Local Stiffness Variations Research Articles

Vibration and Stability Analyses of Submarine Fluid-Conveying Pipelines with Local Stiffness Variation Under External Flow Fields

This study analyzes the vibration and stability characteristics of a submarine fluid-conveying pipeline with local variation in stiffness under the influence of external flow fields. Utilizing the absolute nodal coordinate formulation (ANCF), the dynamic equation for the submarine pipeline with local stiffness variation under arbitrary boundary conditions is derived. Through numerical solutions, curves depicting complex frequency variations as a function of the internal flow velocity of the pipeline system are obtained. Additionally, the effects of external flow velocity, geometrical parameters, and local stiffness variation on the vibration and stability characteristics of the submarine pipeline under three different boundary conditions are investigated. Results indicate that the stability of the pipeline system decreases across the three boundary conditions under the influence of the external flow field. Increased external flow velocities lead to further reductions in system stability. Furthermore, as the length-to-diameter ratio increases and the thickness-to-diameter ratio decreases, the first three orders of frequencies of the pipeline gradually diminish. Enhancing local stiffness contributes to improving the stability of the system, whereas reducing local stiffness has the opposite effect.

Anisotropic Elastic Strain-Gradient Continuum from the Macro-Scale to the Granular Micro-Scale

A multi-scale framework is constructed for the computation of the stiffness tensors of an elastic strain-gradient continuum endowed with an anisotropic microstructure of arbitrarily-shaped particles. The influence of microstructural features on the macroscopic stiffness tensors is demonstrated by comparing the fourth-order, fifth-order and sixth-order stiffness tensors obtained from macro-scale symmetry considerations to the stiffness tensors deduced from homogenizing the elastic response of the granular microstructure. Special attention is paid to systematically relating the particle properties to the probability density function describing their directional distribution, which allows to explicitly connect the level of anisotropy of the particle assembly to local variations in particle stiffness and morphology. The applicability of the multi-scale framework is exemplified by computing the stiffness tensors for various anisotropic granular media composed of equal-sized spheres. The number of independent coefficients of the homogenized stiffness tensors appears to be determined by the number of independent microstructural parameters, which is equal to, or less than, the number of independent stiffness coefficients following from macro-scale symmetry considerations. Since the modelling framework has a general character, it can be applied to different higher-order granular continua and arbitrary types of material anisotropy.

Analytical solution and free vibration analysis for beams with step changes in stiffness

PurposeThis paper aims to investigate analytical solutions of natural frequencies and mode shapes of Euler-Bernoulli beams with step changes in the stiffness.Design/methodology/approachIn this work, analytical solutions for a beam with a single discontinuity was performed. Subsequently, based on an effective matrix formulation, the closed-form expressions of the single discontinuity beam could be conveniently extended to stepped beams with multiple stiffness discontinuities.FindingsThe results of the study show that the natural frequency of the beam can be adjusted by the local stiffness variation, and step location plays a significant role in free vibration responses.Originality/valueThe effects of the stiffness of the segment and step location on the natural frequencies of the stepped beams under different boundary conditions were examined using the proposed analytical scheme. This study provides insights into the design of variable-stiffness beam structures with the capability to adjust natural frequencies.

Surrogate Modeling for Creep Strain-Based Fatigue Prediction of a Ball Grid Array Component

AbstractIn the past years, the finite element analysis (FEA) has proven to be a suitable way for fatigue prediction of electronic equipment based on the physics-of-failure-approach. For this, inelastic strain parameters like creep strain or creep energy density are evaluated in crack susceptible regions of solder joints. Due to the nonlinearity of the creep behavior, which is the basis for these simulations, the computational effort can be significant. This mostly leads to a component-focused approach. Global influences on components like local stiffness variations due to adjacent components, copper traces, or fixations of the printed circuit board (PCB) are often ignored. To make creep-based fatigue predictions suitable for complex printed circuit board assemblies (PCBA), a method for reducing computational effort needs to be established. For this matter, a machine learning-based approach for solder joints has been developed. First, the process for data generation and model training has been established. Thereafter, several methods for input parameter reduction are discussed. Finally, a model is being trained based on the generated simulation data.

AltPrint: new filling and slicing process planning based on deposited material with geometry variation

PurposeThis paper aims to address the development and implementation of “AltPrint,” a slicing algorithm based on a new filling process planning from a variation in the deposited material geometry. AltPrint enables changes in the extruded material flow toward local variations in stiffness. The technical feasibility evaluation was conducted experimentally by fused filament fabrication (FFF) process of snap-fit subjected to a mechanical cyclical test.Design/methodology/approachThe methodology is based on the estimation of the parameter E from the mathematical relationships among the variation of the material in the material flow, nozzle geometry and extrusion parameters. Calibration, validation and analysis of the printed specimens were divided into two moments, of which the first refers to the material responses (flexural and dynamic mechanical analysis) and the second involves the analysis of the printed components with localized flow properties (for estimating the response to cyclic loading). Finite element analysis assisted in the comparison of two snap-fit geometries, one traditional and one generated by AltPrint. Finally, three examples of compliant mechanisms were developed to demonstrate the potential of the algorithm in the generation of functional prototypes.FindingsThe contribution of AltPrint is the variable fill width integrated with the slicing software that varies the print parameters in different regions of the object. The alternative extrusion method based on material rate variation was conceived as an “open software” available in GitHub platform, hence, open manufacturing with initial focus on desktop 3D printer based on FFF. The slicing method provides deposited variable-width segments in an organized and replicable filling strategy, resulting in mechanical properties variations in specific regions of a part. It was implemented and evaluated experimentally and indicated potential applications in parts manufactured by the additive process based on extrusion, which requires local flexibilities.Originality/valueThis paper presents a new alternative method for application in an open additive manufacturing context, specifically for additive extrusion techniques that enable local variations in the material flow. Its potential for manufacturing functional parts, which require flexibility due to cyclic loading, was demonstrated by fabrication and experimental evaluations of parts made in acrylonitrile butadiene styrene filament. The changes proposed by AltPrint enable geometric modifications in the response of the printed parts. The proposed slicing and filling control of parameters is inserted in a context of design for additive manufacturing and shows great potential in the area of product design.

Influence of frost and local stiffness variations on the strain mode shapes of a steel arch bridge

Natural frequencies are probably the most widely used modal characteristics in vibration-based monitoring. However, they can be highly influenced by temperature and this influence can completely mask the effect of even severe damage. This translates into a necessity for time-consuming data-normalization techniques to remove the influence of temperature and identify damage. Displacement mode shapes of homogeneous material structures are less influenced by temperature, but obtaining them in a dense grid, which is required for damage localization, is cumbersome due to the large number of sensors needed. Strain mode shapes on the other hand can be insensitive to temperature variations, while obtaining them in a dense grid is possible when fiber-optic sensors such as fiber-Bragg gratings (FBG) are used. This work presents the results of the continuous monitoring of a steel railway bridge for a period of almost two years, where modal data were collected for a wide temperature range. The bridge is instrumented with eighty FBG strain sensors, multiplexed in four fibers. The natural frequencies and strain mode shapes of ten modes have been automatically identified from operational strain time histories, on an hourly basis. A clear influence of temperature on the natural frequency of most modes is identified, especially during frost periods. On the contrary, the strain mode shapes are mostly insensitive to temperature changes and only these of some higher-order modes are slightly and uniformly influenced when frost occurs. This behavior is confirmed also by a finite element model (FE) of the bridge. Furthermore, the FE model is used to investigate the influence of local stiffness changes on the modal characteristics. A clear and local change of the modal strain amplitude is observed at the location of the reduced stiffness, especially when information from all modes is combined in a sensitive damage index.

Stress calculation on bevel gears with FEM influence vectors

In order to be able to carry out an optimal gear design with the aim of cost reduction and the careful handling of resources, load capacity is an important criterion for the evaluation of a gear. For the calculation of the flank and root load capacity, a precise loaded tooth contact analysis (LTCA) is necessary. With LTCA software like BECAL, influence numbers are used to calculate the deformation of the gear. These influence numbers are calculated with a BEM-module and considered for calculating the local root stress. This method simplifies the coupling stiffness in tooth width direction with a decay function and neglects the influence of local differences in tooth stiffness. In this publication, this simplification shall be questioned and evaluated.Therefore, a new method for calculating stress with FEM influence vectors is presented. This method enables the calculation of full stress tensors at any desired location in the gear with the efficiency of the influence number method. Additionally, the influence of local stiffness variations in the gear is taken into account. Various gear examples show the influence of material connections at the pinion root and the influence of the rim thickness of a wheel on the root stress. To validate the accuracy and the time efficiency of the new calculation method and to compare the results to current state-of-the-art simulations, a well-documented series of tests from the literature is recalculated and evaluated.

Local stiffness and work function variations of hexagonal boron nitride on Cu(111).

Combined scanning tunnelling and atomic force microscopy using a qPlus sensor enables the measurement of electronic and mechanic properties of two-dimensional materials at the nanoscale. In this work, we study hexagonal boron nitride (h-BN), an atomically thin 2D layer, that is van der Waals-coupled to a Cu(111) surface. The system is of interest as a decoupling layer for functional 2D heterostructures due to the preservation of the h-BN bandgap and as a template for atomic and molecular adsorbates owing to its local electronic trapping potential due to the in-plane electric field. We obtain work function (Φ) variations on the h-BN/Cu(111) superstructure of the order of 100 meV using two independent methods, namely the shift of field emission resonances and the contact potential difference measured by Kelvin probe force microscopy. Using 3D force profiles of the same area we determine the relative stiffness of the Moiré region allowing us to analyse both electronic and mechanical properties of the 2D layer simultaneously. We obtain a sheet stiffness of 9.4 ± 0.9 N·m−1, which is one order of magnitude higher than the one obtained for h-BN/Rh(111). Using constant force maps we are able to derive height profiles of h-BN/Cu(111) showing that the system has a corrugation of 0.6 ± 0.2 Å, which helps to demystify the discussion around the flatness of the h-BN/Cu(111) substrate.

Predictions of the elastic modulus of trabecular bone in the femoral head and the intertrochanter: a solitary wave-based approach.

This paper deals with the numerical prediction of the elastic modulus of trabecular bone in the femoral head (FH) and the intertrochanteric (IT) region via site-specific bone quality assessment using solitary waves in a one-dimensional granular chain. For accurate evaluation of bone quality, high-resolution finite element models of bone microstructures in both FH and IT are generated using a topology optimization-based bone microstructure reconstruction scheme. A hybrid discrete element/finite element (DE/FE) model is then developed to study the interaction of highly nonlinear solitary waves in a granular chain with the generated bone microstructures. For more robust and reliable prediction of the bone's mechanical properties, a face sheet is placed at the interface between the last chain particle and thebone microstructure, allowing more bone volume to be engaged in the dynamic deformation during interaction with the solitary wave. The hybrid DE/FE model was used to predict the elastic modulus of the IT and FH by analysing the characteristic features of the two primary reflected solitary waves. It was found that the solitary wave interaction is highly sensitive to the elastic modulus of the bone microstructure and can be used to identify differences in bone density. Moreover, it was found that the use of a relatively stiff face sheet significantly reduces the sensitivity of the wave interaction to local stiffness variations across the test surface of the bone, thereby enhancing the robustness and reliability of the proposed method. We also studied the effect of the face sheet thickness on the characteristics of the reflected solitary waves and found that the optimal thickness that minimizes the error in the modulus predictions is 4mm for the FH and 2mm for the IT, if the primary reflected solitary wave is considered in the evaluation process. We envisage that the proposed diagnostic scheme, in conjunction with 3D-printed high-resolution bone models of an actual patient, could provide a viable solution to current limitations in site-specific bone quality assessment.

3D mechanical characterization of single cells and small organisms using acoustic manipulation and force microscopy

Quantitative micromechanical characterization of single cells and multicellular tissues or organisms is of fundamental importance to the study of cellular growth, morphogenesis, and cell-cell interactions. However, due to limited manipulation capabilities at the microscale, systems used for mechanical characterizations struggle to provide complete three-dimensional coverage of individual specimens. Here, we combine an acoustically driven manipulation device with a micro-force sensor to freely rotate biological samples and quantify mechanical properties at multiple regions of interest within a specimen. The versatility of this tool is demonstrated through the analysis of single Lilium longiflorum pollen grains, in combination with numerical simulations, and individual Caenorhabditis elegans nematodes. It reveals local variations in apparent stiffness for single specimens, providing previously inaccessible information and datasets on mechanical properties that serve as the basis for biophysical modelling and allow deeper insights into the biomechanics of these living systems.

Local myocardial stiffness variations identified by high frame rate shear wave echocardiography

BackgroundShear waves are generated by the closure of the heart valves. Significant differences in shear wave velocity have been found recently between normal myocardium and disease models of diffusely increased muscle stiffness. In this study we correlate in vivo myocardial shear wave imaging (SWI) with presence of scarred tissue, as model for local increase of stiffness. Stiffness variation is hypothesized to appear as velocity variation.MethodsTen healthy volunteers (group 1), 10 hypertrophic cardiomyopathy (HCM) patients without any cardiac intervention (group 2), and 10 HCM patients with prior septal reduction therapy (group 3) underwent high frame rate tissue Doppler echocardiography. The SW in the interventricular septum after aortic valve closure was mapped along two M-mode lines, in the inner and outer layer.ResultsWe compared SWI to 3D echocardiography and strain imaging. In groups 1 and 2, no change in velocity was detected. In group 3, 8/10 patients showed a variation in SW velocity. All three patients having transmural scar showed a simultaneous velocity variation in both layers. Out of six patients with endocardial scar, five showed variations in the inner layer.ConclusionLocal variations in stiffness, with myocardial remodeling post septal reduction therapy as model, can be detected by a local variation in the propagation velocity of naturally occurring shear waves.

Application of Rotation Rate Sensors in Modal and Vibration Analyses of Reinforced Concrete Beams.

The recent rapid development of rotation rate sensor technology opens new opportunities for their application in more and more fields. In this paper, the potential of rotational sensors for the modal analysis of full-scale civil engineering structural elements is experimentally examined. For this purpose, vibrations of two 6-m long beams made of ultra-high performance concrete (UHPC) were measured using microelectromechanical system (MEMS) rotation rate sensors. The beams were excited to vibrations using an impact hammer and a dynamic vibration exciter. The results of the experiment show that by using rotation rate sensors, one can directly obtain derivatives of mode shapes and deflection shapes. These derivatives of mode shapes, often called “rotational modes”, bring more information regarding possible local stiffness variations than the traditional transversal and deflection mode shapes, so their extraction during structural health monitoring is particularly useful. Previously, the rotational modes could only be obtained indirectly (e.g., by central difference approximation). Here, with the application of rotation rate sensors, one can obtain rotational modes and deflection shapes with a higher precision. Furthermore, the average strain rate and dynamic strain were acquired using the rotation rate sensors. The laboratory experiments demonstrated that rotation rate sensors were matured enough to be used in the monitoring and modal analyses of full-scale civil engineering elements (e.g., reinforced concrete beams).

On the resolution of subsurface atomic force microscopy and its implications for subsurface feature sizing.

Ultrasound atomic force microscopy (AFM) has received considerable interest due to its subsurface imaging capabilities, particularly for nanostructure imaging. The local contact stiffness variation due to the presence of a subsurface feature is the origin of the imaging contrast. Several research studies have demonstrated subsurface imaging capabilities with promising resolution. However, there is limited literature available about the definition of spatial resolution in subsurface AFM. The changes in contact stiffness and their link to the subsurface resolution are not well understood. We propose a quantitative approach to assess the resolution in subsurface AFM imaging. We have investigated the influences of several parameters of interest on the lateral resolution. The quantification of the subsurface feature size can be based on threshold criteria (full width at half maximum and Rayleigh criteria). Simulations and experimental measurements were compared, revealing that the optimal choice of parameter settings for surface topography AFM is suboptimal for subsurface AFM imaging.

Finite deformation elastography of articular cartilage and biomaterials based on imaging and topology optimization

Tissues and engineered biomaterials exhibit exquisite local variation in stiffness that defines their function. Conventional elastography quantifies stiffness in soft (e.g. brain, liver) tissue, but robust quantification in stiff (e.g. musculoskeletal) tissues is challenging due to dissipation of high frequency shear waves. We describe new development of finite deformation elastography that utilizes magnetic resonance imaging of low frequency, physiological-level (large magnitude) displacements, coupled to an iterative topology optimization routine to investigate stiffness heterogeneity, including spatial gradients and inclusions. We reconstruct 2D and 3D stiffness distributions in bilayer agarose hydrogels and silicon materials that exhibit heterogeneous displacement/strain responses. We map stiffness in porcine and sheep articular cartilage deep within the bony articular joint space in situ for the first time. Elevated cartilage stiffness localized to the superficial zone is further related to collagen fiber compaction and loss of water content during cyclic loading, as assessed by independent T2 measurements. We additionally describe technical challenges needed to achieve in vivo elastography measurements. Our results introduce new functional imaging biomarkers, which can be assessed nondestructively, with clinical potential to diagnose and track progression of disease in early stages, including osteoarthritis or tissue degeneration.

Tactile Exploration Strategies With Natural Compliant Objects Elicit Virtual Stiffness Cues.

When interacting with deformable objects, tactile cues at the finger pad help inform our perception of material compliance. Nearly all prior studies have relied on highly homogenous, engineered materials such as silicone-elastomers and foams. In contrast, we employ soft plum fruit varying in ripeness; ecological substances associated with tasks of everyday life. In this article, we investigate volitional exploratory strategies and contact interactions, for comparison to engineered materials. New measurement techniques are introduced, including an ink-based method to capture finger pad to fruit contact interactions, and instrumented force and optical sensors to capture imposed force and displacement. Human-subjects experiments are conducted for both single finger touch and two finger grasp. The results indicate that terminal contact areas between soft and hard plums are indistinguishable, but the newly defined metric of virtual stiffness can differentiate between the fruits' ripeness, amidst their local variations in geometry, stiffness, and viscoelasticity. Moreover, it affords discrimination independent of one's touch force. This metric illustrates the tie between the deployment of active, exploratory strategies and the elicitation of optimal cues for perceptual discrimination. Compared to single finger touch, perceptual discrimination improves further in pinch grasp, which is indeed a more natural gesture for judging ripeness.

Density filtering regularization of finite element model updating problems

• A density filtering regularization method is proposed to smooth out strong local stiffness variations. • The density filter controls the length scale of the damaged zone by selecting a proper filter radius. • The method is compared with classical Tikhonov regularization in a numerical case study. • Compared with Tikhonov regularization, density filtering is found to be more successful in identifying the damaged zone. Finite element (FE) model updating is often used as a non-destructive method to detect structural damage. Stiffness parameters of an FE model of the structure are calibrated based on experimental vibration data. If the desired spatial resolution is high, the problem is likely to be ill-conditioned and requires regularization. Tikhonov regularization is frequently used for FE model updating problems, but the selection of a proper regularization parameter and a good initial estimate of the stiffness parameters is difficult. This paper proposes an alternative, density-filtering-based method where the filter radius acts as regularization parameter. Since the filter radius controls the minimal length scale of the identifiable damaged zones, it has a clear physical meaning. Furthermore, an initial estimate of the stiffness parameters is only required as a starting point for the optimization algorithm whereas in the case of Tikhonov regularization it also guides the optimization. Both regularization methods are compared in a numerical case study. The density filtering regularization method is found to be more successful in identifying the damaged zone, while Tikhonov regularization sometimes fails to do so.

Wing twisting by elastic instability: A purely passive approach

The design of morphing structures requires attaining concurrently light-weight, load-carrying and shape adaptable systems that minimize complexity, actuation requirements and part count. Exploiting the external loads to produce local stiffness variations induced by elastic instabilities offers the potential to activate shape deformations purely passively. Following this approach, we present the structural response study of wings capable of attaining compliant buckling-induced twisting deformations. The structure is designed such that a specific level of aerodynamic load triggers the elastic instability in a shear web part of the wing box. The buckling-induced variation in effective shear stiffness, resulting from the development of a stable, reversible diagonal tension field, leads to a twisting deformation. The structural behaviour is characterized by two drastically different mechanical responses, delimited by the onset of elastic instability. The influence of the buckling component design on the attainable change in spanwise angle of attack is investigated for the specific case of a finite composite wing structure under aerodynamic loads. The type of composite material, its thickness, and the fibre orientation are the considered design parameters. The buckling-induced variation in twist angle, and the corresponding aerodynamic pressure redistribution on the wing, is exploited for achieving load alleviation, reducing the global lift coefficient and decreasing the wing root bending moment.

Activation of human aortic valve interstitial cells by local stiffness involves YAP-dependent transcriptional signaling

Differentiation of valve interstitial cells (VICs) into pro-calcific cells is one of the central events in calcific aortic valve (AoV) disease (CAVD). While the paracrine pathways and the responsivity of VICs to mechanical compliance of the surrounding environment are well characterized, the molecular programming related to variations in local stiffness, and its link to cytoskeleton dynamics, is less consolidated. By using a simple method to produce 2D poly-acrylamide gels with stiffness controlled with atomic force microscopy (AFM), we manufactured adhesion substrates onto which human VICs from stenotic valves were plated, and subsequently investigated for cytoskeleton dynamics and activation of the mechanosensing-related transcription factor YAP. As a comparison, we employed VICs from patients undergoing valve substitution for valve insufficiency, a non-calcific AoV disease, which does not involve extensive inflammation. While the two VICs types did not differ for basic responses onto substrates with different stiffness values (e.g. adhesion and proliferation), they were subject to a different dynamics of stiffness-dependent YAP nuclear shuttling, revealing for the first time an intracellular force transduction mechanism distinctive for calcific aortic valve disease. In VICs from stenotic valves, YAP nuclear translocation occurred in concert with an increase in cytoskeleton tensioning and loading of the myofibroblast-specific protein αSMA onto the F-actin cytoskeleton. AFM force mapping performed along radial sections of human calcific valve leaflets identified, finally, areas with high and low levels of rigidity within a similar range to those controlling YAP nuclear translocation in vitro. Since VICs juxtaposed to these areas exhibited nuclear localized YAP, we conclude that subtle variations in matrix stiffness are involved in mechanosensing-dependent VICs activation and pathological differentiation in CAVD.

Impact damage prediction in thin woven composite laminates – Part I: Modeling strategy and validation

An explicit finite element modeling of the 5-harness satin woven composite material is proposed in this paper. It is based on the semi-continuous approach. The bundles are modeled with rod elements and a specific damageable shell element is used to stabilize this truss structure. As the woven pattern geometry plays a key role in damage initiation and propagation, the rods located at the crimp regions where warp and weft yarns cross each other have been offset to represent the bundles undulations. The main objective of the presented modeling strategy is to represent local bending stiffness variations and damage initiation at the crimp regions without using artificial parameters, but only geometric and material parameters.The method has been implemented into the explicit finite element code RADIOSS. The modeling strategy is validated by representing a three-point bending test and a drop weight test. It provides good prediction for the local bending stiffness, the impact force history and the damage size and shape. The strain concentration at the crimp regions is well represented.

Sprouting angiogenesis induces significant mechanical heterogeneities and ECM stiffening across length scales in fibrin hydrogels

Matrix stiffness is a well-established instructive cue in two-dimensional cell cultures. Its roles in morphogenesis in 3-dimensional (3D) cultures, and the converse effects of cells on the mechanics of their surrounding microenvironment, have been more elusive given the absence of suitable methods to quantify stiffness on a length-scale relevant for individual cell-extracellular matrix (ECM) interactions. In this study, we applied traditional bulk rheology and laser tweezers-based active microrheology to probe mechanics across length scales during the complex multicellular process of capillary morphogenesis in 3D, and further characterized the relative contributions of neovessels and supportive stromal cells to dynamic changes in stiffness over time. Our data show local ECM stiffness was highly heterogeneous around sprouting capillaries, and the variation progressively increased with time. Both endothelial cells and stromal support cells progressively stiffened the ECM, with the changes in bulk properties dominated by the latter. Interestingly, regions with high micro-stiffness did not necessarily correlate with remodeled regions of high ECM density as shown by confocal reflectance microscopy. Collectively, these findings, especially the large spatiotemporal variations in local stiffness around cells during morphogenesis in soft 3D fibrin gels, underscore that characterizing ECM mechanics across length scales. provides an opportunity to attain a deeper mechanobiological understanding of the microenvironment's roles in cell fate and tissue patterning.