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Keywords = stiffness primitives

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19 pages, 7346 KB  
Article
Human–Robot Variable-Impedance Skill Transfer Learning Based on Dynamic Movement Primitives and a Vision System
by Honghui Zhang, Fang Peng and Miaozhe Cai
Sensors 2025, 25(18), 5630; https://doi.org/10.3390/s25185630 - 10 Sep 2025
Viewed by 366
Abstract
To enhance robotic adaptability in dynamic environments, this study proposes a multimodal framework for skill transfer. The framework integrates vision-based kinesthetic teaching with surface electromyography (sEMG) signals to estimate human impedance. We establish a Cartesian-space model of upper-limb stiffness, linearly mapping sEMG signals [...] Read more.
To enhance robotic adaptability in dynamic environments, this study proposes a multimodal framework for skill transfer. The framework integrates vision-based kinesthetic teaching with surface electromyography (sEMG) signals to estimate human impedance. We establish a Cartesian-space model of upper-limb stiffness, linearly mapping sEMG signals to end-point stiffness. For flexible task execution, dynamic movement primitives (DMPs) generalize learned skills across varying scenarios. An adaptive admittance controller, incorporating sEMG-modulated stiffness, is developed and validated on a UR5 robot. Experiments involving elastic-band stretching demonstrate that the system successfully transfers human impedance characteristics to the robot, enhancing stability, environmental adaptability, and safety during physical interaction. Full article
(This article belongs to the Section Sensors and Robotics)
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17 pages, 3691 KB  
Article
Lamellar Orientation Analysis and Mechanical Properties of Polyethylene in Stretch-Induced Crystallization
by Mohammed Althaf Hussain, Takeshi Aoyagi, Takeshi Kikutani, Wataru Takarada, Takashi Yamamoto, Syed Farooq Adil and Shigeru Yao
Polymers 2025, 17(11), 1450; https://doi.org/10.3390/polym17111450 - 23 May 2025
Viewed by 825
Abstract
Polyethylene films prepared from orientation-dependent methods are strong and resilient, have reduced permeability, and possess higher tensile strength. A molecular dynamics investigation is performed to reveal the emergence of chain folding and lamellar crystal axis alignment along the stretching axis (tilt angle) in [...] Read more.
Polyethylene films prepared from orientation-dependent methods are strong and resilient, have reduced permeability, and possess higher tensile strength. A molecular dynamics investigation is performed to reveal the emergence of chain folding and lamellar crystal axis alignment along the stretching axis (tilt angle) in the stretch-induced crystallization (SIC) of high-density polyethylene (HDPE), which mimics the internal structure of the fiber. The morphology in phase transition is assessed by the total density (ρ), degree of crystallinity (%χc), average number of entanglements per chain (<Z>), elastic modulus of the mechanical property, and lamellar chain tilt angle (θ) from the stretch-axis. The simulation emphasizes crystal formation by changing the total ρ from 0.85 g·cm−3 to 0.90 g·cm−3 and by tracking the gradual increase in % χc during stretching (~40%) and relaxation processes (~50%). Moreover, the primitive path analysis-based <Z> decreased during stretching and further in the subsequent relaxation process, supporting the alignment and thickening of the lamellar chain structure and chain folding from the random coil structure. The elastic modulus of ~350–400 MPa evidences the high alignment of the lamellar chains along the stretching axis. Consistent with the chain tilt angle of the HDPE in SAXS/WAXS experiments, the model estimated the lamellar chain title angle (θ) relative to the stretching axis to be ~20–35°. In conclusion, SIC is a convenient approach for simulating high stiffness, tensile strength, reduced permeability, and chain alignment in fiber film models, which can help design new fiber morphology-based polymers or composites. Full article
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17 pages, 17792 KB  
Article
A Novel Hand Teleoperation Method with Force and Vibrotactile Feedback Based on Dynamic Compliant Primitives Controller
by Peixuan Hu, Xiao Huang, Yunlai Wang, Hui Li and Zhihong Jiang
Biomimetics 2025, 10(4), 194; https://doi.org/10.3390/biomimetics10040194 - 21 Mar 2025
Cited by 2 | Viewed by 1169
Abstract
Teleoperation enables robots to perform tasks in dangerous or hard-to-reach environments on behalf of humans, but most methods lack operator immersion and compliance during grasping. To significantly enhance the operator’s sense of immersion and achieve more compliant and adaptive grasping of objects, we [...] Read more.
Teleoperation enables robots to perform tasks in dangerous or hard-to-reach environments on behalf of humans, but most methods lack operator immersion and compliance during grasping. To significantly enhance the operator’s sense of immersion and achieve more compliant and adaptive grasping of objects, we introduce a novel teleoperation method for dexterous robotic hands. This method integrates finger-to-finger force and vibrotactile feedback based on the Fuzzy Logic-Dynamic Compliant Primitives (FL-DCP) controller. It employs fuzzy logic theory to identify the stiffness of the object being grasped, facilitating more effective manipulation during teleoperated tasks. Utilizing Dynamic Compliant Primitives, the robotic hand implements adaptive impedance control in torque mode based on stiffness identification. Then the immersive bilateral teleoperation system integrates finger-to-finger force and vibrotactile feedback, with real-time force information from the robotic hand continuously transmitted back to the operator to enhance situational awareness and operational judgment. This bidirectional feedback loop increases the success rate of teleoperation and reduces operator fatigue, improving overall performance. Experimental results show that this bio-inspired method outperforms existing approaches in compliance and adaptability during teleoperation grasping tasks. This method mirrors how human naturally modulate muscle stiffness when interacting with different objects, integrating human-like decision-making and precise robotic control to advance teleoperated systems and pave the way for broader applications in remote environments. Full article
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15 pages, 7388 KB  
Article
Study on Heat Transfer of Copper Foam Microstructure in Phase Change Materials
by Guofeng Zhou and Yuxi Qiao
Sustainability 2025, 17(4), 1681; https://doi.org/10.3390/su17041681 - 18 Feb 2025
Cited by 2 | Viewed by 1109
Abstract
The foam metal, possessing a remarkable skeletal framework, exhibits outstanding specific strength and stiffness, in conjunction with excellent thermal conductivity. Its spatially continuous porous structure not only promotes the infiltration of phase change materials but also renders it an extraordinary enhancer of thermal [...] Read more.
The foam metal, possessing a remarkable skeletal framework, exhibits outstanding specific strength and stiffness, in conjunction with excellent thermal conductivity. Its spatially continuous porous structure not only promotes the infiltration of phase change materials but also renders it an extraordinary enhancer of thermal conductivity within phase change energy storage systems. In order to comprehensively explore the influence of copper foam structure on the heat transfer characteristics of phase change materials, this study constructs a series of structural models of copper foam frames with diverse configurations. By leveraging the finite element analysis approach, it meticulously simulates the melting processes of five unique composite copper foam structures, namely Kelvin, Gyroid, IWP, Primitive, and Hollow hexahedral. Through a detailed analysis of thermal conductivity associated with each structural model, as well as the flux variation and average temperature under a constant flow, the study scrutinizes the heat transfer properties of these disparate structures. The obtained results will provide substantial theoretical support for the optimization design of heat transfer performance in phase change heat storage systems. The results indicate that the effective thermal conductivity of MFPCMs largely depends on the structural type and its unique configuration, rather than just the porosity of the structure. Under isothermal conditions, using the melting time of the Kelvin model as a baseline, the melting time of the PCM in the Gyroid structure was reduced by approximately 20.9%, the IWP structure by 3.8%, the Primitive structure by 28.6%, and the hollow hexahedral structure by 29.9%. Under constant heat flux conditions, the melting time of the phase change material does not depend on the type of metal foam structure. The heat transfer performance of the other structures is all superior to that of the Kelvin structure. At around 150 s, all structures had their PCM completely melted, at which point the highest temperature was observed in the MFPCM based on the primitive structure, and there may be potential for further temperature increase if further studies are conducted. Therefore, these new structures hold broad application prospects in phase change energy storage systems. Full article
(This article belongs to the Section Energy Sustainability)
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22 pages, 10980 KB  
Article
Robot Variable Impedance Control and Generalizing from Human–Robot Interaction Demonstrations
by Feifei Zhong, Lingyan Hu and Yingli Chen
Mathematics 2024, 12(23), 3840; https://doi.org/10.3390/math12233840 - 5 Dec 2024
Cited by 2 | Viewed by 1975
Abstract
The purpose of this study was to ensure the compliance and safety of a robot’s movements during interactions with the external environment. This paper proposes a control strategy for learning variable impedance characteristics from multiple sets of demonstration trajectories. This strategy can adapt [...] Read more.
The purpose of this study was to ensure the compliance and safety of a robot’s movements during interactions with the external environment. This paper proposes a control strategy for learning variable impedance characteristics from multiple sets of demonstration trajectories. This strategy can adapt to the control of different joints by adjusting the parameters of the variable impedance control policy. Firstly, multiple sets of demonstration trajectories are aligned on the time axis using Dynamic Time Warping. Subsequently, the variance obtained through Gaussian Mixture Regression and a variable impedance strategy based on an improved Softplus function are employed to represent the variance as the variable impedance characteristic of the robotic arm, thereby enabling variable impedance control for the robotic arm. The experiments conducted on a self-designed robotic arm demonstrate that, compared to other variable impedance methods, the motion accuracy of the trajectories of joints 1 to 4 improved by 57.23%, 3.66%, 5.36%, and 20.16%, respectively. Additionally, a stiffness-variable segmented generalization method based on Dynamic Movement Primitive is proposed to achieve variable impedance control in various task environments. This strategy fulfills the requirements for compliance and safety during robot interactions. Full article
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16 pages, 2858 KB  
Article
Robot Learning Method for Human-like Arm Skills Based on the Hybrid Primitive Framework
by Jiaxin Li, Hasiaoqier Han, Jinxin Hu, Junwei Lin and Peiyi Li
Sensors 2024, 24(12), 3964; https://doi.org/10.3390/s24123964 - 19 Jun 2024
Cited by 1 | Viewed by 1407
Abstract
This paper addresses the issue of how to endow robots with motion skills, flexibility, and adaptability similar to human arms. It innovatively proposes a hybrid-primitive-frame-based robot skill learning algorithm and utilizes the policy improvement with a path integral algorithm to optimize the parameters [...] Read more.
This paper addresses the issue of how to endow robots with motion skills, flexibility, and adaptability similar to human arms. It innovatively proposes a hybrid-primitive-frame-based robot skill learning algorithm and utilizes the policy improvement with a path integral algorithm to optimize the parameters of the hybrid primitive framework, enabling robots to possess skills similar to human arms. Firstly, the end of the robot is dynamically modeled using an admittance control model to give the robot flexibility. Secondly, the dynamic movement primitives are employed to model the robot’s motion trajectory. Additionally, novel stiffness primitives and damping primitives are introduced to model the stiffness and damping parameters in the impedance model. The combination of the dynamic movement primitives, stiffness primitives, and damping primitives is called the hybrid primitive framework. Simulated experiments are designed to validate the effectiveness of the hybrid-primitive-frame-based robot skill learning algorithm, including point-to-point motion under external force disturbance and trajectory tracking under variable stiffness conditions. Full article
(This article belongs to the Section Sensors and Robotics)
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20 pages, 9545 KB  
Article
Mechanical Behaviour of Photopolymer Cell-Size Graded Triply Periodic Minimal Surface Structures at Different Deformation Rates
by Yunus Emre Yılmaz, Nejc Novak, Oraib Al-Ketan, Hacer Irem Erten, Ulas Yaman, Anja Mauko, Matej Borovinsek, Miran Ulbin, Matej Vesenjak and Zoran Ren
Materials 2024, 17(10), 2318; https://doi.org/10.3390/ma17102318 - 14 May 2024
Cited by 4 | Viewed by 1617
Abstract
This study investigates how varying cell size affects the mechanical behaviour of photopolymer Triply Periodic Minimal Surfaces (TPMS) under different deformation rates. Diamond, Gyroid, and Primitive TPMS structures with spatially graded cell sizes were tested. Quasi-static experiments measured boundary forces, representing material behaviour, [...] Read more.
This study investigates how varying cell size affects the mechanical behaviour of photopolymer Triply Periodic Minimal Surfaces (TPMS) under different deformation rates. Diamond, Gyroid, and Primitive TPMS structures with spatially graded cell sizes were tested. Quasi-static experiments measured boundary forces, representing material behaviour, inertia, and deformation mechanisms. Separate studies explored the base material’s behaviour and its response to strain rate, revealing a strength increase with rising strain rate. Ten compression tests identified a critical strain rate of 0.7 s−1 for “Grey Pro” material, indicating a shift in failure susceptibility. X-ray tomography, camera recording, and image correlation techniques observed cell connectivity and non-uniform deformation in TPMS structures. Regions exceeding the critical rate fractured earlier. In Primitive structures, stiffness differences caused collapse after densification of smaller cells at lower rates. The study found increasing collapse initiation stress, plateau stress, densification strain, and specific energy absorption with higher deformation rates below the critical rate for all TPMS structures. However, cell-size graded Primitive structures showed a significant reduction in plateau and specific energy absorption at a 500 mm/min rate. Full article
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17 pages, 38360 KB  
Article
Design and Characterization of Soft Fabric Omnidirectional Bending Actuators
by Kyungjoon Lee, Khulan Bayarsaikhan, Gabriel Aguilar, Jonathan Realmuto and Jun Sheng
Actuators 2024, 13(3), 112; https://doi.org/10.3390/act13030112 - 14 Mar 2024
Cited by 5 | Viewed by 3353
Abstract
Soft robots, inspired by biological adaptability, can excel where rigid robots may falter and offer flexibility and safety for complex, unpredictable environments. In this paper, we present the Omnidirectional Bending Actuator (OBA), a soft robotic actuation module which is fabricated from off-the-shelf materials [...] Read more.
Soft robots, inspired by biological adaptability, can excel where rigid robots may falter and offer flexibility and safety for complex, unpredictable environments. In this paper, we present the Omnidirectional Bending Actuator (OBA), a soft robotic actuation module which is fabricated from off-the-shelf materials with easy scalability and consists of three pneumatic chambers. Distinguished by its streamlined manufacturing process, the OBA is capable of bending in all directions with a high force-to-weight ratio, potentially addressing a notable research gap in knit fabric actuators with multi-degree-of-freedom capabilities. We will present the design and fabrication of the OBA, examine its motion and force capabilities, and demonstrate its capability for stiffness modulation and its ability to maintain set configurations under loads. The mass of the entire actuation module is 278 g, with a range of omnidirectional bending up to 90.80°, a maximum tolerable pressure of 862 kPa, and a bending payload (block force) of 10.99 N, resulting in a force-to-weight ratio of 39.53 N/kg. The OBA’s cost-effective and simple fabrication, compact and lightweight structure, and capability to withstand high pressures present it as an attractive actuation primitive for applications demanding efficient and versatile soft robotic solutions. Full article
(This article belongs to the Special Issue Soft Robotics: Actuation, Control, and Application)
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20 pages, 9122 KB  
Article
Modal Response Improvement of Periodic Lattice Materials with a Shear Modulus-Based FE Homogenized Model
by Tianheng Luo, Lizhe Wang, Fuyuan Liu, Min Chen and Ji Li
Materials 2024, 17(6), 1314; https://doi.org/10.3390/ma17061314 - 12 Mar 2024
Cited by 5 | Viewed by 1945
Abstract
Lattice materials are widely used in industries due to their designable capabilities of specific stiffness and energy absorption. However, evaluating the mechanical response of macroscopic lattice structures can be computationally expensive. Homogenization-based multi-scale analysis offers an efficient approach to address this issue. To [...] Read more.
Lattice materials are widely used in industries due to their designable capabilities of specific stiffness and energy absorption. However, evaluating the mechanical response of macroscopic lattice structures can be computationally expensive. Homogenization-based multi-scale analysis offers an efficient approach to address this issue. To achieve a simpler, while precise, homogenization, the authors proposed an equidistant segmentation (ES) method for the measurement of the effective shear modulus. In this method, the periodic boundary conditions (PBCs) are approximated by constraining the lateral displacement of nodes between parallel layers of periodic cells. The validations were applied to three typical lattice topologies: body-centered cubic (BCC) lattices, gyroid-, and primitive-triply periodic minimal surface (TPMS) lattices, to predict and compare their anti-vibration capacities. The results demonstrated the rationality and the promising precision of the multi-scale-based equivalent modal analysis through the proposed method and that it eliminated the geometric limitation of lattices with diverse frameworks. Overall, a higher anti-vibration capacity of TPMS was observed. In the study, the authors examined the influence of the relative densities on the balance between the anti-vibration capacity and loading capacity (per unit mass) of the TPMS topologies. Specifically, the unit mass of the TPMS with lower relative densities was able to resist higher frequencies, and the structures were dominated by the anti-vibration capacity. In contrast, a higher relative density is better when emphasizing the loading capacity. These findings may provide notable references to the designers and inform the selection of lattice materials for various industrial applications. Full article
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18 pages, 14551 KB  
Article
Design and Optimization of 3D-Printed Variable Cross-Section I-Beams Reinforced with Continuous and Short Fibers
by Xin Zhang, Peijie Sun, Yu Zhang, Fei Wang, Yun Tu, Yunsheng Ma and Chun Zhang
Polymers 2024, 16(5), 684; https://doi.org/10.3390/polym16050684 - 2 Mar 2024
Cited by 6 | Viewed by 2482
Abstract
By integrating fiber-reinforced composites (FRCs) with Three-dimensional (3D) printing, the flexibility of lightweight structures was promoted while eliminating the mold’s limitations. The design of the I-beam configuration was performed according to the equal-strength philosophy. Then, a multi-objective optimization analysis was conducted based on [...] Read more.
By integrating fiber-reinforced composites (FRCs) with Three-dimensional (3D) printing, the flexibility of lightweight structures was promoted while eliminating the mold’s limitations. The design of the I-beam configuration was performed according to the equal-strength philosophy. Then, a multi-objective optimization analysis was conducted based on the NSGA-II algorithm. 3D printing was utilized to fabricate I-beams in three kinds of configurations and seven distinct materials. The flexural properties of the primitive (P-type), the designed (D-type), and the optimized (O-type) configurations were verified via three-point bending testing at a speed of 2 mm/min. Further, by combining different reinforcements, including continuous carbon fibers (CCFs), short carbon fibers (SCFs), and short glass fibers (SGFs) and distinct matrices, including polyamides (PAs), and polylactides (PLAs), the 3D-printed I-beams were studied experimentally. The results indicate that designed and optimized I-beams exhibit a 14.46% and 30.05% increase in the stiffness-to-mass ratio and a 7.83% and 40.59% increment in the load-to-mass ratio, respectively. The CCFs and SCFs result in an outstanding accretion in the flexural properties of 3D-printed I-beams, while the accretion is 2926% and 1070% in the stiffness-to-mass ratio and 656.7% and 344.4% in the load-to-mass ratio, respectively. For the matrix, PAs are a superior choice compared to PLAs for enhancing the positive impact of reinforcements. Full article
(This article belongs to the Special Issue Additive Manufacturing of Fibre Reinforced Polymer Composites)
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14 pages, 10164 KB  
Article
Prediction of Compressive Behavior of Laser-Powder-Bed Fusion-Processed TPMS Lattices by Regression Analysis
by Uğur Şimşek, Orhan Gülcan, Kadir Günaydın and Aykut Tamer
J. Manuf. Mater. Process. 2024, 8(1), 16; https://doi.org/10.3390/jmmp8010016 - 21 Jan 2024
Cited by 8 | Viewed by 3326
Abstract
Triply periodic minimal surface (TPMS) structures offer lightweight and high-stiffness solutions to different industrial applications. However, testing of these structures to calculate their mechanical properties is expensive. Therefore, it is important to predict the mechanical properties of these structures effectively. This study focuses [...] Read more.
Triply periodic minimal surface (TPMS) structures offer lightweight and high-stiffness solutions to different industrial applications. However, testing of these structures to calculate their mechanical properties is expensive. Therefore, it is important to predict the mechanical properties of these structures effectively. This study focuses on the effectiveness of using regression analysis and equations based on experimental results to predict the mechanical properties of diamond, gyroid, and primitive TPMS structures with different volume fractions and build orientations. Gyroid, diamond, and primitive specimens with three different volume fractions (0.2, 0.3, and 0.4) were manufactured using a laser powder bed fusion (LPBF) additive manufacturing process using three different build orientations (45°, 60°, and 90°) in the present study. Experimental and statistical results revealed that regression analysis and related equations can be used to predict the mass, yield stress, elastic modulus, specific energy absorption, and onset of densification values of TPMS structures with an intermediate volume fraction value and specified build orientation with an error range less than 1.4%, 7.1%, 19.04%, 21.6%, and 13.4%, respectively. Full article
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21 pages, 1847 KB  
Article
Multiscale Homogenization Techniques for TPMS Foam Material for Biomedical Structural Applications
by Ana Pais, Jorge Lino Alves, Renato Natal Jorge and Jorge Belinha
Bioengineering 2023, 10(5), 515; https://doi.org/10.3390/bioengineering10050515 - 25 Apr 2023
Cited by 9 | Viewed by 2827
Abstract
Multiscale techniques, namely homogenization, result in significant computational time savings in the analysis of complex structures such as lattice structures, as in many cases it is inefficient to model a periodic structure in full detail in its entire domain. The elastic and plastic [...] Read more.
Multiscale techniques, namely homogenization, result in significant computational time savings in the analysis of complex structures such as lattice structures, as in many cases it is inefficient to model a periodic structure in full detail in its entire domain. The elastic and plastic properties of two TPMS-based cellular structures, the gyroid, and the primitive surface are studied in this work through numerical homogenization. The study enabled the development of material laws for the homogenized Young’s modulus and homogenized yield stress, which correlated well with experimental data from the literature. It is possible to use the developed material laws to run optimization analyses and develop optimized functionally graded structures for structural applications or reduced stress shielding in bio-applications. Thus, this work presents a study case of a functionally graded optimized femoral stem where it was shown that the porous femoral stem built with Ti-6Al-4V can minimize stress shielding while maintaining the necessary load-bearing capacity. It was shown that the stiffness of cementless femoral stem implant with a graded gyroid foam presents stiffness that is comparable to that of trabecular bone. Moreover, the maximum stress in the implant is lower than the maximum stress in trabecular bone. Full article
(This article belongs to the Section Nanobiotechnology and Biofabrication)
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14 pages, 6385 KB  
Article
Surface Morphology, Compressive Behavior, and Energy Absorption of Graded Triply Periodic Minimal Surface 316L Steel Cellular Structures Fabricated by Laser Powder Bed Fusion
by Bharath Bhushan Ravichander, Shweta Hanmant Jagdale and Golden Kumar
Materials 2022, 15(23), 8294; https://doi.org/10.3390/ma15238294 - 22 Nov 2022
Cited by 14 | Viewed by 2914
Abstract
Laser powder bed fusion (LPBF) is an emerging technique for the fabrication of triply periodic minimal surface (TPMS) structures in metals. In this work, different TPMS structures such as Diamond, Gyroid, Primitive, Neovius, and Fisher–Koch S with graded relative densities are fabricated from [...] Read more.
Laser powder bed fusion (LPBF) is an emerging technique for the fabrication of triply periodic minimal surface (TPMS) structures in metals. In this work, different TPMS structures such as Diamond, Gyroid, Primitive, Neovius, and Fisher–Koch S with graded relative densities are fabricated from 316L steel using LPBF. The graded TPMS samples are subjected to sandblasting to improve the surface finish before mechanical testing. Quasi-static compression tests are performed to study the deformation behavior and energy absorption capacity of TPMS structures. The results reveal superior stiffness and energy absorption capabilities for the graded TPMS samples compared to the uniform TPMS structures. The Fisher–Koch S and Primitive samples show higher strength whereas the Fisher–Koch S and Neovius samples exhibit higher elastic modulus. The Neovius type structure shows the highest energy absorption up to 50% strain among all the TPMS structures. The Gibson–Ashby coefficients are calculated for the TPMS structures, and it is found that the C2 values are in the range suggested by Gibson and Ashby while C1 values differ from the proposed range. Full article
(This article belongs to the Special Issue Design and Post Processing for Metal Additive Manufacturing)
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22 pages, 6890 KB  
Article
Design and Analysis of Biomedical Scaffolds Using TPMS-Based Porous Structures Inspired from Additive Manufacturing
by Rati Verma, Jitendra Kumar, Nishant Kumar Singh, Sanjay Kumar Rai, Kuldeep K. Saxena and Jinyang Xu
Coatings 2022, 12(6), 839; https://doi.org/10.3390/coatings12060839 - 15 Jun 2022
Cited by 49 | Viewed by 6953
Abstract
Gyroid (G) and primitive (P) porous structures have multiple application areas, ranging from thermal to mechanical, and fall in the complex triply periodic minimal surface (TPMS) category. Such intricate bioinspired constructs are gaining attention because they meet both biological and mechanical requirements for [...] Read more.
Gyroid (G) and primitive (P) porous structures have multiple application areas, ranging from thermal to mechanical, and fall in the complex triply periodic minimal surface (TPMS) category. Such intricate bioinspired constructs are gaining attention because they meet both biological and mechanical requirements for osseous reconstruction. The study aimed to develop G and P structures with varying porosity levels from 40% to 80% by modulating the strut thickness to proportionally resemble the stiffness of host tissue. The performance characteristics were evaluated using Ti6Al4V and important relationships between feature dimension, strut thickness, porosity, and stiffness were established. Numerical results showed that the studied porous structures could decrease stiffness from 107 GPa (stiffness of Ti6Al4V) to the range between 4.21 GPa to 29.63 GPa of varying porosities, which matches the human bone stiffness range. Furthermore, using this foundation, a subject-specific scaffold (made of P unit cells with an 80% porosity) was developed to reconstruct segmental bone defect (SBD) of the human femur, demonstrating a significant decrease in the stress shielding effect. Stress transfer on the bone surrounded by a P scaffold was compared with a solid implant which showed a net increase of stress transfer of 76% with the use of P scaffold. In the conclusion, future concerns and recommendations are suggested. Full article
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33 pages, 28519 KB  
Article
A Generalized Strain Energy-Based Homogenization Method for 2-D and 3-D Cellular Materials with and without Periodicity Constraints
by Ahmad I. Gad and Xin-Lin Gao
Symmetry 2021, 13(10), 1870; https://doi.org/10.3390/sym13101870 - 4 Oct 2021
Cited by 5 | Viewed by 2710
Abstract
A generalized strain energy-based homogenization method for 2-D and 3-D cellular materials with and without periodicity constraints is proposed using Hill’s Lemma and the matrix method for spatial frames. In this new approach, the equilibrium equations are enforced at all boundary and interior [...] Read more.
A generalized strain energy-based homogenization method for 2-D and 3-D cellular materials with and without periodicity constraints is proposed using Hill’s Lemma and the matrix method for spatial frames. In this new approach, the equilibrium equations are enforced at all boundary and interior nodes and each interior node is allowed to translate and rotate freely, which differ from existing methods where the equilibrium conditions are imposed only at the boundary nodes. The newly formulated homogenization method can be applied to cellular materials with or without symmetry. To illustrate the new method, four examples are studied: two for a 2-D cellular material and two for a 3-D pentamode metamaterial, with and without periodic constraints in each group. For the 2-D cellular material, an asymmetric microstructure with or without periodicity constraints is analyzed, and closed-form expressions of the effective stiffness components are obtained in both cases. For the 3-D pentamode metamaterial, a primitive diamond-shaped unit cell with or without periodicity constraints is considered. In each of these 3-D cases, two different representative cells in two orientations are examined. The homogenization analysis reveals that the pentamode metamaterial exhibits the cubic symmetry based on one representative cell, with the effective Poisson’s ratio v¯ being nearly 0.5. Moreover, it is revealed that the pentamode metamaterial with the cubic symmetry can be tailored to be a rubber-like material (with v¯ 0.5) or an auxetic material (with v¯ < 0). Full article
(This article belongs to the Special Issue Metamaterials and Symmetry)
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