Variable Stiffness Research Articles

Advancing the dynamic properties of a column with variable flexural stiffness in terms of structural mounting damping, external and internal damping

Advancing the dynamic properties of a column with variable flexural stiffness in terms of structural mounting damping, external and internal damping

Systematic analysis of constitutive models of brain tissue materials based on compression tests

It's crucial to understand the biomechanical properties of brain tissue to comprehend the potential mechanisms of traumatic brain injury. This study, distinct from homogeneous models, integrates axonal coupling in both axial and transverse compressive experiments within a continuum mechanics framework to capture its intricate mechanical behaviors. Fresh porcine brains underwent unconfined compression at strain rates of 0.001/s and 0.1/s to 0.3 strain, allowing for a comprehensive statistical analysis of the directional, regional, and strain-rate-dependent mechanical properties of brain tissue. The established constitutive model, fitted to experimental data, delineates material parameters providing intuitive insights into the stiffness of gray/white matter isotropic matrices and neural fibers. Additionally, it predicts the mechanical performance of white matter matrix and axonal fibers under compressive loading. Results reveal that gray matter is insensitive to loading direction, exhibiting insignificant stiffness variations within regions. White matter, however, displays no significant differences in mechanical properties under axial and transverse loading, with an overall higher average stress than gray matter and a more pronounced strain-rate effect. Stress-strain curves indicate that, under axial compression, white matter axons primarily resist the load before transitioning to a matrix-dominated response. Under transverse loading, axonal fibers exhibit weaker resistance to lateral pressure. The mechanical behavior of brain tissue is highly dependent on loading rate, region, direction, and peak strain. This study, by combining experimentation with phenomenological modeling, elucidates certain phenomena, contributing valuable insights for the development of precise computational models.

Axial compressive behavior of steel-hollow core partially encased composite spliced columns

Steel-hollow core partially encased composite spliced frame beam (SHSFB) amalgamates the advantages of steel and composite structures, offering excellent deformation capacity, seismic performance, material savings, and reduced weight. These advantages are also essential for frame columns. Therefore, axial compression tests were conducted on four steel-hollow core partially encased composite spliced columns (SHSCs) and one steel comparison specimen to investigate their failure modes and compressive performance. The test results revealed that the SHSC does not fully utilize the compressive performance of the composite part under compression. Based on these experimental results, improvements were made to the configuration of SHSC, and a new type of SHSC (NSHSC) was further introduced. Finite element parameter analysis was conducted on the hollow-core partially encased composite (HPEC) short columns and NSHSCs, respectively, to investigate the confined effect on concrete in the HPEC section and the influence of different parameters on the compressive performance of NSHSC. The simulated results show that the effectively confined area of concrete in the HPEC section increases with thicker H-shaped steel flanges and narrower stirrup spacing. The compressive performance and failure modes of NSHSC are determined by the lower strength of either the steel part or the composite part. Finally, by integrating concrete confined area division and the compressive stability of variable stiffness column, the calculation method for the axial compressive bearing capacity of NSHSC was proposed. The calculated values exhibit good agreement with the simulation results.

Variable stiffness performance analysis of layer jamming actuator based on bionic adhesive flaps

Soft actuators made of soft materials cannot generate precisely efficient output forces compared to rigid actuators. It is a promising strategy to equip soft actuators with variable stiffness modules of layer jamming mechanism, which could increase their stiffness as needed. Inspired by the gecko's the array of setae, bionic adhesive flaps with inclined micropillars are applied in layer jamming mechanism. In this paper, after the manufacturing process of the layer jamming actuator based on the bionic adhesive flaps is described, the equivalent stiffness models of the whole actuator are established in the unjammed and jammed states. And the shear adhesive force of a single micropillar is calculated based on the Kendall viscoelastic band model. The finite element simulation results of two bionic adhesive flaps show that the interlaminar shear stress and stiffness increase with the increase of pressure. The measurement of shear adhesive force show that the critical shear adhesive force of the bionic adhesive material is 3.2 times that of polyethylene terephthalate (PET) material, and exhibit the ability of anisotropic adhesion behavior. The variable stiffness performance of the layer jamming actuator based on bionic adhesive flaps is evaluated by three test methods, and the max stiffness reaches 8.027 N mm-1, which is 1.5 times higher than the stiffness of the layer jamming actuator based on the PET flaps. All results of simulation and experiment effectively verify the validity and superiority of applying the bionic adhesive flaps to the layer jamming mechanism to enhance the stiffness.

Vat photopolymerization 3D printing of glass microballoon-reinforced TPMS meta-structures

Advancements in additive manufacturing coincide with the influx of assiduous research in realizing complex structures using printable composite materials with tunable properties. In this research study, photocurable resins with a broad range of mechanical properties were hybridized with ceramic particles to engineer the overall mechanical response. The newly formulated printable resins comprised up to 20 wt.% glass microballoons, balancing the tunability of the composite properties and manufacturability by overcoming light-reinforcement challenges. The compressive and tensile bulk properties were first assessed using additively manufactured samples tested under quasi-static loading. Complementary digital image correlation (DIC) was used to resolve the strain fields, revealing insights about the mechanical behavior and failure modes as a function of reinforcement weight ratio. Despite the expected hyperelastic constitutive behavior and shared macromolecular composition, the neat and hybridized photocurable resins exhibited distinctive mechanical behavior, leading to the characterization of the dynamic properties as a function of temperature to ascertain the underpinnings of respective responses. Triply periodic minimal surface (TPMS) structures were also manufactured using the vat photopolymerization approach to demonstrate the utility of newly formulated printable composite resins. The printed structures were tested under compression at a quasi-static loading rate. The DIC-resolved strains revealed the underlying structural mechanics as a function of the material properties. This case study correlates the mechanics governing particulate-reinforced elastomers with the observed variations in strain development, stiffness, load-bearing capacity, and specific energy absorption for TPMS structures. Finite element analysis (FEA) based on hyperelastic potential and using the properties of the bulk resin closely matched the deformation patterns from the experimental DIC results. The outcomes of this research reveal the potential for tunable, 3D printed sports gear for impact mitigation in various biomechanical loading conditions.

Forced vibration characteristics of viscoelastic variable stiffness laminated composite plates using time and frequency domain approaches

The linear forced vibration characteristics of viscoelastic variable stiffness laminated composite plates (VVSLC) are studied using a generalized Maxwell model and finite element method. The integral form of the viscoelastic constitutive relation is converted to the incremental form for finite element formulation based on the Reissner–Mindlin plate theory. The recursive relations are developed to compute the current time-step solution using only the previous time-step solution. The periodic response directly in the time domain is obtained using shooting technique coupled with Newmark’s time integration method. The implementation of shooting technique for Boltzmann integral-based viscoelasticity for curvilinear fibre composite plates is done for the first time in this study. For the comparison purpose, the response/resonance frequency/modal loss factor is also obtained using equivalent complex modulus based viscoelastic correspondence principle. It is observed that the variation in fibre orientation and boundary conditions leads to significant variations in response, stress/moment resultant amplitude and the damping factor of the VVSLC plates. Further, the present time domain based approach is capable of predicting damping factor at all forcing frequencies whereas complex eigenvalue analysis can predict damping factor only at discrete resonance frequency. Based on the detailed studies, it is found that the curvilinear fibre composite plates depict a significant reduction in response/moment resultants compared to straight fibre composite plates.

Static and Dynamic Characteristics of 3D-Printed Orthogonal Hybrid Honeycomb Panels with Tunable Poisson’s Ratio

By adjusting the two wall angles of the orthogonal hybrid honeycomb (OHH), the tunable Poisson’s ratio change from negative to positive values and the variation in stiffness can be achieved. To effectively analyze its static and dynamic characteristics, a two-dimensional equivalent Kirchhoff–Love model (2D-EKM) is established based on the variational asymptotic method (VAM).This model aids in effectively addressing the complexity arising from anisotropy. The obtained equivalent orthotropic properties are validated through unit-cell uniaxial compression tests and three-point bending experiments on 3D-printed specimens. The numerical simulation results suggest that the VAM-based 2D-EKM can predict the in-plane and out-of-plane static behaviors of OHH panels, with a maximum error below 10%. Particularly in the dynamic analysis of a four-sided fixed OHH panel, the analysis time required by 2D-EKM is only 0.37% of that needed for the 3D FE model. The OHH-ZPR panel exhibits exceptional resistance to deformation, with a maximum deformation under in-plane tension reaching only 27% of that in the OHH-PPR panel. Moreover, each 1% increase in the height–length ratio results in a respective increase of 275.62% and 281.93% in equivalent bending stiffness along both directions. This highlights that enhancing this ratio effectively boosts the fundamental frequency compared to the elastic modulus ratio, effectively prevents low-frequency resonance occurrences, and offers vital insights for the design and optimization of OHH panels.

Development of pre-magnetized magnetorheological elastomer for bidirectionally variable stiffness applications

Development of pre-magnetized magnetorheological elastomer for bidirectionally variable stiffness applications

Hypostomus plecostomus-inspired soft sucker to adsorb slippery tissues: a stabilizing post-valvular cavity and stiffness gradient materials provide excellent adsorption performance

The hard suckers commonly used in surgical operations often cause adsorption extrusion damage to the biological tissue. To tackle this problem, from the perspective of bionics, through in-depth observation and research on the special sucker adsorption process and adsorption mechanism of hypostomus plecostomus (HP), this paper proposes a bionic soft hypostomus plecostomus sucker (BSHPS) with a variable stiffness gradient structure with a good adsorption performance on soft moist irregular biological tissues. The BSHPS comprises a lip disc, a pre-valvular cavity, and a post-valvular cavity. Through the volume changes of the pre- and post-valvular cavities, a pressure difference is generated between the inside and outside of the sucker, enabling the lip disc to remain sealed. The experiments were carried out by an automatic tensile force measurement system equipped with a vacuum pump, and the results showed that in slippery environment, the adsorption performance of the BSHPS is improved by a maximum of 61.9% compared to that in dry environment. On a biological tissue surface, the adsorption force is as high as 13.7765 N. The most important advantage of the proposed BSHPS is that it can be firmly adsorbed the surface of soft moist irregular biological tissues, effectively slowing down or avoiding adsorption extrusion damage to the biological tissue. Therefore, the BSHPS is expected to have good application prospects in modern surgical medicine.

A comprehensive experimental analysis of the local passive response across the healthy porcine left ventricle

This work provides a comprehensive characterization of porcine myocardial tissue, combining true biaxial (TBx), simple triaxial shear (STS) and confined compression (CC) tests to analyze its elastic behavior under cyclic loads. We expanded this study to different zones of the ventricular free wall, providing insights into the local behavior along the longitudinal and radial coordinates. The aging impact was also assessed by comparing two age groups (4 and 8 months). Resulting data showed that the myocardium exhibits a highly nonlinear hyperelastic and incompressible behavior. We observed an anisotropy ratio of 2-2.4 between averaged peak stresses in TBx tests and 1-0.59-0.40 orthotropy ratios for normalised fiber-sheet-normal peak stresses in STS tests. We obtained a highly incompressible response, reaching volumetric pressures of 2-7 MPa for perfused tissue in CC tests, with notable differences when fluid drainage was allowed, suggesting a high permeability. Regional analysis showed reduced stiffness and anisotropy (20-25%) at the apical region compared to the medial, which we attributed to differences in the fiber field dispersion. Compressibility also increased towards the epicardium and apical regions. Regarding age-related variations, 8-month animals showed stiffer response (at least 25% increase), particularly in directions where the mechanical stress is absorbed by collagenous fibers (more than 90%), as supported by a histological analysis. Although compressibility of perfused tissue remained unchanged, permeability significantly reduced in 8-month-old animals. Our findings offer new insights into myocardial properties, emphasizing on local variations, which can help to get a more realistic understanding of cardiac mechanics in this common animal model. Statement of significanceIn this work, we conducted a comprehensive analysis of the passive mechanical behavior of porcine myocardial tissue through biaxial, triaxial shear, and confined compression tests. Unlike previous research, we investigated the variation in mechanical response across the left ventricular free wall, conventionally assumed homogeneous, revealing differences in terms of stiffness and compressibility. Additionally, we evaluated age-related effects on mechanical properties by comparing two age groups, observing significant variations in stiffness and permeability. To date, there has been no such in-depth exploration of myocardial elastic response and compressibility considering regional variations along the wall and may contribute to a better understanding of the cardiac tissue’s passive mechanical response.

Pattern formation on hydrophobic PDMS substrates by evaporating droplets: combined effect of substrate stiffness, relative humidity and particle size

Desiccation patterns left by micro-droplets of water impregnated with particles on hydrophobic substrates have been analyzed with respect to variations in the elastic stiffness of the substrates, particle size and relative humidity. The complex and unique patterns obtained, have been analyzed and explained in terms of the time scales of moving Triple Phase Line (TPL) on substrate and substrate relaxation rate. The rate of TPL movement is found to depend on the relative humidity and substrate stiffness. In turn, this affects the contact angle hysteresis. Particle movement is a result of viscous drag and inertia apart from electrostatic interactions. We have successfully explained the myriad patterns obtained from drying droplets via systematic rheological measurements along with an understanding of the role of all the effective forces and their time scales of action.

Bending analysis of thin plates with variable stiffness resting on elastic foundation via a two-network strategy physics-informed neural network method

A physics-informed neural network method based on a two-network strategy is introduced to address the bending problem of thin plates with variable stiffness resting on an elastic foundation. This problem is governed by a fourth-order partial differential equation (PDE), and the use of a one-network strategy to solve the PDE directly may lead to convergence issues due to singular points. Following the principles of Kirchhoff plate theory, the governing PDE is equivalently transformed into four second-order PDEs. A two-network strategy is employed for solution. We present numerical examples under various load conditions, plate geometries, foundation types, thicknesses, and material properties. The obtained results are validated against finite element method (FEM) solutions and literature. Discussions on alternative network strategies were conducted, and this study reveals that the presented two-network strategy have proven to be effective and robust. It also facilitates easier imposition of boundary conditions.

Joints mechanical characteristics of prefabricated subway station considering bending stiffness difference

In prefabricated subway stations, the presence of joints leads to an uneven circumferential distribution of structural stiffness. However, there has been limited research focusing on the variability in bending stiffness of joints so far. Therefore, this paper proposes a theoretical framework to study deformation characteristics considering the differences in bending stiffness. This study aim to analyze the deformation characteristics of prefabricated structures, with a specific focus on the impact of variations in bending stiffness on the overall structural behavior. The research scope includes the calculation methods for the bending stiffness of joints, predicting maximum settlement of the top plate, and analyzing the influence of key parameters such as joint positions, geometric shapes, and dimensions, overburden density γ, lateral earth pressure coefficient λ, overburden thickness hf, and concrete density ρ on the joint bending stiffness. Results validate the reliability of the proposed method for calculating joint bending stiffness and demonstrate the key factors contributing to differences in bending stiffness.

A new approach to the calculation of variable tangent bending stiffness for helical strands

As the cross-section of the helical strand increases, the effect of its nonlinear bending characteristics becomes significant. To accurately simulate the response of helical strands under such conditions using the finite element method, determining the tangent bending stiffness of helical strands is indispensable. However, the approach of calculating the tangent bending stiffness of helical strands based on the stick-slip state of wires is not universally applicable across all strand models. In this study, we propose an approach for calculating the tangent bending stiffness of strands based on two mechanical models of helical strands. This proposed approach uses the ratio of the “actual increment” to the “theoretical maximum increment” of the nonlinear component of the wire axial force to calculate the contribution of one wire to the tangent bending stiffness of the strand. Significantly, this approach can be applied to different strand models, each of which may adopt different slip criteria. By comparing the results with the numerical solutions, we validate the effectiveness of the proposed approach for calculating the tangent bending stiffness of helical strands on different strand models. Furthermore, it is pointed out that the analytical results of wire sliding may vary significantly depending on the adopted slip criteria.

A Reconfigurable Soft Helical Actuator with Variable Stiffness Skeleton.

Due to their exceptional adaptability, inherent compliance, and high flexibility, soft actuators have significant advantages over traditional rigid actuators in human-machine interaction and in grasping irregular or fragile objects. Most existing soft actuators are designed using preprogramming methods, which schedule complex motions into flexible structures by correctly designing deformation constraints. These constraints restrict undesired deformation, allowing the actuator to achieve the preprogrammed motion when stimulated. Therefore, these actuators can only achieve a certain type of motion, such as extension, bending, or twisting, since it is impossible to adjust the deformation constraints once they are embedded into the structures. In this study, we propose the use of variable stiffness materials, such as shape memory polymer (SMP), in the structural design of soft actuators to achieve variable stiffness constraints. A reconfigurable soft helical actuator with a variable stiffness skeleton is developed based on this concept. The skeleton, made of SMP, is encased at the bottom of a fiber-reinforced chamber. In its high-stiffness state, the SMP constrains the deformation toward the skeleton when the actuator is pressurized. This constraint is removed once the SMP skeleton is heated, endowing the actuator with the ability to switch between bending and helical motion in real-time. A theoretical model is proposed to predict the behavior of the actuator when driven by pressure, and experiments are conducted to verify the model's accuracy. In addition, the influence of different design parameters is investigated based on experimental results, providing reference guidelines for the design of the actuator.

An analytic solution for bending of multilayered structures with interlayer-slip

Layered structures are prevalent in both natural environments and engineered composite materials. The elastic bending behavior of these structures is primarily governed by properties of their abundant interfaces. While the behavior of two- and three-layered beams has been extensively studied, this research shifts the focus to the impact of elastic shearing at interfaces on the deflection of multilayered structures comprising a substantial number of layers. We present an analytical solution indicating that the bending properties of multilayered beams and plates are nonlinearly dependent on interfacial stiffness. Denoting Se as the effective bending stiffness of an n-layered beam of length L, and S0 as the bending stiffness of a perfectly bound counterpart, we arrive at SeS0=11+(n2−1)tanhαLαL where αL represents a dimensionless parameter related to geometry and material properties. The analytical solutions, validated through finite element simulations, highlight the substantial variations in stiffness across different layered structures. This solution could also be instrumental in assessing interfacial damage and delamination in lamellar composites.

Active prediction compensation strategy: A new positioning compensation technique for improving the accuracy of the dual ball screw feed mechanism under load

The dual ball screw feed mechanism (DBSFM) is commonly employed in high-end machining applications. However, its accuracy is challenging to enhance due to variations in the axial stiffness of the dual actuators under load, making geometric error compensation (GEC) difficult. To address this, our research establishes a comprehensive error model that integrates geometric error and load-induced error (LIE) to improve feeding accuracy. The axial stiffness matrix of the DBSFM is identified using motor current information, and an active prediction error matrix is defined based on the geometric error model, milling force model, and axial stiffness matrix. We propose and analyze the active prediction compensation (APC) strategy as a new method to enhance accuracy under load. Experimental validation using a gantry-type machine tool demonstrates that the APC strategy can reduce the positioning error of the DBSFM to ±2 μm under load, representing significant improvements over the established GEC method. Specifically, the APC strategy achieves a 53.07% and 57.04% enhancement in accuracy along the two axes. This work illustrates the effectiveness of the APC strategy in reducing positioning errors and improving feeding accuracy in DBSFM machining processes.

Design of a novel intelligent adaptive fractional-order proportional-integral-derivative controller for mitigation of seismic vibrations of a building equipped with an active tuned mass damper

The primary objective of this study is to introduce a novel adaptive fractional order proportional–integral–derivative (FOPID) controller. The adaptive FOPID controller’s parameters are dynamically adjusted in real-time using five distinct multilayer perceptron neural networks. The extended Kalman filter (EKF) is employed to facilitate the parameter-tuning process. A multilayer perceptron neural network, trained using the error Backpropagation algorithm, is employed to identify the structural system and estimate the plant. The real-time estimated Jacobian is applied to the controller to control the model. The stability and robustness of the adaptive interval type-2 fuzzy neural networks controller are enhanced by utilizing the EKF and the feedback error learning strategy for compensator tuning. This improvement increases resilience against estimation errors, seismic disturbances, and unknown nonlinear functions. The primary objective is to address the challenges posed by maximum displacement, acceleration, and drift, as well as the uncertainties arising from variations in stiffness and mass. In order to validate the reliability of the proposed controller, the performance investigation is carried out on an 11-story building equipped with an active tuned mass damper under far and near-field earthquakes. Numerical findings show the remarkable effectiveness of the proposed controllers compared to their predecessors. In addition, it is revealed that the inclusion of the adaptive interval type-2 fuzzy neural networks compensator has increased the performance of the proposed controller and shows significant capabilities in reducing the seismic responses of structures during severe earthquake events.

Intra-observer variability in liver stiffness and ultrasound attenuation parameter measurement using vibration-controlled transient elastography in patients with metabolic dysfunction-associated steatotic liver disease

Intra-observer variability in liver stiffness and ultrasound attenuation parameter measurement using vibration-controlled transient elastography in patients with metabolic dysfunction-associated steatotic liver disease

Design and Evaluation of a Novel Passive Shoulder Exoskeleton Based on a Variable Stiffness Mechanism Torque Generator for Industrial Applications

Design and Evaluation of a Novel Passive Shoulder Exoskeleton Based on a Variable Stiffness Mechanism Torque Generator for Industrial Applications