Femur Auxetic Meta-Implants with Tuned Micromotion Distribution

Auxetic Biomedical Metamaterials for Orthopedic Surgery Applications: A Comprehensive Review

Poisson's ratio in auxetic materials shifts from typically positive to negative, causing lateral expansion during axial tension. This scale-independent characteristic, originating from tailored architectures, exhibits specific physical properties, including energy adsorption, shear resistance, and fracture resistance. These metamaterials demonstrate exotic mechanical properties with potential applications in several engineering fields, but biomedical applications seem to be one of the most relevant, with an increasing number of articles published in recent years, which present opportunities ranging from cellular repair to organ reconstruction with outstanding mechanical performance, mechanical conduction, and biological activity compared with traditional biomedical metamaterials. Therefore, focusing on understanding the potential of these structures and promoting theoretical and experimental investigations into the benefits of their unique mechanical properties is necessary for achieving high-performance biomedical applications. Considering the demand for advanced biomaterial implants in surgical technology and the profound advancement of additive manufacturing technology that are particularly relevant to fabricating complex and customizable auxetic mechanical metamaterials, this review focuses on the fundamental geometric configuration and unique physical properties of negative Poisson's ratio materials, then categorizes and summarizes auxetic material applications across some surgical departments, revealing efficacy in joint surgery, spinal surgery, trauma surgery, and sports medicine contexts. Additionally, it emphasizes the substantial potential of auxetic materials as innovative biomedical solutions in orthopedics and demonstrates the significant potential for comprehensive surgical application in the future.

Development of a density-based topology optimization of homogenized lattice structures for individualized hip endoprostheses and validation using micro-FE

Prosthetic implants, particularly hip endoprostheses, often lead to stress shielding because of a mismatch in compliance between the bone and the implant material, adversely affecting the implant's longevity and effectiveness. Therefore, this work aimed to demonstrate a computationally efficient method for density-based topology optimization of homogenized lattice structures in a patient-specific hip endoprosthesis. Thus, the root mean square error (RMSE) of the stress deviations between the physiological femur model and the optimized total hip arthroplasty (THA) model compared to an unoptimized-THA model could be reduced by 81 % and 66 % in Gruen zone (GZ) 6 and 7. However, the method relies on homogenized finite element (FE) models that only use a simplified representation of the microstructural geometry of the bone and implant. The topology-optimized hip endoprosthesis with graded lattice structures was synthesized using algorithmic design and analyzed in a virtual implanted state using micro-finite element (micro-FE) analysis to validate the optimization method. Homogenized FE and micro-FE models were compared based on averaged von Mises stresses in multiple regions of interest. A strong correlation (CCC > 0.97) was observed, indicating that optimizing homogenized lattice structures yields reliable outcomes. The graded implant was additively manufactured to ensure the topology-optimized result's feasibility.

The assessment of implant shape-dependent failure mechanisms in primary total hip arthroplasty using finite element analysis

The three mechanisms known to be responsible for the failure of uncemented femoral stems in primary total hip arthroplasty (THA) are the stress shielding, excessive bone-implant interface stress, and excessive initial micromotion. Since implant designers usually have to sacrifice two mechanisms to improve the other one, the aim of this study was to assess which of them plays a more important role in the failure of uncemented stems. Two hip implant stems which are widely used in the primary THA and their mid-term clinical outcomes are available, were selected. Then, the amount of the three failure mechanisms created by each stem during the normal walking gait cycle was determined for a 70 kg female patient using the finite element method. The results indicated that the stem with better clinical outcome induced an average of 36.6% less stress shielding in the proximal regions of femur bone compared with the other stem. However, the maximum bone-implant interface stress and maximum initial micromotion were, respectively, 30 and 155% higher for the stem with better clinical outcomes. It was therefore concluded that the stress shielding has a more significant impact on the mid-term life of uncemented stems. However, care must be taken to ensure that the other two failure mechanisms do not exceed a certain threshold. It was also observed that the thinner and shorter stem created a smaller amount of stress shielding in the femur bone. The outcomes of this study can be used to design new hip implant stems that can potentially last longer.

Advancement in total hip implant: a comprehensive review of mechanics and performance parameters across diverse novelties

The UK's National Joint Registry (NJR) and the American Joint Replacement Registry (AJRR) of 2022 revealed that total hip replacement (THR) is the most common orthopaedic joint procedure. The NJR also noted that 10-20% of hip implants require revision within 1 to 10 years. Most of these revisions are a result of aseptic loosening, dislocation, implant wear, implant fracture, and joint incompatibility, which are all caused by implant geometry disparity. The primary purpose of this review article is to analyze and evaluate the mechanics and performance factors of advancement in hip implants with novel geometries. The existing hip implants can be categorized based on two parts: the hip stem and the joint of the implant. Insufficient stress distribution from implants to the femur can cause stress shielding, bone loss, excessive micromotion, and ultimately, implant aseptic loosening due to inflammation. Researchers are designing hip implants with a porous lattice and functionally graded material (FGM) stems, femur resurfacing, short-stem, and collared stems, all aimed at achieving uniform stress distribution and promoting adequate bone remodeling. Designing hip implants with a porous lattice FGM structure requires maintaining stiffness, strength, isotropy, and bone development potential. Mechanical stability is still an issue with hip implants, femur resurfacing, collared stems, and short stems. Hip implants are being developed with a variety of joint geometries to decrease wear, improve an angular range of motion, and strengthen mechanical stability at the joint interface. Dual mobility and reverse femoral head-liner hip implants reduce the hip joint's dislocation limits. In addition, researchers reveal that femoral headliner joints with unidirectional motion have a lower wear rate than traditional ball-and-socket joints. Based on research findings and gaps, a hypothesis is formulated by the authors proposing a hip implant with a collared stem and porous lattice FGM structure to address stress shielding and micromotion issues. A hypothesis is also formulated by the authors suggesting that the utilization of a spiral or gear-shaped thread with a matched contact point at the tapered joint of a hip implant could be a viable option for reducing wear and enhancing stability. The literature analysis underscores substantial research opportunities in developing a hip implant joint that addresses both dislocation and increased wear rates. Finally, this review explores potential solutions to existing obstacles in developing a better hip implant system.

Synergizing Algorithmic Design, Photoclick Chemistry and Multi-Material Volumetric Printing for Accelerating Complex Shape Engineering

The field of biomedical design and manufacturing has been rapidly evolving, with implants and grafts featuring complex 3D design constraints and materials distributions. By combining a new coding-based design and modeling approach with high-throughput volumetric printing, a new approach is demonstrated to transform the way complex shapes are designed and fabricated for biomedical applications. Here, an algorithmic voxel-based approach is used that can rapidly generate a large design library of porous structures, auxetic meshes and cylinders, or perfusable constructs. By deploying finite cell modeling within the algorithmic design framework, large arrays of selected auxetic designs can be computationally modeled. Finally, the design schemes are used in conjunction with new approaches for multi-material volumetric printing based on thiol-ene photoclick chemistry to rapidly fabricate complex heterogeneous shapes. Collectively, the new design, modeling and fabrication techniques can be used toward a wide spectrum of products such as actuators, biomedical implants and grafts, or tissue and disease models.

Multi-Scale Topology Optimization of Femoral Stem Structure Subject to Stress Shielding Reduce

Hip replacement femoral implants are made of substantial materials that all have stiffness considerably higher than that of bone, which can cause significant bone resorption secondary to stress shielding and lead to severe complications. The topology optimization design method based on the uniform distribution of material micro-structure density can form a continuous mechanical transmission route, which can better solve the problem of reducing the stress shielding effect. A multi-scale parallel topology optimization method is proposed in this paper and a topological structure of type B femoral stem is derived. Using the traditional topology optimization method (Solid Isotropic Material with Penalization, SIMP), a topological structure of type A femoral stem is also derived. The sensitivity of the two kinds of femoral stems to the change of load direction is compared with the variation amplitude of the structural flexibility of the femoral stem. Furthermore, the finite element method is used to analyze the stress of type A and type B femoral stem under multiple conditions. Simulation and experimental results show that the average stress of type A and type B femoral stem on the femur are 14.80 MPa, 23.55 MPa, 16.94 MPa and 10.89 MPa, 20.92 MPa, 16.50 MPa, respectively. For type B femoral stem, the average error of strain is -1682με and the average relative error is 20.3% at the test points on the medial side and the mean error of strain is 1281με and the mean relative error is 19.5% at the test points on the outside.

Patient-specific femoral implant design using metamaterials for improving load transfer at proximal-lateral region of the femur

Loading configuration of hip joint creates resultant bending effect on femoral implants. So, the lateral side of femoral implant which is under tension retracts from peri‑implant bone due to positive Poisson's ratio. This retraction of implant leads to load shielding and gap opening in proximal-lateral region, thereby allowing entry of wear particle to implant-bone interface. Retraction of femoral implant can be avoided by introducing auxetic metamaterial to the retracting side. This allows the implant to push peri‑implant bone under tensile condition by virtue of their auxetic (negative Poisson's ratio) nature. To develop such implants, a patient-specific conventional solid implant was first designed based on computed-tomography scan of a patient's femur. Two types of metamaterials (2D: type-1) and (3D: type-2) were employed to design femoral meta-implants. Type-1 and type-2 meta-implants were fabricated using metallic 3D printing method and mechanical compression testing was conducted. Three finite element (FE) models of the femur implanted with solid implant, type-1 meta-implant and type-2 meta-implant were developed and analysed under compression loading. Significant correlation (R² = 0.9821 and R² = 0.9977) was found between the experimental and FE predicted strains of the two meta-implants. In proximal-lateral region of the femur, an increase of 7.1% and 44.1% von-Mises strain was observed when implanted with type-1 and type-2 meta-implant over the solid implant. In this region, bone remodelling analysis revealed 2.5% bone resorption in case of solid implant. While bone apposition of 0.5% and 7.7% was observed in case of type-1 and type-2 meta-implants, respectively. The results of this study indicates that concept of introduction of metamaterial to the lateral side of femoral implant can prove to provide higher osseointegration-friendly environment in the proximal-lateral region of femur.

Additively manufactured controlled porous orthopedic joint replacement designs to reduce bone stress shielding: a systematic review

BACKGROUND

Total joint replacements are an established treatment for patients suffering from reduced mobility and pain due to severe joint damage. Aseptic loosening due to stress shielding is currently one of the main reasons for revision surgery. As this phenomenon is related to a mismatch in mechanical properties between implant and bone, stiffness reduction of implants has been of major interest in new implant designs. Facilitated by modern additive manufacturing technologies, the introduction of porosity into implant materials has been shown to enable significant stiffness reduction; however, whether these devices mitigate stress-shielding associated complications or device failure remains poorly understood.

METHODS

In this systematic review, a broad literature search was conducted in six databases (Scopus, Web of Science, Medline, Embase, Compendex, and Inspec) aiming to identify current design approaches to target stress shielding through controlled porous structures. The search keywords included 'lattice,' 'implant,' 'additive manufacturing,' and 'stress shielding.'

RESULTS

After the screening of 2530 articles, a total of 46 studies were included in this review. Studies focusing on hip, knee, and shoulder replacements were found. Three porous design strategies were identified, specifically uniform, graded, and optimized designs. The latter included personalized design approaches targeting stress shielding based on patient-specific data. All studies reported a reduction of stress shielding achieved by the presented design.

CONCLUSION

Not all studies used quantitative measures to describe the improvements, and the main stress shielding measures chosen varied between studies. However, due to the nature of the optimization approaches, optimized designs were found to be the most promising. Besides the stiffness reduction, other factors such as mechanical strength can be considered in the design on a patient-specific level. While it was found that controlled porous designs are overall promising to reduce stress shielding, further research and clinical evidence are needed to determine the most superior design approach for total joint replacement implants.

Remodeling of Architected Mesenchymal Microtissues Generated on Mechanical Metamaterials

Mechanical metamaterials constitute a nascent category of architected structures comprising arranged periodic components with tailored geometrical features. These materials are now being employed as advanced medical implants due to their extraordinary mechanical properties over traditional devices. Nevertheless, to achieve desired tissue integration and regeneration, it is critical to study how the microarchitecture affects interactions between metamaterial scaffolds and living biological tissues. Based on human induced pluripotent stem cell technology and multiphoton lithography, we report the establishment of an in vitro microtissue model to study the integration and remodeling of human mesenchymal tissues on metamaterial scaffolds with different unit geometries. Microtissues showed distinct tissue morphologies and cellular behaviors between architected octet-truss and bowtie structures. Under the active force generated from mesenchymal tissues, the octet-truss and bowtie metamaterial scaffolds demonstrated unique instability phenomena, significantly different from uniform loading using conventional mechanical testing.

Optimal microstructure and mechanical properties of open-cell porous titanium structures produced by selective laser melting

Three-dimensional printing technology enables the production of open cell porous structures. This has advantages but not only in terms of weight reduction. In implant structures, the process of osseointegration is improved, mechanical integration is better, the open cell porous structures resemble a trabecular structure that mimics bone tissue. In this work, we investigated titanium structures made porous by cutting spheres. Based on the patterns of different types of crystal models we created porosity with different strategies. We have shown that there are significant differences in mechanical properties between the porous structures formed with different strategies. We determined the structure that loses the least load-bearing capacity compared to the solid structure, with the same porosity levels and mechanical stresses. We characterized the possibility location and environment of becoming an open cell structure. We performed the calculations with mechanical simulations, which were validated experimentally. The quality of the three-dimensional printing of samples was checked by computed tomography reconstruction analysis.

Additively Manufactured Hierarchical Auxetic Mechanical Metamaterials

Due to the ability to create structures with complex geometry at micro- and nanoscales, modern additive technologies make it possible to produce artificial materials (metamaterials) with properties different from those of conventional materials found in nature. One of the classes with special properties is auxetic materials-materials with a negative Poisson's ratio. In the review, we collect research results on the properties of auxetics, based on analytical, experimental and numerical methods. Special attention of this review is paid to the consideration of the results obtained in studies of hierarchical auxetic materials. The wide interest in the hierarchical subclass of auxetics is explained by the additional advantages of structures, such as more flexible adjustment of the desired mechanical characteristics (the porosity, stiffness, specific energy absorption, degree of material release, etc.). Possibilities of biomedical applications of hierarchical auxetic materials, such as coronary stents, filtration and drug delivery systems, implants and many others, where the ability for high-precision tuning is required, are underlined.

Development of an additively-manufactured functionally-graded expandable implant via the application of the adaptive response surface method: feasibility study on intramedullary humerus nail

The paper introduces the concept of the rational design of a deployable humeral intramedullary nail plug based on a honeycomb structure used for the surgical treatment of humeral shaft fractures. The concept serves for to restore the axial alignment of bone fragments and to maintain stability via bone-nail friction and locking screws. The design nail plug was gained by optimisation process the Latin Hypercube Sampling Design algorithm and Multi-Objective Genetic Algorithm. It was shown that we can use statistical shape function combined by 3 D printing for designing of a new rationally designed implants.

Auxetic Metamaterials for Biomedical Devices: Current Situation, Main Challenges, and Research Trends

Auxetic metamaterials are characterized by a negative Poisson ratio (NPR) and display an unexpected property of lateral expansion when stretched and densification when compressed. Auxetic properties can be achieved by designing special microstructures, hence their classification as metamaterials, and can be manufactured with varied raw materials and methods. Since work in this field began, auxetics have been considered for different biomedical applications, as some biological tissues have auxetic-like behaviour due to their lightweight structure and morphing properties, which makes auxetics ideal for interacting with the human body. This research study is developed with the aim of presenting an updated overview of auxetic metamaterials for biomedical devices. It stands out for providing a comprehensive view of medical applications for auxetics, including a focus on prosthetics, orthotics, ergonomic appliances, performance enhancement devices, in vitro medical devices for interacting with cells, and advanced medicinal clinical products, especially tissue engineering scaffolds with living cells. Innovative design and simulation approaches for the engineering of auxetic-based products are covered, and the relevant manufacturing technologies for prototyping and producing auxetics are analysed, taking into consideration those capable of processing biomaterials and enabling multi-scale and multi-material auxetics. An engineering design rational for auxetics-based medical devices is presented with integrative purposes. Finally, key research, development and expected technological breakthroughs are discussed.

How Artificial Intelligence and Machine Learning Is Assisting Us to Extract Meaning from Data on Bone Mechanics?

Dramatic advancements in interdisciplinary research with the fourth paradigm of science, especially the implementation of computer science, nourish the potential for artificial intelligence (AI), machine learning (ML), and artificial neural network (ANN) algorithms to be applied to studies concerning mechanics of bones. Despite recent enormous advancement in techniques, gaining deep knowledge to find correlations between bone shape, material, mechanical, and physical responses as well as properties is a daunting task. This is due to both complexity of the material itself and the convoluted shapes that this complex material forms. Moreover, many uncertainties and ambiguities exist concerning the use of traditional computational techniques that hinders gaining a full comprehension of this advanced biological material. This book chapter offers a review of literature on the use of AI, ML, and ANN in the study of bone mechanics research. A main question as to why to implement AI and ML in the mechanics of bones is fully addressed and explained. This chapter also introduces AI and ML and elaborates on the main features of ML algorithms such as learning paradigms, subtypes, main ideas with examples, performance metrics, training algorithms, and training datasets. As a frequently employed ML algorithm in bone mechanics, feedforward ANNs are discussed to make their taxonomy and working principles more readily comprehensible to researchers. A summary as well as detailed review of papers that employed ANNs to learn from collected data on bone mechanics are presented. Reviewing literature on the use of these data-driven tools is essential since their wider application has the potential to: improve clinical assessments enabling real-time simulations; avoid and/or minimize injuries; and, encourage early detection of such injuries in the first place.

Auxetic Structures for Tissue Engineering Scaffolds and Biomedical Devices

An auxetic structure utilizing a negative Poisson's ratio, which can expand transversally when axially expanded under tensional force, has not yet been studied in the tissue engineering and biomedical area. However, the recent advent of new technologies, such as additive manufacturing or 3D printing, has showed prospective results aimed at producing three-dimensional structures. Auxetic structures are fabricated by additive manufacturing, soft lithography, machining technology, compressed foaming, and textile fabrication using various biomaterials, including poly(ethylene glycol diacrylate), polyurethane, poly(lactic-glycolic acid), chitosan, hydroxyapatite, and using a hard material such as a silicon wafer. After fabricating the scaffold with an auxetic effect, researchers have cultured fibroblasts, osteoblasts, chondrocytes, myoblasts, and various stem cells, including mesenchymal stem cells, bone marrow stem cells, and embryonic stem cells. Additionally, they have shown new possibilities as scaffolds through tissue engineering by cell proliferation, migration, alignment, differentiation, and target tissue regeneration. In addition, auxetic structures and their unique deformation characteristics have been explored in several biomedical devices, including implants, stents, and surgical screws. Although still in the early stages, the auxetic structure, which can create mechanical properties tailored to natural tissue by changing the internal architecture of the structure, is expected to show an improved tissue reconstruction ability. In addition, continuous research at the cellular level using the auxetic micro and nano-environment could provide a breakthrough for tissue reconstruction.

Influence of sequential opening/closing of interface gaps and texture density on bone growth over macro-textured implant surfaces using FE based mechanoregulatory algorithm

Intramedullary implant fixation is achieved through a press-fit between the implant and the host bone. A stronger press-fit between the bone and the prosthesis often introduces damage to the bone canal creating micro-gaps. The aim of the present investigation is to study the influences of simultaneous opening/closing of gaps on bone growth over macro-textured implant surfaces. Models based on textures available on CORAIL and SP-CL hip stems have been considered and 3D finite element (FE) analysis has been carried out in conjunction with mechanoregulation based tissue differentiation algorithm. Additionally, using a full-factorial approach, different combinations (between 5 µm to 15 µm) of sliding and gap distances at the bone-implant interface were considered to understand their combined influences on bone growth. All designs show an elevated fibrous tissue formation (10.96% at 5 µm to 29.38% at 40 µm for CORAIL based textured model; 11.45% at 5 µm to 32.25% at 40 µm for SP-CL based textured model) and inhibition of soft cartilaginous tissue (75.64% at 5 µm to 53.94% at 40 µm for CORAIL based model; 76.02% at 5 µm to 53.60% at 40 µm SP-CL based model) at progressively higher levels of normal micromotion, leading to a fragile bone-implant interface. These results highlight the importance of minimizing both sliding and gap distances simultaneously to enhance bone growth and implant stability. Further, results from the studies with differential texture density over CORAIL based implant reveal a non-linear complex relationship between tissue growth and texture density which might be investigated in a machine learning framework.

Innovative Surface Modification Procedures to Achieve Micro/Nano-Graded Ti-Based Biomedical Alloys and Implants

Due to the growing aging population of the world, and as a result of the increasing need for dental implants and prostheses, the use of titanium and its alloys as implant materials has spread rapidly. Although titanium and its alloys are considered the best metallic materials for biomedical applications, the need for innovative technologies is necessary due to the sensitivity of medical applications and to eliminate any potentially harmful reactions, enhancing the implant-to-bone integration and preventing infection. In this regard, the implant’s surface as the substrate for any reaction is of crucial importance, and it is accurately addressed in this review paper. For constructing this review paper, an internet search was performed on the web of science with these keywords: surface modification techniques, titanium implant, biomedical applications, surface functionalization, etc. Numerous recent papers about titanium and its alloys were selected and reviewed, except for the section on forthcoming modern implants, in which extended research was performed. This review paper aimed to briefly introduce the necessary surface characteristics for biomedical applications and the numerous surface treatment techniques. Specific emphasis was given to micro/nano-structured topographies, biocompatibility, osteogenesis, and bactericidal effects. Additionally, gradient, multi-scale, and hierarchical surfaces with multifunctional properties were discussed. Finally, special attention was paid to modern implants and forthcoming surface modification strategies such as four-dimensional printing, metamaterials, and metasurfaces. This review paper, including traditional and novel surface modification strategies, will pave the way toward designing the next generation of more efficient implants.

Motility Improvement of Biomimetic Trachea Scaffold via Hybrid 3D-Bioprinting Technology

A trachea has a structure capable of responding to various movements such as rotation of the neck and relaxation/contraction of the conduit due to the mucous membrane and cartilage tissue. However, current reported tubular implanting structures are difficult to impelement as replacements for original trachea movements. Therefore, in this study, we developed a new trachea implant with similar anatomical structure and mechanical properties to native tissue using 3D printing technology and evaluated its performance. A 250 µm-thick layer composed of polycaprolactone (PCL) nanofibers was fabricated on a rotating beam using electrospinning technology, and a scaffold with C-shaped cartilage grooves that mimics the human airway structure was printed to enable reconstruction of cartilage outside the airway. A cartilage type scaffold had a highest rotational angle (254°) among them and it showed up to 2.8 times compared to human average neck rotation angle. The cartilage type showed a maximum elongation of 8 times higher than that of the bellows type and it showed the elongation of 3 times higher than that of cylinder type. In cartilage type scaffold, gelatin hydrogel printed on the outside of the scaffold was remain 22.2% under the condition where no hydrogel was left in other type scaffolds. In addition, after 2 days of breathing test, the amount of gelatin remaining inside the scaffold was more than twice that of other scaffolds. This novel trachea scaffold with hydrogel inside and outside of the structure was well-preserved under external flow and is expected to be advantageous for soft tissue reconstruction of the trachea.

Energy Absorption and Mechanical Performance of Functionally Graded Soft-Hard Lattice Structures

Today, the rational combination of materials and design has enabled the development of bio-inspired lattice structures with unprecedented properties to mimic biological features. The present study aims to investigate the mechanical performance and energy absorption capacity of such sophisticated hybrid soft–hard structures with gradient lattices. The structures are designed based on the diversity of materials and graded size of the unit cells. By changing the unit cell size and arrangement, five different graded lattice structures with various relative densities made of soft and hard materials are numerically investigated. The simulations are implemented using ANSYS finite element modeling (FEM) (2020 R1, 2020, ANSYS Inc., Canonsburg, PA, USA) considering elastic-plastic and the hardening behavior of the materials and geometrical non-linearity. The numerical results are validated against experimental data on three-dimensional (3D)-printed lattices revealing the high accuracy of the FEM. Then, by combination of the dissimilar soft and hard polymeric materials in a homogenous hexagonal lattice structure, two dual-material mechanical lattice statures are designed, and their mechanical performance and energy absorption are studied. The results reveal that not only gradual changes in the unit cell size provide more energy absorption and improve mechanical performance, but also the rational combination of soft and hard materials make the lattice structure with the maximum energy absorption and stiffness, in comparison to those structures with a single material, interesting for multi-functional applications.

Idealized 3D Auxetic Mechanical Metamaterial: An Analytical, Numerical, and Experimental Study

Mechanical metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most well-known mechanical metamaterials is auxetics, which demonstrates negative Poisson's ratio (NPR) behavior that is very beneficial in several industrial applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experimentally. The noted structure is constructed of three types of struts-one loaded purely axially and two loaded simultaneously flexurally and axially, which are inclined and are spatially defined by angles θ and φ. Analytical relationships for elastic modulus, yield stress, and Poisson's ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler-Bernoulli and Timoshenko. Moreover, two finite element approaches one based on beam elements and one based on volumetric elements are implemented. Furthermore, several specimens are additively manufactured (3D printed) and tested under compression. The analytical results had good agreement with the experimental results on the one hand and the volumetric finite element model results on the other hand. Moreover, the effect of various geometrical parameters on the mechanical properties of the structure was studied, and the results demonstrated that angle θ (related to tension-dominated struts) has the highest influence on the sign of Poisson's ratio and its extent, while angle φ (related to compression-dominated struts) has the lowest influence on the Poisson's ratio. Nevertheless, the compression-dominated struts (defined by angle φ) provide strength and stiffness for the structure. The results also demonstrated that the structure could have zero Poisson's ratio for a specific range of θ and φ angles. Finally, a lightened 3D re-entrant structure is introduced, and its results are compared to those of the idealized 3D re-entrant structure.