Stiffness Decay Research Articles

Experimental study of dynamic shear stiffness decay characteristics of interbedded soil: a case study in Yangtze River floodplain

Experimental study of dynamic shear stiffness decay characteristics of interbedded soil: a case study in Yangtze River floodplain

Sensitivity to intensity and distribution of the temperature field in the nonlinear thermo-mechanical analysis of laminated glass plates

Glass laminates consist of stiff glass plies permanently shear-coupled by polymeric interposed layers. When an external temperature rise occurs, the interlayers undergo a dramatic stiffness decay. As a consequence, not only the sectional warping typical of alternating stiff/soft composites is intensified, but also the overall behavior may evolve counter-intuitively. When slender elements prone to geometric nonlinearities are involved, even small thermal variations in intensity or distribution may act as uncertainty factors, strongly affecting the outcome. This paper proposes an efficient, robust, and accurate numerical framework to perform the sensitivity analysis to thermo-mechanical actions in glass plates. A large deformation isogeometric Kirchhoff-Love shell model enriched with through-the-thickness warping is employed, together with a generalized arc-length method involving a suitable temperature parameter as an additional unknown, namely the thermal amplifier or a spatial distribution coefficient. Numerical experiments are presented to highlight the effects that even small temperature variations produce on the equilibrium paths and the influence of the stiffness loss in the interlayer on the structural behavior and the accuracy of the models.

Simplified nonlinear model and 3D printing model experiment verification of longitudinal joints of shield tunnel segments

The segment joints represent vulnerable and core-bearing areas within shield tunnel structures. Their flexural stiffness, starting from the contact surface of longitudinal joints to the bolt hole, exhibits continuous changes under bending loads, typically demonstrating nonlinear mechanical characteristics. This study investigates the influence of joint contact surfaces on flexural stiffness, extending from the joint contact surface to damaged concrete in the compressed zone. A new simplified model for the variable nonlinear stiffness of longitudinal segment joints in shield tunnels is proposed, considering the flexural stiffness of the joint contact surface and the width of the damaged concrete zone in the segment ring while simulating the flexural stiffness decay induced by the opening of segment joints. Based on the minimum potential energy principle, a design calculation method for joint flexural stiffness is derived, establishing the nonlinear bending stiffness coupling relationship between the segment and the joint. Through similarity theory, 3D printing technology, and indoor loading tests, the theoretical model's accuracy regarding tunnel segment joints is verified. This theoretical model provides a basis for designing and assessing the performance of tunnel-segment joints.

Compressive behavior of hierarchical brick‐and‐mortar structures obtained by fused deposition modeling

AbstractNature is a never‐ending fount of inspiration to solve engineering problems. In light of this, the goal of this work is to propose and study structures that mimic materials found in nature, more specifically nacre. These structures were designed to be manufactured using fused deposition modeling since this is an accessible way to reproduce complex geometries. The manufactured biomimetic materials were tested in uniaxial compression in two different directions. In addition, an elastoplastic numerical analysis was used to better understand the compressive behavior of the studied structures. The comparison between experimental and numerical analysis reveals that the overall behavior results from two competing mechanisms, that is, an increase in stiffness due to strain‐hardening and a stiffness decay promoted by damage propagation. Moreover, it was possible to see that the structures continue to bear load while they retain the structural integrity, which is dominated by the crushing strength of each type of structure.Highlights Additive manufactured nacre‐inspired structures were proposed. Influence of different geometries in the compressive behavior was assessed. Behavior was linked to competition between strain‐hardening and damage growth. Load‐bearing capacity was related to the structural integrity of elements. The crack deflection mechanism was identified in some specimens.

A coupled ductile damage model for metal matrix composites: Development and application

The prediction of failure behavior in metal matrix composites remains a significant challenge in both composition design and process optimization. An accurate prediction of metal matrix composites damage evolution is a crucial for enhancing the quality of metal matrix composites forming. As the material undergoes plastic deformation, it experiences void initiation and growth, resulting in consequential microstructural transformations, stiffness degradation, and mechanical property shifts. In this work, we employed a model to predict damage progression and stiffness decay in metal matrix composites. Leveraging the Gurson-Tvergaard-Needleman framework, this homogenization model accounts for the impact of the evolution of voids and reinforcing phases, on the composite's mechanical properties. The influences of reinforcing phases on voids nucleation and growth were particularly considered, and also the interaction of voids, matrix, reinforcing phases, and stiffness were integrated to discuss their impacts on damage evolution and mechanical performances of the metal matrix composites. The model was implemented as an Abaqus VUMAT subroutine, with its validity gauged by analyzing the influence of model parameters on failure mechanisms and inherent elastoplastic traits. Utilizing the flanging process of carbon nanotube-reinforced aluminum matrix composites as a case study, a significant agreement was observed between experimental and simulated force-displacement profiles, as well as crack evolution routes.

Effect of soil structuring on stiffness evaluated by triaxial and seismic flat dilatometer tests

Granitic residual soils are considered structured soils. The bonding between the particles and the fabric inherited by the original rock play an important role in controlling the mechanical behaviour. These materials considered as “cemented” soils are often seen as non-textbook materials, since they do not fit into the usual behaviour of transported soils in the light of classical Soil Mechanics theories. To study the stiffness of the granitic residual soils located in Guarda (northeast of Portugal) several SDMT tests carried out on structured soils (natural granitic residual soils and artificial cemented soils) and triaxial tests (carry out with internal instrumentation), performed on samples collected at the same depth, at similar confining stresses, to those involved in the SDMT tests. The results show that in the stiffness decay curve the value of the stiffness modulus (EDMT or GDMT) increase with the increasing level of cementation. In addition, the strain levels involved in the calculation of the stiffness modulus (EDMT or GDMT) decreases with the increase of the cementation level, which can have important consequences for practical purposes of geotechnical design.

The Seismic Design Process of RC Column Components in SDOF System considering the Earthquake Duration Effect

In order to study seismic design process of RC (reinforced concrete) column components considering the effect of earthquake duration, the degradation law of capacity under random amplitude hysteresis history was conducted by the research group, and the estimation method for the energy dissipation capacity of RC column components was suggested. Furthermore, the correlation between the stiffness decay index and energy dissipation capacity, hysteresis histories, and structural parameters was proposed, and the performance classification criteria based on the stiffness decay index was established. On this basis, the connection between the stiffness decay index and structural parameters and seismic parameters was established, and the seismic design process of RC column components in SDOF (single degree of freedom) system was proposed. The research indicated that the proposed seismic design process based on stiffness decay index can effectively consider the effect of earthquake duration. The stiffness decay index is more suitable for defining structural damage than deformation index and Park-Ang index. The stiffness decay index establishes quantitative relationships with seismic parameters and structural parameters, facilitating performance-based design in engineering practice. The increase in earthquake duration exacerbates the damage of RC column components, and this effect is more pronounced at the beginning of the earthquake and gradually decreases over time.

Seismic site response analysis of liquefiable soil deposits focusing on the ground surface response spectrum

A numerical algorithm is developed for conducting one-dimensional non-linear ground response analysis of layered sites, capable of reproducing liquefaction phenomena and accounting for the simultaneous dissipation of excess pore water pressure through soil grains. Τhe shear wave propagation algorithm is based on the plasticity constitutive model for sand Ta-Ger, expressed in a one dimensional p-q space form. This model demonstrates remarkable versatility in representing complex patterns of the cyclic behavior of sand, such as stiffness decay and strength reduction due to pore-water pressure buildup. The calibration of the model is based on shear modulus reduction and damping curves for drained loading conditions, as well as liquefaction resistance curves for undrained conditions. A detailed presentation of the numerical model formulation is provided, outlining the numerical approach for solving the wave propagation and consolidation differential equations. To validate model predictions, the recorded seismic ground response of the Port Island array during the 1995 Kobe earthquake is utilized. Furthermore, the model is applied to estimate the elastic response spectra at the surface of soil profiles with liquefiable layers (ground type S2) as per EC8:2004. The investigation involves the ground response analysis of various soil p3rofiles, all including a liquefiable zone, excited by a suite of earthquake motions at their base. The acceleration time histories are extracted from the PEER Ground Motion Database, having characteristics compatible with the NGA-estimated response spectrum at the bedrock as well as key seismological parameters such as the earthquake magnitude Mw and the horizontal distance from the fault RJB. Two different methods are employed for selecting the base excitations: amplitude-scaled records to match a target response spectrum and spectral-matched records. From the results, an idealized response spectrum is derived in terms of the design spectrum parameters S, η, ΤΒ and TC. The findings demonstrate that the idealized ground surface response spectrum is minimally sensitive to the method used for base excitation selection.

The exact distributional model for free vibrations of shear-bending multi-cracked Timoshenko beams

The influence of shear deformation in the dynamics of beam-like problems is usually studied by means of a First order Shear Deformation Theory (FSDT) due to the original Timoshenko formulation. In comparison to higher order theories, the FSDT is able to embed additional concentrated flexibilities due to the presence of cracks by making use of the principle of the fracture mechanics. Precisely, flexural and shear concentrated flexibilities due to the first and second mode of the crack growth, respectively, can be included in the latter model. Despite various procedures suggested in the literature, the formulation of closed form solutions of free vibrations of multi-cracked Timoshenko beams is available for the case of concentrated flexural flexibilities only. In this work an original distributional model, to account for both flexural and shear concentrated flexibilities due to multiple cracks, is presented. New governing equations of the Timoshenko beam, enriched by suitable distributional terms, over a single integration domain are formulated. An integration procedure of the governing equations by making use of the generalised function theory is presented and an original closed form solution of vibration modes and frequency equation is obtained. The closed form solution allows a parametric study to discuss the influence of the concentrated shear and flexural stiffness decay due to the presence of multiple cracks.

Conventional and lightweight aggregate one-way reinforced concrete slabs subjected to fire and repeated loads: comparative experimental study

ABSTRACT This study presents experiments on nine one-way, reinforced concrete slabs with a slab weight reduction approach utilising lightweight expanded clay aggregate (LECA). All slabs’ sizes, steel reinforcing, and concrete mix composition were equal. They were subjected to the same repeated linear load and high-temperature conditions. The slabs were classified into three groups based on the presence of LECA. The main variables were the LECA ratio (0, 20, 40) % of coarse aggregate and the exposure temperatures (ambient, 400, 700) ℃. The repeated load was applied according to the ACI-19 code, 50% of the ultimate load for seven cycles. The results showed that the presence of LECA reduced flexural strength and fire resistance. The deflection of the slabs increased with the LECA. The most significant reduction in ultimate load capacity was approximately 35.1%, with a maximum increase in slab deflection of 37.2%. However, the stiffness decay was significant, about 50%.

Evolution law of small strain shear modulus of expansive soil: From a damage perspective

It is of great significance to study the nonlinear evolution law of the small strain shear modulus of expansive soil for analyzing the deformation behavior of soil or geotechnical structure and the seismic site response. Existing studies rarely discuss the damage mechanism of the small strain shear modulus of expansive soil, and the corresponding damage model describing the small strain stiffness decay law is lacking. In this study, a series of resonance column tests were carried out to investigate the effects of mean effective stress, loading and unloading stress paths and vibration cycles on the nonlinear decay law of small strain shear modulus of expansive soil, and the damage mechanism was discussed in detail. Subsequently, a novel damage model describing the decay law of small strain shear modulus of expansive soil was proposed and verified by the results of resonant column tests. The results show that the decay process of the small strain shear modulus with the shear strain is essentially the damage of the soil structure, which can be characterized mathematically by damage model. The mean effective stress and the larger overconsolidation ratio caused by the unloading process can inhibit the damage, while the vibration cycles can cause small reduction in small strain shear modulus and promote the damage. The proposed damage model with clear physical meaning can well describe the evolution law of small strain shear modulus of expansive soil, and has higher accuracy than the traditional model.

Extended UH model and deformation prediction of high-speed railway subgrade

For the rapidity of trains in high-speed railway, it is crucial to guarantee the reliable and safe operation. Strict controls are needed to prevent excessive subgrade deformation. In order to perform more accurate subgrade deformation calculation, the constitutive model used in simulation should demonstrate the small-strain stiffness for uneven settlement calculation, and illustrate time-induced deformation for post-construction deformation. An E-UH model is established based on the original UH model. In the E-UH model, the elastic hysteresis relation is added to describe the initial high stiffness and nonlinear stiffness decay. In addition, the E-UH model also couples the equivalent formula between overconsolidated characteristics and time-induced deformation. Then the effectiveness of this new model is testified by element test prediction. By means of the second development interface of a finite element software, the E-UH model is developed as a subroutine and applied to numerical simulation of subgrade deformation. The simulation represents that the E-UH model is capable of performing deformation prediction during the subgrade construction and post-construction phases, and indicates that considering small-strain stiffness can make the uneven settlement more prominent. This research provides a practical and efficient constitutive model for numerical simulation of the high-speed railway subgrade deformation.

Identification of mixed mode damage types on rock-concrete interface under cyclic loading

The study of the mixed mode Ⅰ-Ⅱ fracture damage characteristics of the rock-concrete interface under cyclic loading is essential to grasp the operation of gravity dams under seismic loading. To reveal the mixed mode fracture damage characteristics of the rock-concrete interface under cyclic loading, a four-point shear (FPS) test for rock-concrete specimens was carried out at first. The entire fracture damage process of rock-concrete specimens was monitored in real-time by acoustic emission (AE) and digital image correlation (DIC), the widely used nondestructive monitoring techniques. The mechanical test results show that the modal angle is related to the stiffness decay of rock-concrete specimens. The quantitative identification method of tensile and shear damage based on machine learning algorithm can quantitatively identify the damage types at the interface of rock-concrete specimens. The influence of rock type and modal angle on the interface damage mechanism was quantified by the damage identification method, and the spatial and temporal evolution of tensile and shear damage with cyclic loading was determined. The spatial and temporal evolution characteristics of the damage were compared with the DIC strain contours of the corresponding stages to reveal the mechanism of the influence of the damage evolution law on the crack expansion path.

30. Influence of toggling on pullout force and screw diameter increase in spine fixation

<h3>BACKGROUND CONTEXT</h3> Pedicle screw fixation provides spinal stabilization and maintains normal vertebral motions in degenerative spondylolisthesis and scoliosis. Pedicle screw fixation requires several parameters to be optimized at the screw-bone interface to minimize clinical and biomechanical failure, including screw trajectory, bone density and screw sizing. Although prior studies have demonstrated screw loosening as an effect of toggling, they ultimately focus on the magnitude of the pullout force after cyclic loading rather than screw-bone interface throughout cycling. <h3>PURPOSE</h3> A stiffness decay model may help to better predict stability and investigate the effects of pedicle screw diameter to pedicle width ratio on overall screw stability following cyclic loading in the thoracolumbar spine. <h3>OUTCOME MEASURES</h3> Pullout force, toggling forces, decay functions. <h3>METHODS</h3> Thoracolumbar vertebrae (T1-L5) were harvested from two cadaveric spines. Pedicle screws were placed using a standard surgical technique. Five-hundred cycles toggle testing was conducted with a uniaxial load frame followed by axial pullout tests. Exponential decay models with a stiffness coefficient were computed to examine toggling force over the number of toggle cycles for each screw. Linear regression modeling and Pearson's correlation tests were used to compare the decay coefficient with the ratio of the screw diameter to the pedicle diameter, the pullout strength, and pedicle loosening. Subgroup analysis was performed between under-sized (70% pedicle diameter) screws. <h3>RESULTS</h3> Sixty-eight pedicles were harvested. Of the 44 viable pedicles, 33 (75%) were from the thoracic spine and 11 (25%) were from the lumbar spine. There were 23 pedicle screws in the undersized group and 21 pedicle screws in the normal-sized group. The average screw diameter was 53% (SD 5%) of the pedicle diameter in the undersized group and 77% (SD 8%) of the pedicle diameter in the normal-sized group (p < 0.001). A significant association was found between the screw to pedicle diameter ratio and the natural log of the stiffness decay coefficient (p = 0.035). The average pullout force was 170 N (SD 75) in the under-sized pedicle group and 194 N (SD 109) in the normal-sized group (p=0.40). Higher pullout force was associated with a lower stiffness decay coefficient (p = 0.005). Both pullout force and the natural log of the stiffness decay coefficients were associated with the drop in maximum toggling force after 500 cycles (p = 0.026 and p < 0.001, respectively). Utilizing the stiffness decay coefficient provided a better fit model for the predicted drop in maximum toggling force with a lower Akaike information criterion. <h3>CONCLUSIONS</h3> Pedicle screws with a high stiffness decay coefficient during toggle testing had lower pullout strengths. While higher pedicle screw to bone diameter ratios were associated with increased stiffness decay coefficient, there was no relationship between pedicle screw size and pullout strength. In subgroup analysis, however, increasing pedicle screw to bone diameter ratios were associated with lower pullout strength in the normal-sized group. Clinically, selecting a screw size that maximizes the pedicle diameter-screw ratio may not always lead to better fixation in all spine levels or regions. <h3>FDA DEVICE/DRUG STATUS</h3> This abstract does not discuss or include any applicable devices or drugs.

Stiffness decay characteristics and disturbance effect evaluation of structured clay based on in-situ tests

The structure of the sedimentary clay influences its mechanical behavior in non-negligible ways. This paper proposes an effective approach for investigating the in-situ stiffness characteristics from shear modulus and strain decay curves (G–γ curves) based on self-boring pressuremeter and seismic dilatometer tests. To evaluate the excavation disturbance effects on the structured clay, the stiffness parameters from pre-bored pressuremeter tests are compared with the results of self-boring pressuremeter tests. The result indicates that the complete in-situ G–γ curves can be acquired by integrating the strain-dependent tangent shear modulus Gt from self-boring pressuremeter tests and the small-strain modulus G0 from seismic dilatometer tests. Simultaneous observations of the G–γ curves with hyperbolic shapes in semi-logarithmic coordinates at the same strain scale show the similarity of the stiffness decay mode of the soil at different depths. The increase in the measured values of Gt and G0 with depth can be attributed to the improved consolidation pressures and cemented strength in the structured clay. Additionally, the G/G0–γ curves measured by the in-situ tests generally agree well with the results predicted by the Stokoe model. The excavation disturbance weakens the stiffness of the structured clay, as evidenced by Gt from the pre-bored pressuremeter data being significantly smaller than that from self-boring pressuremeter tests at the same depth. Based on quantitative analysis, the disturbance degree computed from the measured results has a low sensitivity to the soil depth and a strong negative correlation with the strain level of the soil. This study provides an effective method for predicting the stiffness parameters of structured soil based on in-situ tests.

Investigations of structure strength and ventilation performance for agriproduct corrugated cartons under long‐term transportation trip

AbstractLoad‐carrying capability of corrugated cartons packaging fresh agriproducts must be significant enough. Collapse of the carton stacked on the pallet in an environment‐controlled container is commonly observed during the shipping trip. A homogenization approach of the corrugated paperboard is adopted to dramatically reduce the computational time in the present study. A creep model is further implemented into the numerical analysis to describe the stiffness decay of the carton over the relatively long period. A finite element analysis is conducted to investigate the mechanical performance of the carton locating at bottom of the stacked pile. Simulation results show that the carton performs local buckling deformations similar to the experimental observations. The vented carton based on the modified design exhibits rather smaller deformations after the transportation journey. Moreover, the modified design provides better uniformity of ventilation based on the computational fluid dynamics analysis. Current procedure is promising for the selection of liner and fluting that compose the corrugated paperboard and the assessment of the ventilation of cartons in the early design stage.

Characteristics and Prediction of Fatigue Resistance between Asphalt Pavement Layers Based on Shear Stiffness Decay Rate

Abstract The evaluation of fatigue performance between asphalt pavement layers highly depends on fatigue life and shear stiffness. However, fatigue life and shear stiffness are comprehensive evaluation indexes. In the study of the formation mechanism and decay process of fatigue resistance, both of them cannot provide effective theoretical support. In this study, the shear stiffness decay curve was obtained through a four-point shear fatigue test under different loading conditions. The initial shear stiffness and the shear stiffness decay rate of interlayers were chosen to evaluate the initial resistance and process resistance. The effects of temperature, loading frequency, compressive stress, and shear stress on the evolution of interlayer fatigue performance were investigated. The findings of this study revealed that first, with the increase of the compressive stress perpendicular to the interlayer interface, the interlayer shear stiffness decay curve transitions from a cubic curve type to a quadratic curve type and gradually changes to a linear equation. Second, the ranking of influence degree of four factors on initial resistance and process resistance was obtained, and the influence mechanism analysis was carried out based on the variance analysis result. Finally, a multiple nonlinear regression model was established successfully to predict the fatigue life and to explain the internal connection between the initial shear stiffness, shear stiffness decay rate, and fatigue life.

CFRP Fatigue Damage Detection by Thermal Methods.

In this work, the fatigue damage of CFRP uniaxial composite specimens were studied using thermal methods to determine the fatigue behavior. The aim was to evaluate the fatigue damage as a function of the number of cycles. Consequently, the damage process was studied in terms of a global indicator, considering the stiffness decay, and in terms of local parameters, considering the evolution of temperature maps acquired during the fatigue tests. A direct correlation between the damage index, corresponding to 90% of the fatigue life, and the temperature variation of the most stressed area was found. Another parameter taken into consideration was the heating rate during the application of the first thousands cycles. This parameter was proportional to the stress amplitude, making it a useful parameter since it refers to the initial part of the specimen fatigue life.

Fatigue damage evolution using NDT techniques for Health Monitoring of CFRP laminates

In this work, an experimental method based on ultrasonic measurements with piezoelectric transducers (PZTs) was proposed for monitoring the evolution of fatigue damage on a batch of carbon fabric Open Hole specimens. The amplitudes of the recorded ultrasonic sinusoidal waves in packets were evaluated with pitch-catch modality during the different phases of the fatigue life and correlated to the applied loads.The examination of the ultrasonic data showed high sensitivity of the UT signal respect to stiffness decay and to fatigue damage associated with delamination near the hole. Occasional ultrasound measurements with the consolidated pulse-echo Phased Array technique were carried out by the authors at regular time intervals during the tests to evaluate the state of damage in relation to the degradation of the signal detected with the PZT sensors.The results have shown the potential capability of the applied experimental technique for real-time detection of delamination on composite elements subjected to time-varying loads.

Conventional and bubbled slab strips under limited repeated loads: A comparative experimental study

This work primarily aimed to compare the bubble slabs experimentally with solid slabs under the influence of limited repeated four-point loads. Therefore six slab strips were manufactured in the same forms, except the cross-section type. Three were solid, and the others were voided due to placing 70 mm-diameter balls inside them. In addition, the shear span to effective depth ratio (a/d) was also studied. Accordingly, one slab from each type was tested, with the a/d being either 2, 3.5, or 5. The applied loads were repeated ten cycles at a load level of 25 kN, representing 70 % of the ultimate load estimated according to the ACI-19 code, and then lasted gradually until the slabs' collapse. The results recorded that the balls' presence made slabs failed abruptly due to shear mode regardless of the a/d. For the same slab type, the slabs' strength, stiffness, and toughness reduced as the a/d was increased; nevertheless, the ductility showed an opposite trend. Compared to solid similars, the bubble slabs' mechanical measurements, excluding the service stiffness, dropped notably. However, the stiffness decay was small, below 15 %. Moreover, sustainability analysis was performed, and the voided slabs were found to be more eco-friendly than solid ones due to reductions in the CO2 emission and consumed embodied energy, about 14 % and 10 % below those of the solid slabs.