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• Combining ML and FE methods to accelerate the design process of honeycomb structures. • Using 2D unit cell surrogate 3D honeycomb structures. • CDAE with a pixelation strategy is proposed to manage FE data. • LSTM uses latent features and external loads to predict structural dynamic responses. In this study, a novel framework was presented for accelerating the prediction of the mechanical response of honeycomb structures under dynamic crushing, using 2D cells to surrogate 3D honeycomb structures by machine learning (ML). The sizes of different honeycomb structures were designed and the necessary training data obtained through finite element (FE) simulations, but without using any explicit design parameters of the honeycomb cells in the ML model. A pixelization method of FE model was proposed to separate the complete cell structure from the honeycomb FE grid data and convert it into a matching pixel map. FE data was structuralized while reducing the large amount of computational power consumed in identifying complex array structures. Unsupervised automatic extraction of low-dimensional features of pixel maps was performed using a convolutional denoising autoencoder (CDAE). The crushing velocity and the extracted latent features were used as the input of the long-short term memory (LSTM) network to predict the crushing deformation and stress-strain curve of the honeycomb structure under different dynamic loading. Results showed that the constructed ML model could describe the dynamic crushing response behavior. Compared with the traditional FE method, the prediction model was 4.45 × 103 and 1.05 × 103 times faster in predicting the stress-strain and structural deformation response, respectively. The mechanical response prediction model provided a method for rapidly evaluating the dynamic mechanical response behavior of similar periodic array structures using FE model data, which could be beneficial for the design and development of equipment based on bionic structures. [ABSTRACT FROM AUTHOR]

• Lattice structure of honeycomb is proposed to improve structural crashworthiness. • Four single-cells of lattice structures (different Poisson's ratios) are considered. • Effect of basic parameters of single-cell on structural crashworthiness is discussed. • Multi-objective optimization method is proposed using GRA coupling EW. A spatial lattice structure is proposed to improve the structural crashworthiness and energy absorption. First, a single-cell structure is proposed via a bionic honeycomb, and then the single-cell structure is arrayed to form a spatial lattice structure. The finite element model of the spatial lattice structure for crashworthiness analysis is established. The theoretical model of the plateau stress of the lattice structure under compressive conditions is derived, and its accuracy is verified by the corresponding finite element analysis. After that, the effect of geometrical parameters of single-cell structure on crashworthiness is analyzed. Then, geometrical parameters of single-cell structure and number of single-cell in the X, Y , and Z directions are used as design variables, the mass, and overall size are used as constraints, and specific energy absorption and collision peak force are used as optimization objectives. The multi-objective crashworthiness optimization of spatial lattice structure is carried out, and the optimal lattice structure design is determined via the gray relational analysis coupling entropy weight method. The validity of the finite element model and optimal design is verified by the drop weight impact test. The crashworthiness optimization of spatial lattice structures has important guiding significance for the design of energy-absorbing structures. [Display omitted] [ABSTRACT FROM AUTHOR]

• Comparative impact tests of novel FHCB were performed. • Foam filling enhances impact resistance. • Gradient design can optimize foam energy absorption. Auxetic structures have attracted a lot of attention as they can meet the requirements of impact resistance and lightweight performance of protective structures in aerospace and defense industries. To enhance the impact resistance and improve the capacity of energy absorption of auxetic structures, foam-filled hybrid-chiral honeycomb beams (FHCB) were designed and fabricated through SLM (Selective laser melting) printing method and foaming method. The localized impulse loading was generated through the impact from foam projectile, accelerated by light gas gun. The dynamic responses of EHCB (empty hybrid-chiral honeycomb beam) and FHCB were compared. In the experimental results, FHCB showed enhanced impact resistance and higher SEA (specific energy absorption) value than EHCB. A validate finite element model was used to study the influence of cell-wall thickness on the impact resistance of EHCB and FHCB. Results indicated that by changing the cell-wall thickness, the potential energy absorption capacity of the filled foam can be fully utilized. Furthermore, the impact resistance of FHCB can be effectively improved by using a gradient cell-wall thickness arrangement. This study can provide reference for the optimal design of blast mitigation and impact resistant structures. [ABSTRACT FROM AUTHOR]

The diagonal-enhanced square grid configuration inspired by glass sponge has great potential in mechanics, with geometries serving as honeycomb cores for sandwich panels, which can improve the structure's energy absorption capabilities. Modeling the hexagonal honeycomb core (HHC) sandwich panels, a finite element numerical model for low-speed impact of sandwich panels with high accuracy is proposed, and low-speed impact response of bio-inspired diagonal-enhanced square honeycomb core (BSHC) sandwich panels is studied. The impact response of BSHC sandwich panels, Hexagonal honeycomb core (HHC) sandwich panels and ordinary square honeycomb core (OSHC) sandwich panels were studied with the same relative densities and the same face-sheets. BSHC can lead to significantly enhanced the peak loads and stiffness of the sandwich panels. BSHC sandwich panels not only have excellent energy absorption performance, but also outperform HHC sandwich panels in terms of resistance to impact deformation. BSHC can transfer dynamic loads from the front face-sheet to the back face-sheet efficiently without stress concentration in the core itself. A theoretical analysis of the energy absorption capacity of the BSHCs and HHC were performed to illustrate the energy absorption mechanism. In addition, the peak load and contact energy of BSHC sandwich panels and HHC sandwich panels were theoretically predicted under low-speed impact. • The BSHC lead to significant peak load and higher stiffness of sandwich panels, increasing impact resistance. • The BSHC sandwich panels have excellent energy absorption performance. • The BSHC can effectively reduce the stress and deformation of sandwich panels. [ABSTRACT FROM AUTHOR]

Structural response and failure modes of honeycomb sandwich panels subjected to a shock (impulsive pressure) followed by a high velocity projectile impact were investigated using detailed finite element simulations. Performance of sandwich panels was quantified by maximum transverse deflection of the bottom face sheet and core crushing strain along with an investigation of their optimal behavior. Three failure modes were observed in panels – core failure, top face failure, and tearing and detachment from support. Failure maps of honeycomb sandwich panels were constructed to show the failure mode of panels as a function of shock intensity, projectile velocity and panel core relative density. In addition, a limited set of simulations were carried out to study the role of incident angle of projectile on the overall performance of a panel. These simulations showed that maximum deflection occurred for vertically impacting projectiles. However, we found that this did not directly translate to maximum core crushing strain in sandwich panels. The results provide new insight into the performance and failure of sandwich panels under complex dynamic loading conditions, and further highlight the potential of these panels for development of threat-resistant structural systems. [ABSTRACT FROM AUTHOR]

• High-velocity impact resistance of doubly curved CFRP sandwich panels is presented. • Impact tests are carried out by using a single-stage air gas gun test machine. • An analytical model is developed to describe the ballistic limit velocity. • Parametric analyses are carried out for various radius of curvature of the panels. This work describes the high-velocity impact behavior of doubly curved sandwich panels. The sandwich panels are manufactured using carbon/fiber epoxy composite face sheets, polyurethane foam core and 3D-printed PLA plastic cellular auxetic (re-entrant) honeycombs. High-velocity impact tests are carried out by using a single-stage air gas gun test machine. A spherical steel projectile with the radius of 5 mm is impacted to the center of the specimens with the speed of 100 m/s. The experimental data are used to validate explicit finite element models of the doubly curved structures. An analytical model is also developed for the ballistic limit of the flat and doubly curved sandwich panels, and the analytical results are compared to those obtained from the numerical ones. Parametric numerical analyses of the high-speed impact of the curved sandwich panels are then carried out considering various radii of curvature of the panels. The results show that the energy absorption is increased as the curvature is decreased for the panels with both foam and re-entrant core. In addition, the core configuration provides a key role in the impact resistance of the sandwich panels. Re -entrant models show an increase in specific energy absorption (SEA) compared to the foam core types. [Display omitted] [ABSTRACT FROM AUTHOR]

• The ballistic impact effect and failure characteristics of AU honeycomb sandwich panel built with CFRP rear face sheet were experimentally investigated. • The ballistic performance of AU honeycomb sandwich panel is compared with HEX honeycomb sandwich panels and AF honeycomb sandwich panels. • Numerical results are in good agreement with experiments and can accurately describe damage mode. • The effect of the face-sheet type and thicknesses and unit cell angle on the damage of AU honeycomb sandwich panels are numerically studied. This work showed a numerical and experimental investigation examining the ballistic impact performance of auxetic honeycomb sandwich panels (AHSPs) built with a carbon fiber reinforced polymer (CFRP) bottom-sheet. At first, twelve honeycomb sandwich panels (HSPs) were analyzed under ballistic impact test conditions. The HSPs consisted of Q345 steel top-sheets, CFRP bottom-sheet, and a honeycomb aluminum core with three kinds of cell configurations (regular, reentrant, and enhanced reentrant hexagons, respectively). The performances of the HSPs were compared to a control set of Al foam-cored sandwich panels of identical areal densities. The results demonstrated that the auxetic honeycomb core improves the ballistic impact performance of HSPs by reducing the residual velocity and enhancing the damage tolerances. For the numerical research, the HSPs responses are deduced by finite element modeling. Parametric investigations were conducted to investigate the influences of the honeycomb type, unit cell angle and face-sheet type on the ballistic resistance of the HSPs. Numerical studies present that the ballistic limits and the HSP perforation energy are significantly influenced by the above factors. [Display omitted]. [ABSTRACT FROM AUTHOR]

• The dynamic responses and energy absorption characteristics of aluminium honeycomb sandwich panels under ice wedge impact are investigated. • A three-dimensional nonlinear finite element model of AHSP under ice impact is established. • The ice wedge impact tests of AHSPs were conducted. • The plastic deformation energy absorption and ice facture energy dissipation mechanism is revealed. In this paper, the dynamic responses and energy absorption characteristics of aluminium honeycomb sandwich panels (AHSPs) under ice wedge impact are numerically and experimentally investigated. A three-dimensional nonlinear finite element model of AHSP under ice impact is established based on a concrete constitutive ice model in the commercial package ANSYS/LS-DYNA. The impact force-displacement curves and energy absorption properties as well as the crushing process of ice wedge are numerically achieved. In addition, the ice wedge impact tests of AHSPs were conducted by using a horizontal impact experimental apparatus. Furthermore, the effects of impact parameters and structural parameters on the dynamic responses and energy absorption are performed. Results show that the numerical results of ice wedge-AHSP impact dynamic responses are consistent well with the experimental results. The permanent deformation profiles of face sheets are approximately axisymmetric about the vertical and horizontal centerline. The ice impact energy is mainly converted into the plastic deformation energy of AHSP and rebound kinetic energy of ice wedge as well as the fracture energy of ice wedge. With the increase of the impact energy and thickness of face sheets, the energy dissipation ratio of ice broken increases dramatically and the energy dissipation by ice wedge makes an increasingly contribution to the impact energy absorption. [ABSTRACT FROM AUTHOR]

Abstract: Strength enhancement and deformation localisation are typical features of the dynamic response of cellular materials. Several one-dimensional shock models have been developed to explain these features. A unified framework of one-dimensional plastic shock wave models was established in this paper. Based on an arbitrary plastic hardening constitutive model for cellular materials, general solutions, although implicit, have been derived for two impact scenarios. For a rigid–power-law hardening (R-PLH) idealisation involved in three material parameters, namely the yield stress, the strength index and the strain-hardening index, closed-form/semi-closed-form solutions of the physical quantities across the shock front have been derived. The linearly hardening and locking idealisations are found to correspond to the two opposite limit cases with the strain-hardening index of one and infinity, respectively. The shock models based on three different idealisations are verified with cell-based finite element models including an irregular honeycomb and a closed-cell foam. It is found that the force responses predicted by the shock models are not very sensitive to the choice of the idealisations and they are in good agreement with the cell-based finite element results. Deformation features predicted by the shock models are compared well with the cell-based results when the impact velocity is not very low. The comparisons show that using more realistic constitutive models such as the R-PLH idealisation may present more accurate predictions. [Copyright &y& Elsevier]

Abstract: The underwater blast response of free-standing sandwich plates with a square honeycomb core and a corrugated core has been measured. The total momentum imparted to the sandwich plate and the degree of core compaction are measured as a function of (i) core strength, (ii) mass of the front face sheet (that is, the wet face) and (iii) time constant of the blast pulse. Finite element calculations are performed in order to analyse the phases of fluid–structure interaction. The choice of core topology has a strong influence upon the dynamic compressive strength and upon the degree of core compression, but has only a minor effect upon the total momentum imparted to the sandwich. For both topologies, a reduction in the mass of the front (wet) face reduces the imparted momentum, but at the expense of increased core compression. Conversely, an increase in the time constant of the blast pulse results in lower core compression, but the performance advantage over a monolithic plate in terms of imparted momentum is reduced. The sandwich panel results are compared with analytical results for monolithic plates of mass equal to that of (i) the sandwich panel and (ii) the front face alone. (Case (i) represents a rigid core while (ii) represents a core of negligible strength.) For most conditions considered, the sandwich results lie between these limits reflecting the coupled nature of core deformation and fluid–structure interaction. [ABSTRACT FROM AUTHOR]

Abstract: Energy absorption characteristics of regular polygonal columns and angle elements under dynamic axial compression are investigated by using non-linear explicit finite element code LS-DYNA. The influence of central angle on deformation mode and mean crushing force of angle elements is studied. Based on two types of deformation mechanisms known by experiments, two types of initial indentation triggers are introduced. By assuming appropriate boundary condition on the edges, a simplified finite element model is adopted in the analysis of angle elements and validated by comparing with full polygonal column model. Numerical investigations are also carried out to study the influence of angle on angle elements with three and four panels by using the simplified model. Several useful conclusions are drawn about the axial crushing of polygonal columns and angle elements and can be used to guide the design of crashworthiness structures. In addition, a comparison is conducted between the numerical results and theoretical predictions of the mean forces of some special angle elements. Good agreement is obtained. [Copyright &y& Elsevier]

Abstract: The in-plane dynamic crushing of 2D hexagonal-cell honeycombs has been simulated using finite elements to explore the dynamic response of cellular materials and to investigate the features of the crushing front and to examine the assumptions employed in a one-dimensional shock theory [Reid SR, Peng C. Dynamic uniaxial crushing of wood. Int J Impact Eng 1997;19:531–70; Tan PJ, Reid SR, Harrigan JJ, Zou Z, Li S. Dynamic compressive strength properties of aluminium foams. Part II – shock theory and comparison with experimental data and numerical models. J Mech Phys Solids 2005;53:2206–30]. It has been demonstrated that progressive cell crushing is observed to propagate through the material in a ‘shock’ like manner when the crushing velocity exceeds a critical value. The simulations show that there exists a zone at the shock front across which there are essentially discontinuities in the material ‘particle velocity’, ‘stress’ and ‘strain’ as defined herein. At supercritical crushing velocities the thickness of this zone remains about one cell size, which varies little with the crushing velocity and the relative density. Densification strain increases as crushing velocity increases and asymptotes to a limit once a shock front forms. It has also been shown that the one-dimensional shock theory [Reid SR, Peng C. Dynamic uniaxial crushing of wood. Int J Impact Eng 1997;19:531–70; Tan PJ, Reid SR, Harrigan JJ, Zou Z, Li S. Dynamic compressive strength properties of aluminium foams. Part II – shock theory and comparison with experimental data and numerical models. J Mech Phys Solids 2005;53:2206–30], which was based on an equivalent rigid-perfectly plastic-locking stress–strain curve, tends to overestimate slightly the crushing stress and energy absorbed. [Copyright &y& Elsevier]

Abstract: The influence of the cell micro-topology on the in-plane dynamic crushing of honeycombs is studied by means of explicit dynamic finite element simulation using ANSYS/LS-DYNA. Firstly, under the assumption that the edge length and thickness are the same, the dynamic properties of the honeycombs filled by cells with different shapes (equilateral triangular or quadratic cells) and micro-arrangements (regular or staggered arrangement) are numerically analyzed. The full-scale in-plane dynamic crushing of the specimen, as well as the micro-structure transformation during the deformation, is discussed. Based on these, the influence of the cell micro-arrangement on the energy absorption ability of the honeycombs is clarified. The results show that owing to the differences in the micro-topology, triangular or quadratic honeycombs display different local deformation properties during the crushing. The variation of the cell arrangement patterns changes the local dynamic evolution characteristic of stress waves. ‘>’ and ‘<’ mode local deformation bands form at the sides of the stagger-arranged honeycombs, which results in lateral compression shrinkage during the crushing. The plateau stresses also increase with the impact velocity by a square law. The empirical equations for honeycombs filled with different cells (equilateral triangular or quadratic cells) and micro-arrangements (regular or staggered arrangement) at high impact velocities are formulated in terms of impact velocity, and the cell geometrical (edge length and thickness) and topology (edge connectivity) parameters. [Copyright &y& Elsevier]

Abstract: The in-plane impact behavior of honeycomb structures randomly filled with rigid inclusions was studied by using the finite element method to clarify the effect of inclusions on the deformation process, mean stress, densification strain, and absorbed energy. The deformation processes of the models were disturbed by inclusions; shear bands were pinned, and the cell regions surrounded by inclusions were shielded. Mean stress, densification strain, and absorbed energy per unit volume normalized by the values of the model without inclusions were found to be only dependent on the fraction of inclusions. As the volume fraction of inclusions increased, the normalized mean stress linearly increased and the normalized densification strain linearly decreased. The normalized absorbed energy per unit volume could be approximated by an inverted parabolic equation. The energy absorption of models with inclusions having volume fractions from 0 to 0.25 was larger than that of the models without inclusions. In particular, honeycomb models with fractions of inclusion from 0.1 to 0.2 exhibited the maximum absorbed energy. The model with a volume fraction larger than 0.4 could not be compressed because the inclusions in the model had already percolated before deformation. The in-plane impact behavior of honeycomb structures as energy absorbing materials can be designed by using the approximate equation and selecting the volume fraction of inclusions. [Copyright &y& Elsevier]

The static and dynamic experimental results of a polycarbonate circular cell honeycomb subjected to inplane biaxial loading are simulated through numerical analysis using the finite element method. The experimental results were presented in Part I of this two part paper (Chung and Waas, Int. J. Impact Eng. (2001), in preparation). Through several comparisons between the experimental and numerical results, the biaxial inplane crushing mechanisms of the circular cell honeycomb material are studied. The finite element simulations are able to accurately capture the essential features observed and measured in the experiments. [Copyright &y& Elsevier]