Initial Peak Stress Research Articles

Experimental and Simulation Study of Fiber-Reinforced and Foam-Filled Anti-Tetrachiral and Re-Entrant Structures

Negative Poisson's ratio (NPR) honeycomb structures exhibit excellent properties, including resistance to compression, impact resistance, and energy absorption. To better study NPR structures, this paper investigates two different methods to enhance the mechanical properties and energy absorption capabilities of re-entrant and anti-tetrachiral structures. Fiber reinforcement and polyurethane foam filling methods were used to address material enhancement issues, aiming to achieve structures with high specific energy absorption. Specimens were fabricated using selective laser sintering technology with three different material configurations, including nylon, carbon fiber-reinforced nylon, and glass fiber-reinforced nylon, for comparative analysis. Additionally, some specimens were filled with polyurethane foam. Quasi-static compression tests indicated that both glass fiber-reinforced nylon and foam filling significantly improved the material's stiffness, initial peak stress, and energy absorption, although the "auxetic" effect was weakened. Subsequently, finite element methods were used to simulate the deformation modes and mechanical properties of the two NPR structures, and the numerical results showed good agreement with the experimental results.

Effects of specimen thickness and fiber length on tensile and cracking behavior of UHPFRC: Uniaxial tensile test and micromechanical modeling

This study aims to investigate the effects of specimen thickness and fiber length on the tensile and cracking behaviors of ultra-high-performance fiber-reinforced concrete (UHPFRC). To this end, a uniaxial tensile test was conducted with three specimen thicknesses (30, 50, and 100 mm) and two fiber lengths (13 and 20 mm), and the fiber orientation, dispersion and specimen void were quantitatively evaluated based on image recognition. The test results indicated that fiber orientation was improved with the decreased specimen thickness and increased fiber length. Meanwhile, the initial cracking and peak stress, capacity to limit cracking were enhanced with the decreased specimen thickness. A modified prediction model considering the wall effect, flattening and squeezing effect was developed to predict the probability density function p(θ) of fiber orientation angle. Additionally, the uniformity factor μ2 was introduced to predict crack number, and the relationship between the μ2 and parameter ψ = (Vf × lf/df)/t was determined. Furthermore, a model was developed to convert the main crack width into uniaxial tensile strain. All models and relationships were validated using test data. A micromechanical model that considered the predicted p(θ) and conversion model was established to predict the uniaxial tensile response of UHPFRC, which was also successfully validated using test data.

Compressive Mechanical Properties and Energy Absorption of Cubic Spherical Hollow Cellular Material Based on the Rod and Curved Surface Structure

Cellular materials, such as lattices and honeycombs, were widely used for structural protection owing to their excellent mechanical properties. By combining the excellent characteristics of lattice and honeycomb curved surface structures, this study designed a cell called Cubic Spherical Hollow (CSH), which had the advantages of orthogonal isotropy and better spatial connectivity. Inspired by the micro-structural arrangement of bamboo fiber and conch shell, we designed the new CSH cellular materials through the interlayer offset strategy. Then, the effects of interlayer offset on the mechanical properties and compression deformation behavior were explored experimentally and simulatively. Compared with other cellular materials, CSH cellular materials exhibited excellent mechanical properties with higher specific strength and specific modulus. The arrangement offsets of the CSH cells between different layers led to a change in the deformation mechanism from a rod’s compressive mode to a combination of a rod’s compressive mode and curved surface’s bending mode. The initial peak stress and plateau stress decreased with the increased arrangement offsets of the CSH since the extruded protrusions of the structure filled the holes and reduced the lateral expansion behavior of the material in the pressurized environment. This phenomenon also reduced the transverse expansion and prevented the sudden change in stress in the constrained space, indicating that the structural deformation was stable and had excellent cushioning and energy absorption properties. In this study, the cellular material design strategy opens a new avenue for energy absorption.

Energy absorption of the kirigami-inspired pyramid foldcore sandwich structures under low-velocity impact

Foldcore sandwich structures offer a promising alternative to conventional honeycomb sandwiches in the field of lightweight structures, demonstrating significant potential as efficient energy absorption devices. The dynamic behavior of foldcore sandwich structures is crucial in response to low-velocity impacts in various engineering scenarios such as bird strikes, airdrops, and vehicle collisions. This study investigates the dynamic responses of a kirigami-inspired pyramid foldcore sandwich subjected to low-velocity impacts, which has previously exhibited remarkable energy absorption efficiency under quasi-static compression. Through a combination of experimental investigations and numerical simulations under impact conditions, it is observed that the pyramid foldcore initially undergoes pronounced localized deformation which results in a sensitivity to the loading rate and causes the high initial peak stress. Different from the mechanism observed under quasi-static compression, additional stationary plastic hinges on the facets are triggered during the post-buckling stage, thereby slightly enhancing the overall energy absorption. Moreover, the multi-layer pyramid foldcores with graded geometries are proposed, characterized by varying height and wall thickness for each layer. The graded pyramid foldcores significantly reduce the initial peak stress while maintaining energy absorption efficiency. In comparison with the conventional square honeycomb and Miura-ori foldcore under the impact velocity of 10 m/s, the uniformity ratio of the graded pyramid foldcore decreases by 70.9 % and 80.5 %, while the specific energy absorption improves by 0.97 % and 138.37 %, respectively. To summarize, the graded pyramid foldcore shows outstanding energy absorption efficiency, indicating its potential as a high-performance sandwich structure for impact applications.

Investigation on the energy absorption characteristics of novel graded auxetic re-entrant honeycombs

In this work, innovative graded auxetic re-entrant honeycombs constructed by adjusting the geometric parameters of a core unit cell are proposed, and their deformation modes and energy absorption characteristics with different impact speeds are systematically investigated. The novel graded design utilizes structural hierarchy on the meso-scale and functional gradient on the macro-scale. The numerical simulation models are verified by comparing the experimental results. The results show that compared with the ungraded honeycomb (URH), one of the graded honeycombs (GRHs), named GRH1, can greatly improve the specific energy absorption by 36.4%, 10.8%, and 6.00% for the quasi-static, low, and high-speed impact at a strain of 0.6. At the same time, the initial peak stress of GRH1 is decreased by 43.2% and 27.1% compared with that of URH for low and high-speed impact, respectively. It could be indicated that the GRH1 was an ideal energy-absorbing structure. This work provides a new route for designing graded auxetic honeycombs with enough insight to understand the deformation mechanism of the structures, which could be used in lightweight buffer protective systems.

In‐Plane Crushing Response of a Novel Arc‐Curved Hybrid Honeycomb with Negative Poisson's Ratio

Incorporating arc‐curved configuration into auxetic honeycomb can evenly distribute pressure, reduce stress concentration, and avoid fracture. In this work, a novel arc‐curved chiral star‐shaped honeycomb (ACSH) has been proposed by combining the chiral honeycomb (CH), the star‐shaped honeycomb (SSH), and arc‐curved configurations. The crushing response of the ACSH is studied experimentally and numerically. In order to verify the accuracy of simulation, quasi‐static compression experiment is carried out on the ACSH sample fabricated by 3D printing. Subsequently, the crashworthiness of the ACSH is compared with other honeycombs. Particularly, under the crushing velocity of 2 m s−1, the ACSH exhibits exceptional specific energy absorption, which is 179% higher than that of the conventional SSH. Additionally, it is also found that introducing arc‐curved configuration can effectively reduce initial peak stress. Moreover, the effect of functionally graded design on crashworthiness is systematically analyzed. The findings indicate that the initial peak stress decreases with the decrease of gradient rate. When crushing velocity increases to 80 m s−1, the SEA of the ACSH increases with the increase of gradient rate. This work investigates the crushing response of a novel honeycomb, which can provide a reference for designing and optimizing novel lightweight honeycombs with better crashworthiness.

Intelligently optimized arch-honeycomb metamaterial with superior bandgap and impact mitigation capacity

Engineering applications concurrently face challenges related to vibration, impact, load-bearing and energy absorption. Here, an arch-honeycomb metamaterial with split-ring resonators is proposed for wave attenuation and impact mitigation, with better energy absorption and lower initial peak stress. The split-ring resonators effectively induce bandgaps below 3 kHz, and the mechanisms of bandgap generation and polarization are studied through mode shapes, frequency contours and equivalent mass densities. Subsequently, a machine learning-based optimization framework is introduced to tailor the bandgaps, leading to a 155.59% increase in bandgap width. Furthermore, superior vibration isolation and impact mitigation are confirmed through experiments. Obvious attenuation peaks are observed in the bandgaps of the acceleration transmission spectrum in frequency domain. In time domain, the impact test demonstrates peak weakening and delay. The metamaterials offer advantages in wave attenuation, impact mitigation, load-bearing and energy absorption, providing valuable insights for the advancement of multifunctional metamaterials and their practical engineering applications.

Optimization of functionally graded solid-network TPMS meta-biomaterials

The current study enhances the performance of solid-network triply periodic minimal surface (TPMS) cellular materials through using cell size grading along with the Taguchi method. Cell size grading is a novel technique used to control the size of pores and the surface area without changing the relative density. In this context, experimental compression testing was conducted on six distinct geometries of cell size graded TPMS structures (Diamond, Fischer–Koch S, Gyroid, IWP, Primitive, and Schoen–F-RD) manufactured with dental resin using a masked stereolithography (MSLA) printer. The findings indicated that mean total energy absorption was greater for smaller initial cell sizes (4 and 6 mm) compared to larger sizes (12 mm). Consistent patterns were also observed with respect to final cell sizes. Upon examination of the stress-strain relationships between D and I-WP, it is evident that D exhibits a higher initial peak stress point. However, subsequent to a significant decline, it exhibits a tremendous degree of volatility before recovering. Conversely, I-WP demonstrated greater stability throughout the experiments, with a notably greater maximum stress effect. A significant influence was observed from the initial cell size on stress, with larger sizes leading to a reduction in absorbed energy. The acquired results serve as an essential basis for the identification of optimized designs that may be implemented to enhance the structures' durability.

Mechanical properties and regulatory strategy of twinned tetrahedral lattice structures

Given the outstanding mechanical performance of lattice metamaterials, novel structural forms and performance modulation strategies have garnered considerable attention. Herein, we develop a twined tetrahedral lattice structure (TTL) with a bending defect inside the unit cell. Mechanical properties before and after the introduction of defects in TTLs were studied using experiments and numerical simulations. The developed structure exhibits strictly stretching-dominated properties in the absence of bending defects. Whereas, the bending-dominant component of TTLs is elevated with increasing bending angle that can increase energy absorption efficiency. Moreover, the relative elastic modulus and initial peak stress can be reduced by even more than 70 % and 50 %, respectively, as the bending angle increases. Besides, a theoretical model for the relative elastic modulus of TTL at θ = 0° was established based on the displacement method on the Representative Volume Element (RVE), including both Euler-Bernoulli beam theory and Timoshenko beam theory. However, the two solutions show consistent results for strictly stretching-dominated structures. The accuracy of solutions is verified by experiments and simulations. The plateau stress theoretical model for TTLs was derived from the deformation process of the RVE based on plastic hinge theory. The theoretical solutions under different θ align well with numerical and experimental results. Overall, TTLs have superior relative elastic modulus, relative yield strength, and specific energy absorption compared to common lattice structures. The developed TTLs provide a new perspective on the property regulation of mechanical metamaterials.

Study on Microscopic Characteristics and Rock Mechanical Properties of Tight Sandstone after Acidification–Supercritical CO2 Composite Action: Case Study from Xujiahe Formation, China

Acidified CO2 fracturing is a viable method for increasing production in deep, tight sandstone reservoirs. However, the potential mechanism of changes in pore structure and mechanical properties of sandstone under acidified CO2 supercritical composite is not clear. Understanding this mechanism is important for the study of crack initiation and extension in tight sandstone reservoirs. This study utilizes sandstone samples from the Xujiahe Formation reservoir in Rongchang District as experimental specimens. The primary focus is to analyze the changes in pore structure and mechanical properties of these samples after acidification–supercritical CO2 composite action. Nuclear magnetic resonance (NMR) and uniaxial compression tests are employed as the main investigative techniques. The results show that there was a physicochemical synergy between the acidification–supercritical CO2 composite effect; the crack initial stress, damage stress, and peak stress of the sandstone after 16 MPa supercritical CO2 acidification treatment were reduced by 20%, 49.5%, and 49.8%, respectively; the crack volumetric strain accelerated and the sandstone evolved from brittle to ductile damage; and the larger pore space and microcracks of the sandstone increased significantly after the treatment, which can be attributed to the gradual dissolution of intergranular cement leading to the formation of new pores connected to the existing pore network. The change mechanism of sandstone after acidification–supercritical CO2 compound treatment is also proposed.

Inverse machine learning framework for optimizing gradient honeycomb structure under impact loading

In this study, an inverse design framework was constructed to explore gradient honeycomb structures (HCS) with high impact resistance. By establishing the relationship between the height of the cell and the cell-wall angle, HCS with different gradient modes were designed. The developed machine learning (ML) framework consisted of a forward regression model based on neural network (NN) and an inverse optimization model based on generative adversarial network (GAN). The regression model surrogated finite element analysis (FEA) to rapidly provide corresponding mechanical properties for the generated data of GAN. To ensure that the generated data met the desired design targets, additional physical constraints were incorporated into the generator of the GAN. This ensured that the network output not only consisted of valid data but also exhibited superior impact resistance. The results demonstrated that the trained ML model optimized both specific energy absorption (SEA) and initial peak stress of HCS. It even discovered high-performance gradient designs that outperformed the original data, with a maximum energy absorption 49.5% higher than that of uniform HCS. Moreover, the gradient modes and structural parameters of superior designs were identified, which is of great significance for the gradient design of HCS under impact loading. As a general design approach, this ML framework holds significant potential for the optimization design of metamaterials in other structures or with different mechanical properties.

Effect of grain orientation on the energy absorption performance of Chinese fir wood under quasi-static compression

ABSTRACT The compressive response and energy absorption of Chinese fir wood with different grain orientations along the longitudinal (L) and radial (or tangential) directions were studied through uniaxial quasi-static compression tests. The results indicated that the wood compressive behavior changed from out-of-plane to in-plane, similar to honeycomb materials when the grain orientation was changed from longitudinal to transverse. The initial peak stress (σp ) and plateau stress (σpl ) decreased upon increasing the grain angle (θ), especially below 45°, and more slowly above 45°. The wood compressive failure modes and energy absorption ability were also strongly dependent on the grain orientation, and the energy absorption per unit volume and energy absorption efficiency decreased as θ increased. Energy absorption diagrams and mathematical models were established to evaluate the optimum energy absorption point to guide the selection of energy-absorbing wood.

In‐Plane Impact Characteristics of Auxetic Rotating Triangular Honeycomb Inspired by a Rotating Rigid Structure

Inspired by rotating rigid structures, an auxiliary rotating triangular honeycomb structure (ARTH) is designed in this article. The structure has dual platform stress, which can reduce the initial peak stress generated during collisions, reducing injuries to pedestrians and vehicle occupants. The accuracy of the finite element numerical model is verified by experiments, and a series of researches are carried out. The mechanical properties of the structure at different velocities are studied and the classification diagram of deformation modes is obtained. Under low‐speed impact load, ARTH has two deformation stages and two stress plateau regions, in which the stress of the second plateau is more than twice that of the first plateau. Then, a theoretical model based on plastic dissipation theory predicts the stress platform at different deformation stages under quasi‐static conditions. Parametric analysis shows that increasing wall thickness t can significantly improve the stress platform and energy absorption, but the negative Poisson's ratio effect is weakened. The influence of angle θ on the first stage deformation of ARTH is significant. These studies can provide some references for the design of double‐platform stress and the reduction of initial peak stress of rotating auxiliary structures.

Design methodology for functional gradient star-shaped honeycomb with enhanced impact resistance and energy absorption

To enhance the impact resistance and energy absorption capacity of the honeycomb, a "gradient" design approach has been developed, incorporating the angle gradient, thickness gradient, and dual gradient star-shaped honeycomb (SSH). Subsequently, the impact mechanical properties of these gradient SSHs at various impact velocities are examined using numerical analysis. The results indicate that enhancing the initial stress peak and plateau stress of SSH, thereby improving its impact resistance and energy absorption rate, can be achieved through two modifications. Firstly, by configuring a layer with a smaller cell angle gradient at the impact end while utilizing a layer with a larger cell angle gradient at the bottom. Alternatively, by employing a layer with a larger wall thickness gradient at both the impact and fixed ends and a layer with a smaller wall thickness gradient in the middle. Furthermore, it has been observed that the deformation of dual gradient SSHs under dynamic loads is primarily governed by a thickness gradient. The results offer valuable insights that can be utilized in optimizing honeycomb structure design and investigating the mechanical properties influenced by the non-uniform distribution of honeycomb.

Research on the cushioning and energy absorption characteristics of gradient sinusoidal negative Poisson’s ratio honeycomb structures

In this study, we designed improved cellular materials (CMs) with good energy absorption capacities, proposing new types of CMs with negative Poisson ratios by introducing sinusoidal cell walls and three different gradients. The amplitude of the sinusoidal wall, cell periodicity, and cell wall thickness were modulated in three layers across the structure (denoted as AG-CM, PG-CM, and WTG-CM, respectively). The influence of the different gradient parameters on the dynamic response of the CMs was analysed. The finite element method was used to explicitly simulate the deformation behaviour, dynamic shock stress, and energy absorption characteristics of the proposed structures at different impact speeds and directions. The initial peak stress in the face of the impact of the CM with a reasonable gradient setting was lower than that of the non-gradient CM. In contrast, its energy absorption was higher than that of the non-gradient CM. WTG-CM exhibited the highest energy absorption for a low-speed impact (7 m/s). For a medium and high speed impacts (35 m/s and 70 m/s), AG-CM exhibited the highest energy absorption in the face of positive gradient impact, whereas WTG-CM exhibited the highest energy-absorbing energy when impacting against the gradient. Under similar impact rates, the energy absorption energy of the different CMs varied by 32.1%. For the same CM, the maximum difference in absorption energy between shock modes was 33.8%.

3D printed bending-stretching coupled non-self-similar hierarchical cellular topology under in-plane loading

Ultralight hierarchical metamaterial is a type of promising structure in aerospace and transportation applications owing to the high stiffness/strength to density ratio. Though some hierarchical topologies with distinct in-plane configurations have been reported, the topology with superior mechanical behaviors under plastic deformation is urgent to be tailored. The present study develops a novel bending-stretching coupled Non-Self-Similar Hierarchical Topology (NSSHT) via additive fabricating methodology, and gives an insight into the mechanical responses and energy absorption capacities. It is identified that the softening post initial peak stress is triggered by the bending of the oblique membrane in the first order unit cell when edge length ratio (γ) is low, while by the initial rotation of second order unit cell when γ is high. Compared to the quasi-static measurements, the dynamic specific initial peak stress of NSSHT with uniform wall thickness (η= 1) was enhanced up to 131.9%. The deformation modes at distinct stress stages are different under quasi-static and dynamic loads. For specific energy absorption capacity, the NSSHT with non-uniform wall thickness behaves better, and the majority is dissipated at stress enhancement stage. The developed novel hierarchical structures enable to provide a wider spectrum of choices for tailoring high-performance lightweight components.

Dynamic Compressive and Flexural Behaviour of Re-Entrant Auxetics: A Numerical Study.

Re-entrant auxetics offer the potential to address lightweight challenges while exhibiting superior impact resistance, energy absorption capacity, and a synclastic curvature deformation mechanism for a wide range of engineering applications. This paper presents a systematic numerical study on the compressive and flexural behaviour of re-entrant honeycomb and 3D re-entrant lattice using the finite element method implemented with ABAQUS/Explicit, in comparison with that of regular hexagonal honeycomb. The finite element model was validated with experimental data obtained from the literature, followed by a mesh size sensitivity analysis performed to determine the optimal element size. A series of simulations was then conducted to investigate the failure mechanisms and effects of different factors including strain rate, relative density, unit cell number, and material property on the dynamic response of re-entrant auxetics subjected to axial and flexural loading. The simulation results indicate that 3D re-entrant lattice is superior to hexagonal honeycomb and re-entrant honeycomb in energy dissipation, which is insensitive to unit cell number. Replacing re-entrant honeycomb with 3D re-entrant lattice leads to an 884% increase in plastic energy dissipation and a 694% rise in initial peak stress. Under flexural loading, the re-entrant honeycomb shows a small flexural modulus, but maintains the elastic deformation regime over a large range of strain. In all cases, the compressive and flexural dynamic response of re-entrant auxetics exhibits a strong dependence on strain rate, relative density, and material property. This study provides intuitive insight into the compressive and flexural performance of re-entrant auxetics, which can facilitate the optimal design of auxetic composites.

Multifunctional properties of carbon fiber integrated cement composite – A review and insights

This article examines the strength characteristics of carbon fiber-reinforced cement composite (CFRCC). The research explores the residual mechanical characteristics and microstructure of concrete reinforced with carbon fiber. The review also focused on the determination of the effect of CFRCC on the improvement of strength, microstructure, crystalline phase shift, and hydration products of the cement composites. The review indicates that the inclusion of carbon fibers can intensify the flexural and splitting strengths of CFRCC, but the compressive strength is magnified to a lesser extent. In addition to the initial elastic modulus and peak stress of carbon fiber-reinforced cement composite, a discernible strain-rate hardening effect was also observed. This indicates that carbon fiber-reinforced cement composite has a promising future as cement composite reinforcements. The review of the characteristics of the composites also suggests their applicability in tunnel building in the cement composite. It is determined that carbon fiber-reinforced cement composite has a stronger capacity to withstand impact loads, and further information about its features will be supplied. The scanning electron microscopy (SEM) result demonstrates that the single and most significant failure mode under stress is carbon fiber breaking and the pull-out of carbon fibers. Thus, the review reveals that carbon fibers have a limited but positive act on enhancing the mechanical properties of cement composites.

Behavior and constitutive model of ultra-high-performance concrete under monotonic and cyclic tensile loading

Ultra-high-performance concrete (UHPC) holds great promise for constructing lightweight and high-performance concrete structures. Hence, the proportion of live load increases, in turn, leads to a higher live-to-dead load ratio. UHPC structures suffer from cyclic stress amplitude in higher possibility. Therefore, the behavior and constitutive model of UHPC under cyclic tensile loading is of significance for the understanding of bearing capacity and deformation property for structures subjected to cyclic loading, which, nevertheless, is seldomly reported. In this regard, the present study conducted direct tensile tests on 35 UHPC dog-bones with four steel fiber volume fractions (i.e., 0%, 1%, 2%, and 3%) and two fiber shapes (i.e., straight and hooked-end). A constitutive model for UHPC under tensile loading was proposed, implemented into OpenSees, and employed in numerical simulations of UHPC beams subjected to bending in cyclic loading. The numerical results were compared with test results on UHPC beams for model verification. The experimental and numerical results show that the UHPC with straight fiber volume fractions less than 1% demonstrated a brittle failure, whereas the UHPC with straight fiber volume fractions higher than 1% or with a hooked-end fiber volume fraction of 2% exhibited a ductile failure. The increase in fiber volume fraction resulted in great enhancements of the initial crack and peak stresses, and the peak and ultimate strains, and the energy absorption capacity. Besides, the use of hooded-end fibers also led to a slight improvement in tensile strain behavior of UHPC but negatively affected the initial crack stress and peak stress. It also provided sufficient bonding between fiber and matrix. The envelope curves and failure patterns for UHPC under monotonic and cyclic loading are close. The proposed constitutive model for UHPC under tensile loading is composed of an envelope curve that is assumed bi-linear for strain softening UHPC or tri-linear for strain hardening UHPC, an unloading curve and a reloading curve described by an exponential function, and a damage index defined as the reduction of unloading modulus. The proposed constitutive model for UHPC under tensile loading can provide acceptable results for the prediction of the bearing capacity and deformation property of UHPC beams without reinforcements subjected to bending in cyclic loading.

Experimental Characterization and Numerical Modelling of the Impact Behavior of PVC Foams

BackgroundPolyvinyl chloride (PVC) foams are widely used in crashworthiness and energy absorption applications due to their low density and the capability of crushing up to large deformations with limited loads. This property is due to their particular constitutive behavior: the stress-strain curve is characterized, after an initial yield or peak stress, by a relevant plateau region followed by a steep increase due to foam densification. Furthermore, the mechanical response of PVC foam is strongly strain rate dependent.ObjectiveThis work aims to characterize the mechanical behavior of PVC foams and to develop a complete constitutive model for impact and energy absorption applications.MethodsCompressive tests are carried out at different speeds on PVC foam samples having different relative densities. Quasi-static and intermediate strain rate tests are performed by a pneumatic machine, while high strain rate tests are conducted by means of a Split Hopkinson Pressure Bar. The uniaxial stress-strain curves are used to calibrate the visco-elastic and visco-plastic constitutive model. In particular, the material behavior is divided into two parallel branches: the former describes the elasto-plastic behavior, while the latter accounts for the visco-elastic one; the plastic branch also includes a multiplicative term accounting for the strain rate sensitivity of the base material.ResultsThe tests highlight a strong compressibility of the foam with negligible lateral expansion. The energy absorption efficiency, as well as the densification strain, is evaluated. The material model is also implemented in Finite Element (FE) simulations of puncture impact tests, validating the results of the calibration procedure.ConclusionsThe calibration of the visco-elasto-plastic material model offers a physically consistent identification of the constitutive response of the PVC foams, showing an effective characterization of the impact behavior of the material.