aimed to combine magnetic resonance (MR) imaging and quantitative fluoroscopy (QF) in subject-specific FE models of upright standing, flexion and extension. Supine MR images of the lumbar spine were acquired from healthy participants using a 0.5 T MR scanner. Nine 3D quasi-static linear FE models of L3 to L5 were created with an elastic nucleus and orthotropic annulus. QF data was acquired from the same participants who performed trunk flexion to 60° and trunk extension to 20°. The displacements and rotations of the vertebrae were calculated and applied to the FE model. Stresses were averaged across the nucleus region and transformed to the disc co-ordinate system (S1 = mediolateral, S2 = anteroposterior, S3 = axial). In upright standing S3 was predicted to be -0.7 ± 0.6 MPa (L3L4) and -0.6 ± 0.5 MPa (L4L5). S3 increased to -2.0 ± 1.3 MPa (L3L4) and -1.2 ±...

Finite element (FE) models driven by medical image data can be used to estimate subject-specific spinal biomechanics. This study aimed to combine magnetic resonance (MR) imaging and quantitative fluoroscopy (QF) in subject-specific FE models of upright standing, flexion and extension. Supine MR images of the lumbar spine were acquired from healthy participants using a 0.5 T MR scanner. Nine 3D quasi-static linear FE models of L3 to L5 were created with an elastic nucleus and orthotropic annulus. QF data was acquired from the same participants who performed trunk flexion to 60° and trunk extension to 20°. The displacements and rotations of the vertebrae were calculated and applied to the FE model. Stresses were averaged across the nucleus region and transformed to the disc co-ordinate system (S1 = mediolateral, S2 = anteroposterior, S3 = axial). In upright standing S3 was predicted to be -0.7 ± 0.6 MPa (L3L4) and -0.6 ± 0.5 MPa (L4L5). S3 increased to -2.0 ± 1.3 MPa (L3L4) and -1.2 ±...

An insightful mechanics-based bottom-up framework is developed for probing the frequency-dependence of lattice material microstructures. Under a vibrating condition, effective elastic moduli of such microstructured materials can become negative for certain frequency values, leading to an unusual mechanical behaviour with a multitude of potential applications. We have derived the fundamental theoretical limits for the minimum frequency, beyond which the negative effective moduli of the materials could be obtained. An efficient dynamic stiffness matrix based approach is developed to obtain the closed-form limits, which can exactly capture the sub-wavelength scale dynamics. The limits turn out to be a fundamental property of the lattice materials and depend on certain material and geometric parameters of the lattice in a unique manner. An explicit characterization of the theoretical limits of negative elastic moduli along with adequate physical insights would accelerate the process of its potential exploitation in various engineered materials and structural systems under dynamic regime across the length-scales. Introduction.-The global mechanical properties can be engineered in lattice materials by intelligently identifying the material microstructures as the properties in these materials are often defined by their structural configuration along with the intrinsic material properties of the constituent members. This novel class of materials with tailorable application-specific mechanical properties (like equivalent elastic moduli, buckling, vibration and wave propagation characteristics with modulation features) have tremendous potential applications for future aerospace, civil, mechanical, electronics and medical applications across the length-scales. Naturally occurring materials cannot exhibit unprecedented and fascinating properties such as extremely lightweight, negative elastic moduli, negative mass density, pentamode material characteristics (meta-fluid), which can be achieved by an intelligent microstructural design [1, 2]. For example, the conventional positive value of Poisson's ratio in a hexagonal lattice metamaterial can be converted to a negative value [3] by making the cell angle θ in figure 1(b) negative. Other unusual and exciting properties can be realized in metamaterials under dynamic condition, such as negative bulk modulus induced by monopolar resonance [4], negative mass density induced by dipolar resonance [5], and negative shear modulus induced by quadrupolar resonance [6]. Elastic cloaks [7] and various other unprecedented dynamic behaviour of such materials have been widely reported in literature [8-14].

In the present study, longitudinal wave propagation in nanorods is studied using nonlocal elasticity theory. The nonlocal constitutive equations of Eringen are used in the formulations. A unified rod theory including lateral inertia, shear and surface stress effects which gives the previous theories as a special case is adopted in the formulation of the displacement field. A modification is proposed to Eringen's nonlocal parameter e 0 by obtaining an explicit relation for it. The nonlocal parameter is calibrated using lattice dynamics. It is obtained that the nonlocal parameter is material and geometry dependent. Considering lateral inertia and surface effects improves longitudinal wave characteristics of nanorods.

The longitudinal wave propagation in multiwalled carbon nanotubes is investigated using the nonlocal elasticity theory. A multiwalled rod model is proposed in the formulation. The van der Waals force is considered in the axial direction. The effect of various parameters like the radius of nanotubes, van der Waals forces and nonlocal parameters on the longitudinal wave propagation in multiwalled carbon nanotubes is discussed. It is obtained that different axial relative motion may exist in doublewalled carbon nanotubes. The present results can be useful in the design of nanoscale linear motors, oscillators and similar nanoscale electromechanical systems.

Purpose Pedicle-screw-based dynamic implants are intended to preserve intervertebral mobility while releasing certain spinal structures. The aim of the study was to determine the as yet unknown optimal stiffness value of the longitudinal rods that fulfils best these opposing tasks.

In this paper, the effect of uniaxial strain on the electronic properties of bilayer armchair graphene nanoribbons (BLAGNRs) is theoretically investigated for the first time. Our calculations based on density functional theory (DFT) reveal the tunable nature of the electronic properties of BLAGNRs with the application of uniaxial strain. We further explore the simultaneous effect of perpendicular electric field and uniaxial strain on the electronic bandgap. The results show that as long as the strain induced bandgap is smaller than a critical value of 0.2 eV, the electric field can significantly modulate the bandgap. In addition, we modified nearest neighbor tight-binding (TB) parameters to include the effect of the hydrogen passivation, which results in an excellent agreement between the electronic bandstructures obtained from DFT and TB calculations. Finally, by employing the nonequilibrium Green's function formalism, an on-off conductance ratio as high as 10 5 is predicted for strained BLAGNRs.

Using atomistic simulations we investigate the thermodynamical properties of a single atomic layer of hexagonal boron nitride (h-BN). The thermal induced ripples, heat capacity, and thermal lattice expansion of large scale h-BN sheets are determined and compared to those found for graphene (GE) for temperatures up to 1000 K. By analyzing the mean square height fluctuations h 2 and the height-height correlation function H(q) we found that the h-BN sheet is a less stiff material as compared to graphene. The bending rigidity of h-BN: i) is about 16% smaller than the one of GE at room temperature (300 K), and ii) increases with temperature as in GE. The difference in stiffness between h-BN and GE results in unequal responses to external uniaxial and shear stress and different buckling transitions. In contrast to a GE sheet, the buckling transition of a h-BN sheet depends strongly on the direction of the applied compression. The molar heat capacity, thermal expansion coefficient and the Gruneisen parameter are estimated to be 25.2 J mol −1 K −1 , 7.2×10 −6 K −1 and 0.89, respectively.

p(HEMA) -poly(hydroxyethyl methacrylate) -is a biocompatible material which in water forms a hydrogel and have multiple biomedical applications. The objective of this paper was to propose a biomaterial based on p(HEMA) for its use as damping element within disc prosthesis on lumbar spine and to analyse its mechanical behaviour. Intervertebral discs from healthy lumbar spine are mainly subjected to compressive stress and they have the capacity to ensure an adequate absorption of mechanical vibrations. In this study the mechanical behaviour of p(HEMA) has been evaluated by compressiondecompression experimental tests on dry and wet biomaterial. The compression-decompression tests were performed with four different speeds: v1 = 0.05 mm/s, v2 = 0.1 mm/s, v3 = 0.15 mm/s and v4 = 0.2 mm/s. The results of this study highlighted the viscoelastic behaviour and damping capacity of swollen p(HEMA) hydrogel.

p(HEMA) -poly(hydroxyethyl methacrylate) -is a biocompatible material which in water forms a hydrogel and have multiple biomedical applications. The objective of this paper was to propose a biomaterial based on p(HEMA) for its use as damping element within disc prosthesis on lumbar spine and to analyse its mechanical behaviour. Intervertebral discs from healthy lumbar spine are mainly subjected to compressive stress and they have the capacity to ensure an adequate absorption of mechanical vibrations. In this study the mechanical behaviour of p(HEMA) has been evaluated by compressiondecompression experimental tests on dry and wet biomaterial. The compression-decompression tests were performed with four different speeds: v1 = 0.05 mm/s, v2 = 0.1 mm/s, v3 = 0.15 mm/s and v4 = 0.2 mm/s. The results of this study highlighted the viscoelastic behaviour and damping capacity of swollen p(HEMA) hydrogel.

Background: Total disc replacement (TDR) and total facet replacement (TFR) have been the focus of recent kinematics evaluations. Yet their concurrent function as a total joint replacement of the lumbar spine's 3-joint complex has not been comprehensively reported. This study evaluated the effect of a TFR specifically designed to replace the natural facets and supplement the function with the natural disc and with TDR. The ability to replace degenerated facets to complement a pre-existing or simultaneously implanted TDR may allow surgeons to completely address degenerative pathologies of the 3-joint complex of the lumbar spine. We hypothesized that TFR would reproduce the biomechanical function of the natural facets when implanted in conjunction with TDR. Methods: Lumbar spines (L1-5, 51.3 Ϯ 14.2 years, N ϭ 6) were tested sequentially as follows: (1) intact, (2) after TDR implantation, and (3) after TFR implantation in conjunction with TDR, all at L3-4. Specimens were tested in flexion-extension (ϩ 8 Nm to Ϫ 6 Nm), lateral bending (Ϯ 6 Nm), and axial rotation (Ϯ 5 Nm). A 400 N compressive follower preload was applied during flexion-extension tests. Three-dimensional segmental motion was recorded and analyzed using analysis of variance in Systat (Systat Software Inc., Chicago, Illinois) and multiple comparisons with Bonferroni correction. Results: The TDR implantation (TDR ϩ natural facets) allowed similar lateral bending (P ϭ .66), but it generally increased flexionextension (P ϭ .06) and axial rotation (P Ͻ .05) range of motion (ROM) at the implanted level compared to intact. The TFR ϩ TDR (following replacement of the natural facets with TFR) decreased ROM to levels similar to intact in lateral bending (P ϭ .70) and axial rotation (P ϭ .23). The TFR ϩ TDR flexion-extension ROM was reduced in comparison to intact and TDR ϩ natural facets (P Ͻ .05). Conclusions: The TFR with TDR was able to restore stability to the lumbar segment after bilateral facetectomy, while allowing near-normal motions in all planes.

We introduce an interesting strategy to develop thermoset composite hydrogels (TCH) integrating calcium deficient hydroxyapatite (CDHA) into poly(2-hydroxyethyl methacrylate) (pHEMA) hydrogels. The process consists in two feasible steps: (1) the temperature driven polymerization of hydroxyethylmetacrilate (HEMa) in water or glycerol solution and, (2) the hardening reaction of CDHA triggered by hydrolysis of α-tricalcium phosphates (α-TCP) in NaHPO 4 water solution at body temperature. SEM investigation show that final morphology of composite is significantly affected by monomer concentration and used solvents (i.e, water or Glycerol). These results are also in agreement with the characterization of mechanical response under compression performed of different TCH typologies. All the reported results confirm that TCH obtained by thermal curing and hardening reaction may represent a promising bone-like material with interesting properties to mimic the native vertebrae/annulus interface for a non-invasive IVD repair strategies.

Mechanically replacing one or more pain generating articulations in the functional spinal unit (FSU) may be a motion preservation alternative to arthrodesis at the affected level. Baseline biomechanical data elucidating the quantity and quality of motion in such arthroplasty constructs is non-existent.

We develop an analytical formulation describing propagating flexural waves in periodically simplysupported nanoribbons by means of Eringen's nonlocal elasticity. The nonlocal length scale is identified via atomistic finite element (FE) models of graphene nanoribbons with Floquet's boundary conditions. The analytical model is calibrated through the atomistic finite element approach. This is done by matching the nondimensional frequencies predicted by the analytical nonlocal model and those obtained by the atomistic FE simulations. We show that a nanoribbon with periodically supported boundary conditions does exhibit artificial pass-stop band characteristics. Moreover, the nonlocal elasticity solution proposed in this paper captures the dispersive behaviour of nanoribbons when an increasing number of flexural modes are considered. *

We develop an analytical formulation describing propagating flexural waves in periodically simplysupported nanoribbons by means of Eringen's nonlocal elasticity. The nonlocal length scale is identified via atomistic finite element (FE) models of graphene nanoribbons with Floquet's boundary conditions. The analytical model is calibrated through the atomistic finite element approach. This is done by matching the nondimensional frequencies predicted by the analytical nonlocal model and those obtained by the atomistic FE simulations. We show that a nanoribbon with periodically supported boundary conditions does exhibit artificial pass-stop band characteristics. Moreover, the nonlocal elasticity solution proposed in this paper captures the dispersive behaviour of nanoribbons when an increasing number of flexural modes are considered. *

of the translational and rotational stiffnesses of a L4-L5 functional spinal unit using a specimen-specific finite element model, Journal of the Mechanical Behavior of Biomedical Materials, http://dx.doi.org/10.1016/ j.jmbbm.2012.04.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

of background data The sagittal profile of lumbar endplates is discrepant from current simplified disc replacement and fusion device design. Endplate concavity is symmetrical in the coronal plane but shows considerable variability in the sagittal plane, which may lead to implantendplate mismatch.

The technical difficulties associated with the development of an intervertebral disc prosthesis include endurance demands on the device, lack of consensus concerning the biomechanical principles governing the articulation of the spinal joint and the performance of materials available for implantation. Although biologically based disc prostheses and augmentations may be the endpoint of spinal disc replacements, these devices and associated technologies will still require decades of work in order to achieve fruition. The more immediate solution will require a durable, biocompatible device capable of restoring range of motion. The evaluation of such a device must include failure testing of critical components as well as a series of fatigue experiments under overloaded conditions. Recent literature citing adjacent level degeneration associated with segmental mobilization and a lack of correlation between successful fusion and clinical success has prompted the need for a dynamic intervertebral disc prosthesis. Combined with a better understanding of the biomechanics and the prospect of an increasing percentage of more elderly patients, the future of spinal fusion for pain and instability may need to be reexamined. The authors propose a novel metal-on-metal design for an intervertebral device that features a fixed center of rotation, a mechanical torsional limit, a unique feature to allow for the location of the device in a patient-specific manner, and means by which the device may be implanted directly anterior or anterolaterally. Physiological ranges of motion are retained by the prosthesis. In addition, initial and long-term fixations are achieved through spines and bone ingrowth coating. The device comprises a retained ball and socket positioned between two baseplates. The ball and socket joint permits articulation through the appropriate physiological range of motion and center of rotation as the baseplates provide a stable platform for implantation. An intervertebral disc prosthesis has been designed and has demonstrated mechanical performance beyond what is required physiologically under preliminary testing.

Background: Lumbar facet joints have been cited as a possible origin of low-back pain. A relationship between disc height decrease and facet joint degeneration has been reported. Facet joint degeneration may also be triggered by nucleotomy, performed on prolapsed discs, which might change the natural load sharing between the anterior and posterior structures of the spine. In this study load bearing of the facet joints was compared between natural and nucleotomised spinal segments. Methods: Nine porcine lumbar motion segments were tested quasi-statically in ±1.5°extension-flexion under 700 N constant compression loading. The kinematics of the spinal segments were recorded as a response to the applied load. These kinematics were subsequently applied to the segments with the ligaments and disc sequentially removed and the reaction forces measured. This was performed in samples with and without nucleotomy. Comparison of the reaction forces allowed a direct comparison between healthy and pathological force transmission over the facet joints. Load sharing was related to the proportion of removed nucleus. Findings: The proportion of applied compression force supported by the facets increased from a mean of 40.7% (standard deviation, SD 10.0%) to 82.0% (SD 7.2%) after nucleotomy averaged over the entire extension-flexion regime. No correlation was observed between facet loading and the proportion of the nucleus removed. Interpretation: Increased facet loading after nucleotomy might cause greater cartilage wear, which may be related to facet joint degeneration. The independence of facet loading on the proportion of nucleus removed might be due to a complete pressure loss once the annulus is incised.

In this contribution the properties and application of the multiscale finite element program MSFEAP are presented. This code is developed on basis of coupling the homogenization theory with the finite element method. According to this concept, the investigation of an appropriately chosen representative volume element yields the material parameters needed for the simulation of a macroscopic body. The connection of scales is based on the principle of volume averaging and the Hill-Mandel macrohomogeneity condition. The latter leads to the determination of different types of boundary conditions for the representative volume element and in this way to the postulation of a well-posed problem at this level. The numerical examples presented in the contribution investigate the effective material behavior of microporous media. An isotropic and a transversally anisotropic microstructure are simulated by choosing an appropriate orientation and geometry of the representative volume element in each Gauss point. The results are verified by comparing them with Hashin-Shtrikman's analytic bounds. However, the chosen examples should be understood as simply an illustration of the program application, while its main feature is a modular structure suitable for further development.

The paper focuses on the reflection characteristics of elastic beams having a periodically varying cross-sectional area. Assuming a weak sinusoidal variation of the beam cross-section along its axis, perturbation methods are employed to determine flexural resonance conditions and analyze the resonant destructive interaction of flexural waves with the periodic beam. This interaction is represented in the form of coupled-wave equations, which are solved analytically, together with relevant boundary conditions, at the ends of the periodic section of the beam. The reflection coefficient is then calculated for beams having different types of periodicity. This study is intended to provide guidelines to control passively the flexural vibration in beams.

In topology optimization of structures, materials and mechanisms, parametrization of geometry is often performed by a grey-scale density-like interpolation function. In this paper we analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials. This allows us to derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design. Thus it is shown that the socalled arti®cial interpolation model in many circumstances actually falls within the framework of microstructurally based models. Single material and multi-material structural design in elasticity as well as in multi-physics problems is discussed.

In the present study, free vibrations and stability of rotating single walled carbon nanotubes (SWCNT) is investigated by nonlocal theory of elasticity; while the CNT is partially resting on an elastic foundation. The governing equations of motion are presented by using Love's shell assumptions. An exact series expansion method of solution is employed and very accurate results are obtained. Some parameter studies including the effects of rotating speed, foundation stiffness, slenderness ratio and nonlocal parameter on the natural frequency and stability margins of the current model are studied. The studies show that rotation rates and foundation elasticity can contribute significantly in the dynamic characteristics of rotating MEMS devices.

Nonlocal elastic rod model is developed and applied to investigate the small-scale effect on axial vibration of nanorods. Explicit expressions are derived for frequencies for clamped-clamped and clamped-free boundary conditions. It is concluded that the axial vibration frequencies are highly over estimated by the classical (local) rod model, which ignores the effect of small-length scale. Present results can be used for axial vibration of single-walled carbon nanotubes.

In the present study, longitudinal wave propagation in nanorods is studied using nonlocal elasticity theory. The nonlocal constitutive equations of Eringen are used in the formulations. A unified rod theory including lateral inertia, shear and surface stress effects which gives the previous theories as a special case is adopted in the formulation of the displacement field. A modification is proposed to Eringen's nonlocal parameter e 0 by obtaining an explicit relation for it. The nonlocal parameter is calibrated using lattice dynamics. It is obtained that the nonlocal parameter is material and geometry dependent. Considering lateral inertia and surface effects improves longitudinal wave characteristics of nanorods.