Deformation Range Research Articles

Preparation of antishrinkage and high strength poly(butylene adipate-co-terephthalate) microcellular foam via in situ fibrillation of polylactide

High-expansion-ratio microcellular poly (butylene adipate-co-terephthalate) (PBAT) foams exhibit severe shrinkage, which hinders their industrial applications. This study provides a facile method to prepare low-shrinkage, high-compressive-strength and high-resilience PBAT foam. CEPBAT/PLA blends (CE = chain extender, PLA = polylactide) were prepared via in situ fibrillation to obtain CEPBAT/PLA-S (CEPBAT/PLA containing PLA spherical phase) foam containing PLA spheres and CEPBAT/PLA-F (CEPBAT/PLA containing PLA fiber phase) foam with PLA nanofibers. The effects of the PLA nanofibers and spheres on the antishrinkage and compression strength of the PBAT foams were studied. The PLA nanofibers exhibited a higher specific surface area than the PLA spheres and a supporting network structure for the PBAT foam, thereby improving its melt strength. As a result, the antishrinkage performance and compression strength of CEPBAT/PLA-F improved by 100 % and 180 %, respectively, compared with the neat PBAT foam after aging for 144 h. However, the permanent deformation of CEPBAT/PLA-F increased only slightly after ten compression cycles. CEPBAT/PLA-F showed better antishrinkage performance, compression strength, and resilience than CEPBAT/PLA-S owing to the interface effect of the PLA nanofibers, whose nanolinear network structure provides enhancement and a larger deformation range under pressure to reduce plastic deformation.

Harnessing Deep Learning of Point Clouds for Morphology Mimicking of Universal 3D Shape‐Morphing Devices

Shape‐morphing devices, a crucial branch in soft robotics, hold significant application value in areas like human–machine interfaces, biomimetic robotics, and tools for biological systems. To achieve 3D programmable shape morphing (PSM), the deployment of array‐based actuators is essential. However, a critical knowledge gap in 3D PSM is controlling the complex systems formed by these soft actuator arrays to mimic the morphology of the target shapes. This study, for the first time, represents the configuration of shape‐morphing devices using point cloud data and employing deep learning to map these configurations to control inputs. Shape Morphing Net (SMNet), a method that realizes the regression from point cloud to high‐dimensional control input vectors, is proposed. It has been applied to 3D PSM devices with three different actuator mechanisms, demonstrating its universal applicability to inversely reproduce the target shapes. Further, applied to previous 2D PSM devices, SMNet significantly enhances control precision from 82.23% to 97.68%. In the demonstrations of morphology mimicking, 3D PSM devices successfully replicate arbitrary target shapes obtained either through 3D scanning of physical objects or via 3D modeling software. The results show that within the deformable range of 3D PSM devices, accurate reproduction of the desired shapes is achievable.

Enhanced velocity and weight-bearing capability of piezoelectric viscous-slip actuators utilising a pentagonal flexible hinge configuration

Abstract This research presents a novel piezoelectric stick–slip actuator design that capable of achieving higher speeds and handling heavier loads. This addresses the requirement for improved performance in the precision engineering industry. The symmetrical configuration of the pentagonal displacement amplification flexible hinge structure produces the transverse motion. The pentagon’s deformable range is sufficiently broad to amplify the piezoelectric stack’s output displacement and convert it into the desired transverse output displacement. To enhance the load capacity of the piezoelectric stick–slip actuator, one can raise the coupling displacement of the driving foot output. The flexible hinge construction undergoes finite element analysis, and the simulation results meet the design assumptions. The structure has been enhanced to mitigate the potential occurrence of jamming. A prototype was constructed and subjected to rigorous testing to examine its performance. The testing results indicate that the highest attainable velocity is 15.8 mm s−1, with an impressive precision of 35.9 nm. Despite being subjected to a load of 308 g, the output displacement remains steady at 0.376 mm s−1. A comparative study of experimental and finite element simulation findings demonstrates the feasibility of the structural design.

Decreasing propagation rate of interfacial debonding between a single carbon fiber and epoxy matrix under cyclic loading

The interfacial debonding of a single carbon fiber transversely embedded in a dumbbell-shaped epoxy sample was generated under cyclic loading, and images were captured using synchrotron radiation X-ray computed tomography. A fatigue testing machine driven by a piezoelectric actuator placed along the beamline for in situ observation was developed for precise alignment. Interfacial debonding was initially observed under a static tensile load and was confirmed to be almost of the same length at both ends of the carbon fiber, implying negligible bending deformation due to inclination. Cyclic loads were then applied to the sample to capture the progressive debonding. The propagation rate of the interfacial debonding decreased as the number of cycles increased. Another sample with a single carbon fiber aligned parallel to the loading direction was prepared following a single-fiber fragmentation test. Interfacial debonding was clearly observed around the fiber breakage. Cyclic loads were also applied to this sample; however, no progression of the interfacial debonding was evident. Degradation of the interfacial strength between the carbon fiber and epoxy matrix was not confirmed under cyclic loading within the elastic deformation range.

Crack tip stress intensification in strain-induced crystallized elastomer

Natural rubber (NR) exhibits strain-induced crystallization (SIC), enhancing tearing strength and crack resistance. However, the reinforcement mechanism along with nonuniform strain around a crack tip remains unclear. We reveal the nonuniform stress field around a crack tip using the DIC-based deformation field data and a hyperelasticity approach. A hyperelastic strain energy density function (W) is derived to be able to replicate stress-strain data across various deformations, encompassing equal and unequal biaxial, uniaxial, and pure shear stretching. These data cover the full range and magnitude of deformations around the crack tip. SIC significantly impacts the singular behaviors of strain and stress near the crack tip, causing a pronounced stress increase and strain decrease within the SIC zone that extends up to approximately 100 μm away from the crack tip. This results in a distinct crossover in singularity power-law index between the SIC zone and the fully amorphous zone. With increasing crack opening, the stress upturn intensifies, and the crossover shifts away from the crack tip due to SIC zone enlargement and local crystallinity increase. These findings deepen our understanding of the physics of SIC near crack tips and its reinforcement mechanism in strain-induced crystallizable soft solid materials.

Determination and Verification of the Johnson–Cook Constitutive Model Parameters in the Precision Machining of Ti6Al4V Alloy

Numerical simulations of the cutting process play a key role in manufacturing and cost optimization. Inherent in finite element analysis (FEA) simulations is the correct description of material behavior during machining. For this purpose, various material models are used to describe the behavior of the material in the range of high deformation, high temperature values, and high strain rates. Very often the Johnson–Cook (JC) material model is used for this purpose; however, the correct determination of the material constants of this model is a key aspect. Therefore, this paper presents a procedure for determining the material constants of the JC model using an analytical method based on normalized tensile and compression testing of the material for different strain rates over a wide temperature range. After determining the material constants, the authors conducted numerical simulations of the orthogonal turning of Ti6Al4V titanium alloy using the obtained constants. Validation of the obtained results with those obtained in experimental studies was also carried out. The outcomes demonstrated that the difference between FEM simulation and experimental tests did not exceed 0.02 mm (14%) in the case of chip thickness,. Much smaller differences were obtained for the temperature in the cutting zone, where the maximum difference was about 45 °C (4%). Comparing the components of the cutting force, we found that, in the case of the main cutting force, in most cases, the differences did not exceed 70 N (8%). After the verification of the obtained results, it was also found that the determined material constants of the Johnson–Cook model can be successfully used in FEM modeling of the cutting process of Ti6Al4V titanium alloy for the adopted range of values of technological parameters.

Integrating Clay Modeling in Implant Fabrication for Craniofacial Defect.

Manufacturing craniofacial implants using 3-dimensional (3D) methods and computed tomography data has become popular. The image object for the defect is produced as the first step, followed by several methods to create the implant. The authors have used a novel method that combines clay modeling with 3D scanning to create implants for craniofacial contour reconstruction. This approach does not require complicated resources. The method allows for high customization and immediate modifications, resulting in implants that achieve an accurate fit and high patient satisfaction. It is particularly beneficial for addressing complex defects and achieving aesthetic improvements. In addition, it reduces the need for cumbersome digital processing and expensive materials, making it a practical and feasible solution for a wide range of craniofacial deformities.

Effect of symmetrical biaxial tension on the magnetic properties of the composite specimen of two steel plates with different mechanical and magnetic properties

The results of studying the behavior of the magnetic characteristics of two-layer material containing layers of annealed sheet low-carbon Steel 15 and sheet metastable austenitic 12Kh18N9Т steel, subjected to cold rolling with a compression of 50 %, under biaxial symmetric tension have been presented. Experiments on biaxial deformation were carried out on the original biaxial testing machine, allowed to determine the physical properties of materials during elastic-plastic deformation independently along two axes. It has been shown that the coercive force of the studied two-layer material vary monotonically over the entire range of elastic-plastic biaxial deformation and can be used as an informative parameter for assessing the it’s stresses and deformations.

Deformation monitoring for fixed-wing UAS through Inverse Mesh-free Method

This study proposes the Inverse Local Radial Point Interpolation Method (iLRPIM) for reconstructing the deformation of irregular plate structures. The proposed methodology eliminates the drawbacks of the existing inverse finite-element method (iFEM), where the Jacobian matrix results in reduced computational accuracy for irregular plate-shape sensing. To this end, this paper released from the element and used the Mesh-Free method to describe the calculated strains. Subsequently, the system equation was formulated by minimizing the error between the measured and calculated strains. The deformation parameters were then computed by solving this system equation. Additionally, compared to iFEM, iLRPIM allows for easier adjustment of the interpolation function, making it more suitable for real-world engineering applications. The effectiveness of iLRPIM has been validated through simulations and practical experiments using four typical models. In simulations of the UAS wing box equivalent model, peak errors were below 0.8 mm for a deformation range of 25 mm. In practical scenarios, peak errors were below 3.1 mm for a deformation range of 85 mm. These results underscore the system’s capability to accurately sense the shapes of irregular plate structures using iLRPIM.

Experimental study on non-load bearing multi-span sandwich wall panels for blast mitigation

Sandwich wall panels are known for their ability to provide resistance over a wide deformation range, rendering them suitable for blast resistance applications. These panels consist of layers of concrete with an insulating core, offering a structural solution with enhanced performance. Quasi-static testing was conducted on multi-span sandwich wall panels with intermediate connections to evaluate their behavior under controlled loading conditions. A total of twelve two-span details were examined and selected to match the standard designs employed in the Tilt-Up Construction (TCA) and Prestressed/Precast Concrete Industry (PCI). Among these details, three belonged to the TCA type with two duplicates, while the remaining two were representative of PCI designs with three duplicates. The results obtained from the quasi-static testing indicate that insulated sandwich wall panels possess sufficient deformation capability to meet the current blast response criteria. To assess the findings of the static experiments to the prevailing response limits, the outcomes were distilled into a multi-linear static resistance analysis. The findings support the use of insulated precast concrete (PC) sandwich wall panels, highlighting their suitability for blast-resistant designs within the constraints of current blast design limitations. Specimens with Halfen connectors showed 32 % higher energy absorption and a 58 % advantage over Stud connectors, making them superior for robust blast resistance applications.

An adhesive, highly stretchable and low-hysteresis alginate-based conductive hydrogel strain sensing system for motion capture

A strain sensor stands as an indispensable tool for capturing intricate motions in various applications, ranging from human motion monitoring to electronic skin and soft robotics. However, existing strain sensors still face difficulties in simultaneously achieving superior sensing performance sufficing for practical applications like high stretchability and low hysteresis, as well as seamless device fabrication like desirable interfacial adhesion and system-level integration. Herein, we develop a highly stretchable and low-hysteresis strain sensor with adhesive poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS)/polyacrylamide (PAAm)‑sodium alginate (SA) composite hydrogel, allowing the successful construction of a wireless motion capture sensing system that can provide precise data collection within a large deformation range. The resultant composite hydrogel displays favorable interfacial adhesion and robust mechanical stability, and the fabricated strain sensor demonstrates a wide working strain range (up to 500 %) with high sensitivity (gauge factor = 11) and ultra-low hysteresis (1.52 %), outperforming previous PEDOT-based hydrogel strain sensors. Enabled by the intriguing material properties and high sensing performance, we further demonstrate the fabrication and integration of a wireless motion capture sensing system for diverse applications like human motion monitoring, gesture recognition, and interactive communication.

EVALUATION OF TECHNOLOGICAL PLASTICITY OF HIGH BORON CORROSION-RESISTANT STEEL DURING HOT DEFORMATION OF PIPES USED FOR SPENT NUCLEAR FUEL STORAGE

Statement of the problem. The sustainable development of the global nuclear power industry in the future depends on how effectively the problems of radiation safety and nuclear proliferation are addressed. Such problems occur, among other things, at the final stage of the nuclear fuel cycle – spent fuel management. This task is currently on the agenda of both the international community and national governments of countries that develop or intend to develop nuclear energy [1−3]. Today, in connection with ensuring the safety of nuclear energy, boron-containing steels are widely used in the world practice as a material for biological protection and for the manufacture of special equipment parts. This is due to the fact that the B10 isotope in steels provides neutron capture [4]. Hexagonal pipes made of high-boron steel were needed to shield the support cover of the compacted spent fuel storage facility at nuclear power plants. Corrosion-resistant steels alloyed with boron are widely used in the nuclear power industry due to their special nuclear properties. During the operation of nuclear power plants, fuel assemblies that have served their useful life must be stored in special storage facilities using containers – hexagonal tubes made of 04Сr14Ti3B2V steel. To reduce costs during in the construction and operation of NPPs, part of the spent nuclear fuel management should be performed at Ukrainian enterprises. This will provide a significant import substitution effect. To manufacture hexagonal tubes from 04Сr14Ti3B2V steel according to the ingot-hot deformation-profiling-heat treatment scheme, it is necessary to develop the parameters of hot deformation and subsequent technological operations. The use of these pipes in compacted spent fuel storage facilities of NPPs will allow to increase the storage capacity by 2 times, which will give a significant national economic effect Material and methods of research. Material used for the study was steel 04Сr14Ti3B2V (CS-82), smelted using two variants (vacuum-induction – “VI” and vacuum-induction followed by vacuum-arc remelting – (“VD”). Steel grade 04Сr14Ti3B2V belongs to high-alloy, corrosion-resistant ferritic steels with a high boron content of up to 2 %. The method of differential thermal analysis was used to study the phase transformation temperatures in the steel. X-ray diffraction and micro-X-ray spectral analysis were used to assess the phase state. The steel samples were tested for weldability After cooling, the welded samples were subjected to X-ray transmission [5]. Hot twisting tests and mechanical tests at high temperatures were also performed. The macro- and microstructure of the metal was studied. Results. The macro- and microstructure of steel was evaluated depending on the smelting method. The phase composition of the steel was studied. The study of the plastic properties of steel ChS-82 by means of penetration and hot twisting tests showed that the temperature range of maximum plasticity is in a wide range (from 1 025 to 1 150 0C) with a rather low resistance to deformation. During hot deformation in the temperature range of 1 175 0C and above, metal fracture was observed along the grain boundaries at the melting points of the Cr−Fe−B boride phase. The optimal temperature range for hot deformation of steel ChS-82 is 1 000−1 050 ⁰С. Scientific novelty. For corrosion-resistant high boron steel used for spent nuclear fuel storage, the temperature range of hot deformation was selected and the structural and phase composition was estimated, which will allow deforming the metal on the piercing mill and manufacturing pipes.

No Radiographic Evidence of Medial Collateral Ligament Elongation in Valgus Osteoarthritic Knees Enables Treatment with Kinematically Aligned Total Knee Arthroplasty.

When performing caliper-verified kinematically aligned total knee arthroplasty (KA TKA) in the osteoarthritic (OA) knee with valgus deformity, an elongated medial collateral ligament (MCL) could result in a valgus setting of the tibial component. The present study analyzed KA TKA in patients with valgus deformities (i.e., tibiofemoral angle > 10 degrees of valgus) and determined (1) the occurrence of radiographic MCL elongation, (2) the incidence of lateral collateral ligament (LCL) and posterior cruciate ligament (PCL) release and the use of constrained components, and (3) whether the 1-year Forgotten Joint Score (FJS), Oxford Knee Score (OKS), Knee Injury and Osteoarthritis Outcome Score for Joint Replacement (KOOS JR), and Likert satisfaction score were comparable to KA TKAs for OA deformities ≤10 degrees of valgus. One hundred and two consecutive patients who underwent KA TKA by a single surgeon were analyzed radiographically and clinically at a minimum follow-up of 1 year. Radiographic MCL elongation was identified by a greater than 1 degree of valgus orientation of the tibial component relative to the OA tibial joint line. Twenty-six patients had a radiographic anatomic tibiofemoral angle greater than 10 degrees of valgus (range of OA deformity: 11-23 degrees of valgus). Seventy-six had an OA deformity ≤10 degrees of valgus (10-degree valgus to -14-degree varus). No patient had MCL elongation or a ligament release, or required constrained components. The median FJS of 78, OKS of 42, and KOOS JR of 76, and the 85% satisfaction rate of the patients with greater than 10 degrees of OA valgus deformity were not significantly different from those with ≤10 degrees of OA valgus deformity (p ≥ 0.17). Because MCL elongation was not detected in OA deformities up to 23 degrees of valgus, the risk of under-correcting the valgus deformity leading to instability and poor outcome scores is low when performing KA TKA using primary components without releasing the LCL and/or PCL. LEVEL OF EVIDENCE:: IV.

Fluid-structure interaction simulation of the three-leaflet aortic valve using COMSOL

The simulation of the aortic valve (AV) remains challenging due to its geometric complexity and the multi-physics nature of the problem. In this study, we utilized COMSOL to establish a three-dimensional, three-leaflet AV fluid-structure interaction model and investigated the influence of material properties on the valve's mechanical behavior in a healthy state. The results indicated that variations in the aortic wall material model had a minor impact on AV hemodynamics. Additionally, while the linear elastic properties of the leaflets limit valve opening and closing, this material model allows for rapid assessment of AV performance within the range of material deformation.

Advancing the performance characteristics of rubber asphalt mixtures through the integration of Basic Oxygen Furnace (BOF) slag: A focus on static and dynamic mechanical enhancements.

To investigate the advantageous effects of incorporating industrial solid waste basic oxygen furnace (BOF) slag on the mechanical characteristics of warm-mixed rubber asphalt (WMRA) and hot-mixed rubber asphalt (HMRA) mixture, varying proportions of BOF slag were substituted for limestone coarse aggregates (0%, 25%, 50%, and 75%). Additionally, a 1.5% dosage of Sasobit warm-mixed modifier was introduced to prepare the rubber asphalt. Subsequent to preparation, both static mechanical tests (including Marshall and indirect tensile tests) and dynamic mechanical tests (including dynamic creep and elastic modulus tests) were conducted to evaluate the influence of BOF slag on the mechanical behavior of WMRA and HMRA mixtures across different substitution levels. Following testing, a two-way analysis of variance (ANOVA) was employed to dissect the impact of BOF slag content and Sasobit warm-mixed modifier on the static and dynamic mechanical properties of the rubber asphalt mixtures. The findings reveal that BOF slag exhibits commendable engineering aggregate properties, enabling substantial substitution of coarse aggregates in both HMRA and WMRA mixtures. As the proportion of BOF slag increases, it enhances the resistance of asphalt mixtures to permanent deformation and cracking under static and dynamic loading conditions, while broadening the range of elastic deformation for both WMRA and HMRA mixtures subjected to repeated loading. Moreover, a synergistic enhancement in the resistance of rubber asphalt mixtures to dynamic load-induced deformation is observed when employing both BOF slag and Sasobit warm-mixed modifier. The findings offer valuable insights for enhancing the performance of WMRA and HMRA mixtures, as well as broadening the utilization of BOF slag and waste rubber.

Reconfigurable, Transformable Soft Pneumatic Actuator with Tunable Three-Dimensional Deformations for Dexterous Soft Robotics Applications.

Numerous soft actuators based on pneumatic network (PneuNet) design have already been proposed and extensively employed across various soft robotics applications in recent years. Despite their widespread use, a common limitation of most existing designs is that their action is predetermined during the fabrication process, thereby restricting the ability to modify or alter their function during operation. To address this shortcoming, in this article the design of a Reconfigurable, Transformable Soft Pneumatic Actuator (RT-SPA) is proposed. The working principle of the RT-SPA is analogous to the conventional PneuNet. The key distinction between the two lies in the ability of the RT-SPA to undergo controlled transformations, allowing for more versatile bending and twisting motions in various directions. Furthermore, the unique reconfigurable design of the RT-SPA enables the selection of actuation units with different sizes to achieve a diverse range of three-dimensional deformations. This versatility enhances the RT-SPA's potential for adaptation to a multitude of tasks and environments, setting it apart from traditional PneuNet. The article begins with a detailed description of the design and fabrication of the RT-SPA. Following this, a series of experiments are conducted to evaluate the performance of the RT-SPA. Finally, the abilities of the RT-SPA for locomotion, gripping, and object manipulation are demonstrated to illustrate the versatility of the RT-SPA across different aspects.

PNIPAAm-based temperature responsive ionic conductive hydrogels for flexible strain and temperature sensing

Conductive hydrogels have received much attention in the field of flexible wearable sensors due to their outstanding flexibility, conductivity, sensitivity and excellent compatibility. However, most conductive hydrogels mainly focus on strain sensors to detect human motion and lack other features such as temperature response. Herein, we prepared a strain and temperature dual responsive ionic conductive hydrogel (PPPNV) with an interpenetrating network structure by introducing a covalent crosslinked network of N-isopropylacrylamide (NIPAAm) and 1-vinyl-3-butylimidazolium bromide (VBIMBr) into the skeleton of the hydrogel composed of polyvinylalcohol (PVA) and polyvinylpyrrolidone (PVP). The PPPNV hydrogel exhibited excellent anti-freezing properties (−37.34 °C) and water retention with high stretchability (∼930 %) and excellent adhesion. As a wearable strain sensor, the PPPNV hydrogel has good responsiveness and stability to a wide range of deformations and exhibits high strain sensitivity (GF=2.6) as well as fast response time. It can detect large and subtle body movements with good signal stability. As wearable temperature sensors, PPPNV hydrogels can detect human physiological signals and respond to temperature changes, and the volumetric phase transition temperature (VPTT) can be easily controlled by adjusting the molar ratio of NIPAAm to VBIMBr. In addition, a bilayer temperature-sensitive hydrogel was prepared with the temperature responsive hydrogel by two-step synthesis, which shows great promising applications in temperature actuators.

Elastoplastic analysis on deformation and failure characteristics of surrounding rock of soft-coal roadway based on true triaxial loading and unloading tests

Since accidents such as roof caving, rock fragmentation, and severe deformation are particularly likely to occur during roadway excavation in soft and thick coal seams, grasping the range and distribution of deformation and fracturing of surrounding rock is of crucial for evaluating roadway stability and optimizing support design in such coal seams. In this study, based on the stress paths encountered during roadway excavation, true triaxial loading and unloading tests were carried out on soft coal, and the deformation and strength evolutions of soft coal under different intermediate principal stress conditions were analyzed. The test results show that the stress–strain relationship in the pre-peak plasticity-strengthening and post-peak plasticity-weakening stages follows a quadratic function, and the strengeth evolution conforms to the Mogi–Coulomb criterion. Moreover, analytical solutions for the displacement of surrounding rock, the radius of the broken zone, and the radius of the plastic zone of soft-coal roadways under excavation stress paths were derived after taking the nonlinear hardening and softening characteristics of the strain of soft coal, the Mogi–Coulomb criterion, the intermediate principal stress, and the dilatancy characteristics of surrounding rock into comprehensive consideration. Finally, in accordance with a practical engineering case, the influences of the intermediate principal stress coefficient, the lateral pressure coefficient, and the support force on the deformation and failure characteristics of the soft-coal roadway were analyzed. The analysis reveals that an increase in intermediate principal stress aggravates the deformation of surrounding rock and enlarges the plastic and broken zones; variations in the lateral pressure coefficient alter the shape of the broken zone and the distribution of surface displacement; and an increase in the support force effectively reduces the plastic zone, broken zone, and surface displacement of the roadway. The research results can provide valuable theoretical basis for the stability evaluation and support design of soft-coal roadways.

MODIFICATION OF THE EXTENDED TUBE MODEL (METM) FOR THE CHARACTERIZATION OF FILLED VULCANIZATES

ABSTRACT The aim of this study is to develop a material model for filled vulcanizates that is physically justifiable. This model builds upon the established extended tube model and is incorporated into a finite element program. The research demonstrates that the intrinsic deformation concept is inadequate for describing nonlinear deformation behavior under the assumption of incompressible, isotropic materials. Consequently, an alternative approach is proposed, employing a strain function rather than direct use of principal strains, to characterize reinforcement behavior. This strain function aligns with the first invariant of the right Cauchy-Green strain tensor over a wide deformation range. At minor deformations, the entanglements’ contribution is considered through an additional reinforcement term. The novel reinforcement function is depicted as a sum of three elements, each representing reinforcement at different strain levels: low, medium, and high. Experimental comparisons show that the Modified Extended Tube Model (METM) effectively captures the stress-strain response of filled systems across all deformation levels. Furthermore, the reinforcement function parameters, derived from fitting the METM to experimental data, offer a quantitative assessment of the fillers’ reinforcing effects, while the extended tube model parameters reflect the network characteristics.

Centrifugal Model Test of Multi-Level Slope under Combined Support of Pile-Anchor and Frame-Anchor

The combination support structure of pile-anchor and frame-anchor is widely used in multi-level slope engineering, but the relevant theoretical research lags behind engineering practice. To make up for this deficiency, this paper takes the multi-level slope under combined support of pile-anchor and frame-anchor as the research object, conducts a model test using the geotechnical centrifuge, analyzes the most relevant structural force and slope deformation in engineering, and provides some reinforcement suggestions. The test results show that the combination support structure of pile-anchor and frame-anchor has a good reinforcement effect on multi-level soil slopes, but the deformation range of the slope is greatly affected by the anchoring structure and the anchor rods located within the deformation zone. The structural force condition is significantly different from traditional structures that place the anchor rod anchoring section in a stable soil layer. According to the structural force characteristics, it is recommended that the support design fully consider the positional relationship between the anchor rods and the sliding surface. The design of the frame-anchor support section should strictly control the anchoring depth, so that the potential sliding surface of the slope can be moved backward, thereby increasing the difficulty of sliding. The design of pile-anchor support should ensure that the anchor rods have sufficient length to provide greater anchoring force, thereby improving the bearing capacity of the pile. These research results can enrich and improve the support design theory of multi-level soil slopes, providing guidance for engineering practice.