Force-displacement Response Research Articles

A proposed approach for failure analysis of lattice transmission towers considering geometric imperfection effects

Different types of geometric imperfections can be observed in power transmission lattice towers. These imperfections include eccentricity resulting from the utilization of steel angles, joint slippage, initial crookedness, and dimensional tolerances in the cross-section of lattice tower members. These imperfections contribute to intricate structural behavior, particularly in members experiencing compressive forces. A comprehensive examination of geometric imperfections in lattice tower is crucial, yet research in this vital area is limited. Therefore, for proper modeling of these imperfections and better prediction of lattice tower failure capacity, it is necessary to provide a suitable approach in the modeling of the tower. In the present paper, a modeling method has been developed to analyze the failure of lattice towers, considering geometric imperfections effects (such as eccentricity, joint slippage, initial crookedness, and cross-section dimensional tolerances in the members). The results of the proposed modeling method have been compared with the results of a full-scale failure test conducted on a 400 kV tower. The results of the study show that the proposed modeling method, considering the effect of geometric imperfections, provides a suitable prediction of the tower’s load-carrying capacity. Also, to investigate the effects of each geometric imperfection, various finite element numerical models were established, and their force–displacement responses were evaluated. The results show that to make an acceptable estimation of the tower failure behavior, it is not enough to introduce geometric imperfections individually into the analysis. Rather, considering the collective effect of imperfections altogether can give an acceptable estimate of the tower’s load-bearing capacity.

Effect of fractal dimension on mechanical behaviour and energy absorption of Menger sponge-inspired fractal structures

The Fractal Dimension (FD) of Menger Fractal Cubes (MFCs) defines their intricate geometry, making them ideal for lightweight structural applications. However, the effect of FD on their structural behaviour is largely unexplored. This study examines AlSi7Mg MFC geometries formed through a recursive process, with densities ranging from 40 to 1958 kg/m³, corresponding to FDs ranging from 2.35 to 2.73. Compression tests and simulations revealed that higher fractal orders increased densification displacement, achieving up to 80 % compressibility, with multi-level extended plateau regions indicating enhanced energy absorption. The fourth-order MFC with an FD of 2.35 and a density of 40 kg/m³ showed a specific energy absorption (SEA) of 6 J/g, demonstrating its potential for weight-efficient, energy-absorbing structures. The outcomes of this study indicate that total energy absorbed increases with an increasing FD, while crush efficiency improves as FD decreases showing better crashworthiness. Moreover, the structures exhibited unique force-displacement responses tailored to their FD. These findings offer valuable insights into optimising thin-walled fractal structures for various engineering applications by adjusting the FD to fine-tune relative density and enhance mechanical performance.

Isolated Rib Response and Fracture Prediction for Young Mid-Size Male, Enabled by Population Specific Material Models and Rib Cross-Sectional Geometry.

Thorax injury remains a primary contributor to mortality in car crash scenarios. Although human body models can be used to investigate thorax response to impact, isolated rib models have not been able to predict age- and sex-specific force-displacement response and fracture location simultaneously, which is a critical step towards developing human thorax models able to accurately predict injury response. Recent advancements in constitutive models and quantification of age- and sex-specific material properties, cross-sectional area, and cortical bone thickness distribution offer opportunities to improve rib computational models. In the present study, improved cortical and trabecular bone constitutive models populated with age-specific material properties, age- and sex-specific population data on rib cross-sectional area, and cortical bone thickness distribution were implemented into an isolated 6th rib from a contemporary human body model. The enhanced rib model was simulated in anterior-posterior loading for comparison to experimental age- and sex-specific (twenty-three mid-size males, age range of 22- to 57-year-old) population force-displacement response and fracture location. The improved constitutive models, populated with age-specific material properties, proved critical to predict the rib failure force and displacement, while the improved cortical bone thickness distribution and cross-sectional area improved the fracture location prediction. The enhanced young mid-size male 6th rib model was able to predict young mid-size male 6th rib experimental force-displacement response and fracture location (overpredicted the displacement at failure by 35% and underpredicted the force at failure by 8% but within ±1 SD). The results of the present study can be integrated into full body models to potentially improve thorax injury prediction capabilities.

Experimental insights into the seismic behaviour of flanged URM walls

Considerable attention has been given to understanding and modelling the seismic response of unreinforced masonry piers with rectangular cross-sections. However, the seismic performance of load-bearing masonry walls with flanges, commonly found in actual building configurations, remains less explored. This study investigates the behaviour of flanged walls through cyclic quasi-static tests on four full-scale C-shaped specimens comprising two primary seismic-resistant walls (webs) interconnected by a single flange. The construction of the specimens varied: two were built using standard solid calcium-silicate bricks with general-purpose mortar, while the other two utilised large-sized calcium-silicate blocks with tongue-and-groove interlocks and a thin layer of cement-based adhesive mortar. All specimens were subjected to cyclic horizontal loading parallel to the webs under consistent overburden load and double-fixed boundary conditions. The primary variable in testing the two walls of each type was the number of cyclic loading repetitions. This paper initially describes the key characteristics of the wall specimens, including geometry, construction details, and mechanical properties. Subsequently, it details the instrumentation plan and test protocol, and summarises the major observations from the tests, illustrating damage evolution and hysteretic force-displacement response. The results highlight the effect of the flange on initial stiffness and lateral force resistance, as well as the influence of block type and loading repetitions on failure mode, displacement capacity, and energy dissipation. Additionally, the study demonstrates the impact of floor slab uplift due to in-plane rocking of the webs on the top boundary conditions and the out-of-plane stability of the flange.

Distinct Element macro-crack networks for expedited discontinuum seismic analysis of large-scale URM structures

Discontinuum analysis is a powerful tool for the detailed seismic assessment of unreinforced masonry (URM) structures, whose widespread use is however still mostly limited to small-scale assemblies or isolated components. Despite their unique capabilities, including the explicit simulation of separation phenomena, collapses and out-of-plane (OOP) failures that are hardly replicable using traditional continuum solutions, the high computational cost entailed by micro-to-meso-scale discontinuum modelling strategies, which are the standard approaches in applied research, presently prevent their employment for building-scale problems. The few available macro-scale discontinuum models specifically conceived for URM, on the other hand, rely on complex geometrical discretization processes that require costly manual work, as well as on less efficient deformable block formulations. In this paper, a new simplified discontinuum macro-model is presented and validated against full-scale laboratory test outcomes on walls, pier-spandrel systems and building specimens, in addition to various meso-scale numerical results, under either in-plane (IP) or OOP actions, and considering quasi-static (monotonic, cyclic) or dynamic loadings. The proposed simulation technique, implemented in a robust Distinct Element Method (DEM) framework, leverages a semi-automated Equivalent Frame discretization algorithm that idealizes masonry piers, spandrels and nodes as an assembly of interlocked rigid macro-blocks connected by a network of zero-thickness interface springs. The latter are herein demonstrated to effectively replicate URM damage at the component-level through fracture energy contact laws, providing macro-scale yet representative failure patterns, as well as adequate predictions of overall strength and deformation capacities. Results obtained show a good agreement between macro- and more sophisticated meso-scale predictions, as well as with experimental outcomes, albeit dissimilarities among measured and computed force-displacement responses – similarly to other simplified strategies – were detected as vertical overburden increases. Notably, for analogous levels of accuracy, the analysis time required by our new macro-models is up to 150 times lower than its meso-counterparts. The use of the proposed simplified strategy also enabled the satisfactory simulation of the quasi-static cyclic and seismic responses of full-scale building-scale specimens, prohibitive tasks using traditional detailed DEM models, while also being up to 10 times faster than previous deformable macro-models.

Analysis of the response of wind-induced vibrations on flexible photovoltaic mounts

Abstract This article investigates a flexible photovoltaic bracket’s response to wind vibration. A finite element model is established using SAP2000 software for time course analysis. Representative units and nodes were selected to analyze internal force response, displacement response, and acceleration response. The prestress and span change rule of the flexible photovoltaic bracket are also explored, and quantitative research is conducted on the size of prestress and span size. The magnitude of the prestress affects a structure’s responsiveness to wind vibration. As prestress grows, so do deflection and acceleration, and the rate at which axial force is increasing also increases. Conversely, when prestress increases, the rate of deflection reduction falls. Consequently, considering the prestress size, it is advised that 50-kN prestressing be used for the support and wind cables. As the span rises, so do the mid-span span and the axial force of the wind cables, while acceleration also increases. The rate of mid-span deflection increases gradually with the flexible PV mount span, but the rate of axial force increase decreases. It is recommended to limit the span to below 50 m.

A Weierstrass approach to the analysis of rarefaction solitary waves in tensegrity mass-spring systems

Abstract The Weierstrass‘ theory of one-dimensional Lagrangian systems and a quasi-continuum approach are employed to study the propagation of solitary waves in tensegrity mass-spring chains, which exhibit softening-type elastic response in the large displacement regime and are subject to external pre-compression. The presented study analytically derives the shape of the traveling rarefaction pulses, and limiting values of the speeds of such pulses. Use is made of a tensegrity-like interaction potential that captures the main features of the real force-displacement response of the examined units. The Weierstrass approach is validated through numerical applications that establish comparisons between the theory developed in the present work and previous results available in literature.

Experimental investigation and numerical analysis of a hybrid bridge isolation system utilizing bonded and unbonded laminated rubber bearings

To enhance the seismic resilience of bridges equipped with nonseismic laminated rubber bearings, a novel seismic isolation system is proposed, leveraging hybrid bonded and unbonded laminated rubber bearings. An experimental program is conducted to investigate the seismic behavior of this innovative hybrid bearing system. Cyclic loadings are applied to bonded, unbonded, and hybrid bearings to assess their force-displacement hysteretic response, energy dissipation, and restoring performance. The experimental findings reveal that unbonded rubber bearings exhibit significant energy dissipation through sliding but show limitations in restorability. Conversely, bonded bearings demonstrate superior restoring capacity but offer limited energy dissipation. The proposed hybrid bearings, combining bonded and unbonded bearings, achieve a favorable equilibrium between energy dissipation and restoring performance. Compared to individual bonded and unbonded bearings, the hybrid bearings exhibit a remarkable increase in energy dissipation by 110 % and restoring performance by 185 %. Furthermore, a numerical simulation method is proposed to accurately capture the critical hysteretic behavior of the hybrid bearings.

Research on the influence of impact damage on force identification for composite material

The invisible damage caused by low-velocity impacts are safety threats to engineering structures. Thus, impact force identification is crucial in the context of composite structures for both structure health monitoring (SHM) and composite structure design. This paper investigates the process of identifying impacts on composite structures subjected to low-velocity impact. Considering the damage evolution in the composite structure during impact, this paper explores the influence of impact damage on the accuracy of force identification. Impact experiments on carbon fiber reinforced polymer (CFRP) laminates were conducted to obtain impact force peaks and displacement responses. Furthermore, a validated finite element model (FEM) is established for more elaborate analysis on the mechanism. The findings reveal that the structural damage can lead to significant deviations in force identification if the damage is not considered. Finally, a neural network is employed to predict the force history taking impact damage into consideration. This research provides a reference for the composite structures design and health monitoring of engineering structures considering impact damage.

Macro-element modelling for lateral response of monopiles with local scour hole via hyperbolic hardening relation

Monopile is a popular choice in the foundation supporting offshore wind turbines (OWTs), with local scour significantly impacting their lateral responses. Macro-element model, which encapsulates the response between the monopile and the surrounding seabed soils into a force-displacement relation, has been extensively developed to describe offshore foundations. However, such kind of models specifically targeting monopiles subjected to lateral loading in local scour remain underdeveloped. This work proposes a macro-element model with a succinct hyperbolic hardening relation for laterally loaded monopiles in local scour conditions, using the evolutionary polynomial regression (EPR) machine learning technique for easy and optimal design. First, the finite element model is verified and extended to generate force-displacement responses considering the monopile geometries, soil characteristics, and local scour geometries. These results are then utilised to determine the optimal hyperbolic hardening relation of the macro-element model. Next, the EPR technique is employed to determine the relationship between the hyperbolic hardening relation parameters and the influencing factors. Finally, the macro-element model is successfully evaluated by comparing with measurements from centrifuge tests and numerical solutions by finite element analysis, demonstrating its applicability in practical design and the ability to reproduce FEA results with a significant reduction in computational cost.

Hybrid simulation testing of two-storey low-aspect-ratio nuclear RC shear walls with normal- and high-strength reinforcement: Seismic performance evaluation and economic assessment

Low-aspect-ratio reinforced concrete (RC) shear walls have been commonly used in several nuclear facilities in containment and safety-related structures. Despite being a potential alternative to reduce rebar congestion and subsequently minimize complex construction activities typically associated with nuclear facilities, there has been limited experimental research on investigating the impact of using high-strength reinforcement (HSR) on the seismic performance of such walls, particularly in a multi-storey context. This lack of research is mainly due to considerable challenges imposed when testing such multi-storey nuclear RC shear walls in most laboratories. Therefore, the current study presents the experimental results of two two-storey low-aspect-ratio nuclear RC shear walls that were tested utilizing the seismic hybrid simulation testing technique. In this respect, walls W1-NSR and W2-HSR were designed using normal-strength reinforcement (NSR) and HSR, respectively, where the two test walls had comparable capacities to allow for direct comparisons. Both walls were subjected to various ground motion levels, spanning from operational to design and beyond-design earthquake scenarios. The experimental findings are then presented to include the force-displacement responses, the multi-storey effects, ductility capacities, lateral and rotational stiffnesses, rebar strains, and cracking patterns of the test walls. Subsequently, an economic assessment was carried out to quantify the total rebar weights and the corresponding construction costs of such walls. In addition, the expected seismic repair costs were determined based on a three-dimensional digital image correlation technique that provided information on the damage states of the test walls under different earthquake levels. The results show that although W1-NSR and W2-HSR attained similar force and moment capacities, W2-HSR achieved a relatively higher ductility capacity than W1-NSR. However, larger cracks were observed in W2-HSR compared to W1-NSR, which was attributed to the associated larger rebar spacing in the former relative to the latter. The economic assessment results demonstrate that using HSR minimized the rebar weights and construction costs, while both walls had similar seismic repair costs at their design and beyond-design earthquake levels. Both the seismic performance and economic assessment results presented in the current study are expected to aid future editions of relevant design standards in adopting HSR in nuclear construction practice.

Engineering static non-reciprocity in mechanical metamaterials

Non-reciprocity has recently been achieved in static fields by mechanical metamaterial that combines large non-linearity and asymmetric geometry. Novel devices are then designed to obtain one-way mechanical functionalities. Non-linearity is the fundamental part that regulates static non-reciprocity, but the influential path remains difficult to quantify. In this work, we employ the geometrically exact beam model to obtain the nonlinear deformation profile of mechanical metamaterials, and build nonlinear equations that govern the deformation behavior. A new two-step method is proposed to solve the nonlinear governing equations, which avoids Jacobi matrix singularity. We establish an accurate model that predicts the non-reciprocal mechanical behavior and verify its accuracy by finite element method. To gain further insight into non-linearity’s influences on mechanical non-reciprocity, we investigate mechanical metamaterials with curved beams, explore the effects of initial curvature on non-reciprocity, and engineer their non-reciprocity to obtain different non-reciprocal force–displacement responses. Our work offers beneficial vehicles to realize static direction-selective functionalities, contributing to shock absorption, vibration damping, and mechanical energy manipulation.

Cyclic loading experiments on seismic performance of precast concrete superposed shear walls with CFST end columns

The seismic performance of precast concrete shear walls is a major concern when considering their application in earthquake-prone regions. To improve the seismic performance and constructability of conventional precast concrete superposed shear walls, an innovative design, termed Precast Concrete Superposed Shear Walls with CFST End Columns (PCSSWEC), has been proposed. Given the limited research on the seismic performance of PCSSWECs, cyclic loading experiments were conducted on three full-scale PCSSWEC specimens and one monolithic RC shear wall specimen. The design axial compression ratio (ACR) and the thickness of the steel tube were employed as research variables. Experimental observations and results gave a comprehensive view of the hysteretic behavior of PCSSWECs, reflecting a favorable seismic performance (in terms of failure modes, global and local damage, force-displacement responses, load-bearing capacity, stiffness and strength degradation, deformability, ductility, and energy dissipation capacity). The experiment also revealed significant differences between PCSSWECs and monolithic RC shear walls in concrete crack development and deformation characteristics, confirming that the CFST columns and the wall panel could work together until the failure phase. Moderately increasing the ACR (0.3–0.5) was beneficial for PCSSWECs. However, increasing the steel tube thickness (3.5 mm–5.0 mm) could lead to unfavorable degradation in strength and stiffness and weaken ductility. In addition, a simplified method was proposed to evaluate the flexural strength of PCSSWECs.

Hyperelastic material models for simulating deformation of silicone ring pessaries

Pessaries are removable gynecological prosthetic devices that provide mechanical support for temporary or long-term symptom relief of pelvic floor disorders, such as pelvic organ prolapse and stress urinary incontinence. To date, limited mechanical tests have been performed on physical pessary designs to characterize their behaviour under load; however, custom pessary manufacturing is expensive and time consuming. As an alternative, finite element (FE) modeling can provide detailed numerical insight into the response of a pessary design under load but to date has seen limited application, with little data available for pessary silicone materials. This study aimed to identify hyperelastic material models for two silicone materials used in custom pessary cocoon moulded manufacturing towards FE analysis of ring with support (RWS) pessaries. It was hypothesized that hyperelastic material models could be identified to capture the force and deformation response of multiple RWS sizes under different boundary conditions and silicone materials (Shore 60A and 40A). To understand the material characteristics of pessary silicone, uniaxial tension and compression tests were performed then the experimental data was fit with Mooney-Rivlin (MR) material models. To ensure the material models characterize the pessary behaviour, data from mechanical tests representing the RWS pessary folding and modified 3-point bending were compared to FE recreations (FEBio) of the same tests with the MR materials applied to the pessaries. The FE model results demonstrated good agreement in the force-displacement response for the fold and 3-point bending models for different pessary sizes and silicone stiffnesses. This work demonstrates the hyperelastic material models’ efficacy and will enable future studies to improve biomechanical analysis of silicone pessary designs.

Experimental and numerical investigation of damage in multilayer sandwich panels with square and trapezoidal corrugated cores under quasi-static three-point bending

Multilayer composite sandwich panels with corrugated cores have the potential for structural applications requiring high stiffness and strength-to-weight ratios. This study aims to experimentally and numerically investigate the bending response of sandwich panels with novel square and trapezoidal corrugated core configurations fabricated from E-glass fiber-reinforced epoxy composites, both with and without polyurethane foam filling. Quasi-static three-point bending tests were conducted to evaluate and compare the flexural stiffness and maximum load capacity of the panel designs. The cores were manufactured using vacuum-assisted resin transfer molding. Key results showed that changing the core geometry from square to trapezoidal improved the bending stiffness by up to 26 %. Incorporating polyurethane foam further increased the bending stiffness by up to 41 % and maximum load by up to 47 % compared to solid cores. Failure initiation and progression were governed by matrix cracking in the face sheets and cores, followed by core cell wall buckling and delamination. Finite element modeling using ABAQUS captured the progressive damage behavior, exhibiting good agreement with experimental force-displacement responses. Failure modes included matrix cracks, fiber fractures, core buckling and delamination. This study provides valuable insights into the mechanical performance of innovative corrugated core sandwich panel designs under quasi-static bending loads. The validated FE approach also enables virtual testing and optimization of composite sandwich structures.

An experimental and theoretical investigation on the hyper-viscoelasticity of polyamide 12 produced by selective laser sintering.

Polyamide 12 (PA12) is vastly utilized in many additive manufacturing methods, such as Selective Laser Sintering (SLS), and a better understanding of its mechanical behaviors promotes available knowledge on the behaviors of 3D-printed parts made from this polymer. In this paper, SLS-produced standard tensile specimens are studied under monotonic and cyclic tension tests, as well as stress relaxation experiments, and the obtained force-displacement responses are shown to be consistent with a hyper-viscoelastic material model. This finding is also observed in typical pantographic structures produced by the same manufacturing parameters. To propose a constitutive model for predicting these behaviors, the convolution integral of a strain-dependent function and a time-dependent function is developed where the material parameters are determined with the use of both short-term and long-term responses of the specimens. Numerical results of the presented model for standard test specimens are shown to be in good agreements with the experimental ones under various loading conditions. To prove the capabilities of the proposed model in studying any SLS-produced part, finite element implementation of the constitutive equations is shown to provide numerical results in agreement with the empirical findings for tensile loading of the 3D-printed pantographic structure.

A new cohesive-based modelling of moisture-dependent mode II delamination of carbon/epoxy composites

The cohesive zone model (CZM) is widely employed for simulating delamination and debonding behaviour in engineering structures. However, the choice of CZM shape impacts the accuracy of simulation results. Therefore, the selection of a suitable Traction-Separation Law (TSL) with appropriate cohesive parameters is crucial. This study focuses on simulating the mode II delamination of unidirectional carbon/epoxy composites under varying moisture content levels (0%, 2.2%, 3.8%, and 5.3%) using the End Notched Flexure (ENF) test. Trapezoidal TSL (TTSL) with varying pseudo-plasticity parameter (Γ) was implemented and compared. A guideline was proposed in this study to aid in the selection of cohesive parameters, and a relationship between these parameters and moisture content was established. The results indicate that Γ = 0.99 yields a more accurate force-displacement response compared to Γ = 0. The estimated cohesive zone length falls within the range of 2.0–2.4 mm. During crack growth, the analysis reveals that, at the peak force, a region approximately 0.5–0.6 mm ahead of the crack tip undergoes total failure. Simultaneously, damage initiation occurs in the region 2.3–2.4 mm beyond the complete failure zone.

Theoretical method for predicting the failure mode of reinforced concrete shear walls subjected to axial tension and cyclic lateral loads

Reinforced concrete shear walls may exhibit various failure modes when subjected to combined axial tension-flexure-shear loads. This study developed a theoretical method for predicting the failure mode of RC walls subjected to combined axial tension and cyclic lateral loads, in which the force-displacement response curve was compared to the predicted flexural, shear and sliding strength capacity curves. The formulas for calculating the axial elongation and horizontal crack widths of tensile RC walls were proposed, and the influence of these two aspects was fully considered in the estimation of shear strength and sliding strength degradation. The proposed method was validated against test data of ten RC wall specimens which underwent various failure modes, including flexural, shear, sliding, flexural-sliding, and shear-sliding failure modes. Comparisons between experimental and theoretical results indicated that the proposed method predicted the failure modes and lateral strength with acceptable accuracy. As the proposed method accurately estimated the shear and sliding strength degradation, it provided the insights on the shifting of dominated behaviors (e.g., flexural- or shear-dominated behavior to sliding-dominated behavior). Finally, strength design formulas specified in Chinese, US and European codes were verified against test data. The flexural strength of RC walls was reasonably estimated by the JGJ 3–2010 (Chinese code), ACI 318–19 (US code) and Eurocode 8 (European code) design formulas. Among the three codes, JGJ 3–2010 provided a more reasonable estimate on shear strength of tensile RC walls than the other two codes.

Stair‐Stepping Mechanical Metamaterials with Programmable Load Plateaus

AbstractMaterials with target load plateaus offer the potential for developing innovative vibration suppression and isolation systems for applications such as satellite platforms, submarines, and electric vehicles. However, implementing these materials can pose significant challenges. In this study, stair‐stepping mechanical metamaterials with programmable load plateaus are presented, which are created via a three‐level (unit, module, and 3D object) construction strategy. The strategy inspired by the inverse design concept achieves tunability in the number and properties of load plateaus within the force–displacement profiles of the metamaterials. This approach even yields appealing stair‐stepping response patterns, as validated by experiments and finite element simulations. Promisingly, programming the unit from its initial configuration to a “zero stiffness” configuration enables these metamaterials excellent vibration isolation performance. Furthermore, two reversible methods are proposed for switching among various unit configurations, namely shape memory programming and supporting payload. This innovative design strategy for programmable load plateaus opens up new possibilities for creating metamaterials with customized force–displacement responses. It also provides opportunities to incorporate multimodal vibration isolation capabilities into precision devices.

A minimalist elastic metamaterial with meta-damping mechanism

A novel elastic mechanical metamaterial with extreme damping performance has been achieved skillfully by coupling snap-through and pseudo-constant-force behaviors. The proposed meta-damping mechanism is systematically expounded to tailor synthetical force–displacement response for programming hyper energy dissipations. Within this framework, detailed designs in functional sub-structures and collaborative design strategy combined with parametric optimization in integrated structure are further presented synthetically. By additive manufacturing and loading–unloading cyclic experiments, the physical realization of meta-damping elastic metamaterials reveals the extraordinary specific damping capacity (Ψ=7.03), which exceeds any research reported previously and is immensely close to the theoretical limit. Remarkably, this minimalist design method, with only two necessary functional components, reconciles the contradiction between load-bearing and damping dissipation, with strong multi-directional and periodic expansibility. This work has far-reaching implications on the compact design of recoverability, reusability, frequency-independent, material-independent elastic mechanical metamaterials for superior dynamic applications such as impact absorption, vibration reduction, and energy trapping.