Dynamic compression of metallic sandwich structures during planar impulsive loading in water

The compressive response of rigidly supported stainless steel sandwich panels subject to a planar impulsive load in water is investigated. Five core topologies that spanned a wide range of crush strengths and strain-dependencies were investigated. They included a (i) square-honeycomb, (ii) triangular honeycomb, (iii) multi-layer pyramidal truss, (iv) triangular corrugation and (v) diamond corrugation, all with a core relative density of approximately 5%. Quasi-statically, the honeycombs had the highest peak strength, but exhibited strong softening beyond the peak strength. The truss and corrugated cores had significantly lower strength, but a post yield plateau that extended to beyond a plastic strain of 60% similar to metal foams. Dynamically, the transmitted pressures scale with the quasi-static strength. The final transmitted momentum increased slowly with core strength (provided the cores were not fully crushed). It is shown that the essential aspects of the dynamic response, such as the transmitted momentum and the degree of core compression, are captured with surprising fidelity by modeling the cores as equivalent metal foams having plateau strengths represented by the quasi-static peak strength. The implication is that, despite considerable differences in core topology and dynamic deformation modes, a simple foam-like model replicates the dynamic response of rigidly supported sandwich panels subject to planar impulsive loads. It remains to ascertain whether such foam-like models capture more nuanced aspects of sandwich panel behavior when locally loaded in edge clamped configurations.     

Metallic sandwich panels subjected to multiple intense shocks

The mechanical response and fracture of metal sandwich panels subjected to multiple impulsive pressure loads (shocks) were investigated for panels with honeycomb and folded plate core constructions. The structural performance of panels with specific core configurations under multiple impulsive pressure loads is quantified by the maximum transverse deflection of the face sheets and the core crushing strain at mid-span of the panels. A limited set of simulations was carried out to find the optimum core density of a square honeycomb core sandwich panels under two shocks. The panels with a relative core density of 4%–5% are shown to have minimum face sheet deflection for the loading conditions considered here. This was consistent with the findings related to the sandwich panel response subjected to a single intense shock. Comparison of these results showed that optimized sandwich panels outperform solid plates under shock loading. An empirical method for prediction of the deflection and fracture of sandwich panels under two consecutive shocks – based on finding an effective peak over-pressure – was provided. Moreover, a limited number of simulations related to response and fracture of sandwich panels under multiple shocks with different material properties were performed to highlight the role of metal strength and ductility. In this set of simulations, square honeycomb sandwich panels made of four steels representing a relatively wide range of strength, strain hardening and ductility values were studied. For panels clamped at their edge, the observed failure mechanisms are core failure, top face failure and tearing at or close to the clamped edge. Failure diagrams for sandwich panels were constructed which reveal the fracture and failure mechanisms under various shock intensities for panels subjected to up to three consecutive shocks. The results complement previous studies on the behavior and fracture of these panels under high intensity dynamic loading and further highlights the potential of these panels for development of threat-resistant structural systems.     

Structural performance of near-optimal sandwich panels with corrugated cores

An experimental and computational study of the bending response of steel sandwich panels with corrugated cores in both transverse and longitudinal loading orientations has been performed. Panel designs were chosen on the basis of failure mechanism maps, constructed using analytic models for failure initiation. The assessment affirms that the analytic models provide accurate predictions when failure initiation is controlled by yielding. However, discrepancies arise when failure initiation is governed by other mechanisms. One difficulty is related to the sensitivity of the buckling loads to the rotational constraints of the nodes, as well as to fabrication imperfections. The second relates to the compressive stresses beneath the loading platen. To address these deficiencies, existing models for core failure have been expanded. The new results have been validated by experimental measurements and finite element simulations. Limit loads have also been examined and found to be sensitive to the failure mechanism. When face yielding predominates, appreciable hardening follows the initial non-linearity, rendering robustness. Conversely, for designs controlled by buckling (either elastic or plastic) failure initiation is immediately followed by softening. The implication is that, when robustness is a key requirement, designs within the face failure domain are preferred.     

Imperfection sensitivity of pyramidal core sandwich structures

Lightweight metallic truss structures are currently being investigated for use within sandwich panel construction. These new material systems have demonstrated superior mechanical performance and are able to perform additional functions, such as thermal management and energy amelioration. The subject of this paper is an examination of the mechanical response of these structures. In particular, the retention of their stiffness and load capacity in the presence of imperfections is a central consideration, especially if they are to be used for a wide range of structural applications. To address this issue, sandwich panels with pyramidal truss cores have been tested in compression and shear, following the introduction of imperfections. These imperfections take the form of unbound nodes between the core and face sheets—a potential flaw that can occur during the fabrication process of these sandwich panels. Initial testing of small scale samples in compression provided insight into the influence of the number of unbound nodes but more importantly highlighted the impact of the spatial configuration of these imperfect nodes. Large scale samples, where bulk properties are observed and edge effects minimized, have been tested. The stiffness response has been compared with finite element simulations for a variety of unbound node configurations. Results for fully bound cores have also been compared to existing analytical predictions. Experimentally determined collapse strengths are also reported. Due to the influence of the spatial configuration of unbound nodes, upper and lower limits on stiffness and strength have been determined for compression and shear. Results show that pyramidal core sandwich structures are robust under compressive loading. However, the introduction of these imperfections causes rapid degradation of core shear properties.     

Three-dimensional Composite Lattice Structures Fabricated by Electrical Discharge Machining

We present a novel method for fabricating carbon fiber composite sandwich panels with lattice core construction by means of electrical discharge machining (EDM). First, flat-top corrugated carbon fiber composite cores were fabricated by a hot press molding method. Then, two composite face sheets were bonded to each corrugated core to create precursor sandwich panels. These panels were transformed into sandwich panels with near-pyramidal truss cores by EDM plunge-cutting the corrugated core between the face sheets with a shaped cuprite electrode. The flat top corrugation permits adhesive to be applied consistently, and the selected dimensions leave a substantial bond area after cutting, resulting in a strong core-to-sheet bond. The crushing behavior of this novel construction was investigated in flatwise compression, and the results were compared to analytical expressions for strength and stiffness.     

The impulsive response of sandwich beams: Analytical and numerical investigation of regimes of behaviour

An analytical model is developed to classify the impulsive response of sandwich beams based on the relative time-scales of core compression and the bending/stretching response of the sandwich beam. It is shown that an overlap in time scales leads to a coupled response and to the possibility of an enhanced shock resistance. Four regimes of behaviour are defined: decoupled responses with the sandwich core densifying partially or completely, and coupled responses with partial or full core densification. These regimes are marked on maps with axes chosen from the sandwich beam transverse core strength, the sandwich beam aspect ratio and the level of blast impulse. In addition to predicting the time-scales involved in the response of the sandwich beam, the analytical model is used to estimate the back face deflection, the degree of core compression and the magnitude of the support reactions. The predictions of the analytical model are compared with finite element (FE) simulations of impulsively loaded sandwich beams comprising an anisotropic foam core and elastic, ideally plastic face-sheets. The analytical and numerical predictions are in good agreement up to the end of core compression. However, the analytical model under-predicts the peak back face deflection and over-predicts the support reactions, especially for sandwich beams with high strength cores. The FE calculations are employed to construct design charts to select the optimum transverse core strength that either minimises the back face deflections or support reactions for a given sandwich beam aspect ratio or blast impulse. Typically, the value of the transverse core strength that minimises the back face deflection also minimises the support reactions. However, the optimal core strength depends on the level of blast impulse, with higher strength cores required for greater blasts.     

An analytic model for the water blast response of one-dimensional marine structure coated with elastic foam

The water blast response of one-dimensional marine structures coated with elastic foam is theoretically investigated. The foam coating is modeled by a group of concentrated masses separated by parallel massless nonlinear spring and damper, simulating the micro inertia, stiffness, and rate-dependent effects exhibited by common cellular materials. An analytic model for the wet face response, inclusive of fluid-structure interaction, is developed. The model addresses cavitation and takes into account the momentum of reconstituted water attached to the wet face. The first-order double asymptotic approximation method is used to compute the pressure during the spring-back and succeeding phase. The fidelity of the analytic model has been assessed by the finite element analysis.     

Elastic structural response of prismatic metal sandwich tubes to internal moving pressure loading

The analytical and numerical modeling of the structural response of a prismatic metal sandwich tube subjected to internal moving pressure loading is investigated in this paper. The prismatic core is equivalent to homogeneous and cylindrical orthotropic solids via homogenization procedure. The sandwich tube with the “effective” homogenized core is modeled using multi-layer sandwich theory considering the effects of transverse shear deformation and compressibility of the core; moreover, the solutions are obtained by using the precise integration method. Several dynamic elastic finite element (FE) simulations are carried out to obtain the structural response of the tube to shock loading moving at different velocities. The comparison between analytic solutions and FE simulations demonstrates that the transient analytical model, based on the proposed sandwich model, is capable of predicting the critical velocity and the dynamic structural response of the sandwich tube with the “effective” homogenized core with a high degree of accuracy. In addition, the critical velocity predicted using FE simulations of the complete model is not in agreement with that of the effective model. However, the structural response and the maximum amplification factors obtained using FE simulations of the complete model are nearly similar to that of the effective model, when the shock loading moves at the critical velocity. The influences of the relative density on the structural response are studied, and the capabilities of load bearing for sandwich tubes with different cores are compared with each other and with the monolithic tube. The results indicate that Kagome and triangle-6 are preferred among five topologies.     

Structural modeling of sandwich structures with lightweight cellular cores

An effective single layered finite element (FE) computational model is proposed to predict the structural behavior of lightweight sandwich panels having two dimensional (2D) prismatic or three dimensional (3D) truss cores. Three different types of cellular core topology are considered: pyramidal truss core (3D), Kagome truss core (3D) and corrugated core (2D), representing three kinds of material anisotropy: orthotropic, monoclinic and general anisotropic. A homogenization technique is developed to obtain the homogenized macroscopic stiffness properties of the cellular core. In comparison with the results obtained by using detailed FE model, the single layered computational model can give acceptable predictions for both the static and dynamic behaviors of orthotropic truss core sandwich panels. However, for non-orthotropic 3D truss cores, the predictions are not so well. For both static and dynamic behaviors of a 2D corrugated core sandwich panel, the predictions derived by the single layered computational model is generally acceptable when the size of the unit cell varies within a certain range, with the predictions for moderately strong or strong corrugated cores more accurate than those for weak cores. The project supported by the National Basic Research Program of China (2006CB601202), the National Natural Science Foundation of China (10328203, 10572111, 10572119, 10632060), the National 111 Project of China (B06024), the Program for New Century Excellent Talents in University (NCET-04-0958), the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment, and the Doctorate Foundation of Northwestern Polytechnical University.     

The resistance of metallic plates to localized impulse

The responses of metallic plates and sandwich panels to localized impulse are examined by using a dynamic plate test protocol supported by simulations. The fidelity of the simulation approach is assessed by comparing predictions of the deformations of a strong-honeycomb-core panel with measurements. The response is interpreted by comparing and contrasting the deformations with those experienced by the same sandwich panel (and an equivalent solid plate) subjected to a planar impulse. Comparisons based on the center point displacement reveal the following paradox. The honeycomb panel is superior to a solid plate when subjected to a planar impulse, but inferior when localized. The insights gained from an interpretation of these results are used to demonstrate that a new design with a doubly-corrugated soft core outperforms solid plates both for planar and localized impulses.     

Underwater blast loading of sandwich beams: Regimes of behaviour

Finite element (FE) calculations are used to develop a comprehensive understanding of the dynamic response of sandwich beams subjected to underwater blast loading, including the effects of fluid–structure interaction. Design maps are constructed to show the regimes of behaviour over a broad range of loading intensity, sandwich panel geometry and material strength. Over the entire range of parameters investigated, the time-scale associated with the initial fluid–structure interaction phase up to the instant of first cavitation in the fluid is much smaller than the time-scales associated with the core compression and the bending/stretching responses of the sandwich beam. Consequently, this initial fluid–structure interaction phase decouples from the subsequent phases of response. Four regimes of behaviour exist: the period of sandwich core compression either couples or decouples with the period of the beam bending, and the core either densifies partially or fully. These regimes of behaviour are charted on maps using axes of blast impulse and core strength. The simulations indicate that continued loading by the fluid during the core compression phase and the beam bending/stretching phase cannot be neglected. Consequently, analyses that neglect full fluid–structure interaction during the structural responses provide only estimates of performance metrics such as back face deflection and reaction forces at the supports. The calculations here also indicate that appropriately designed sandwich beams undergo significantly smaller back face deflections and exert smaller support forces than monolithic beams of equal mass. The optimum transverse core strength is determined for minimizing the back face deflection or support reactions at a given blast impulse. Typically, the transverse core strength that minimizes back face deflection is 40% below the value that minimizes the support reaction. Moreover, the optimal core strength depends upon the level of blast impulse, with higher strength cores required for higher intensity blasts.     

Dynamic response of doubly-curved anisotropic sandwich panels impacted by blast loadings

Problems related with the modeling and dynamic response to blast loadings of doubly-curved sandwich panels with laminated face sheets are developed. In this respect, the implications of the panel curvature, of anisotropy and stacking sequence of face sheets, of transverse orthotropy of the core, and of structural damping on dynamic response to time-dependent loads are highlighted. As concerns the blast pulses considered in this analysis, these are related to in-air explosions or of traveling shock-waves. Other parameters, mainly geometrical, are also considered in the numerical simulations, and their implications on the dynamic response are put into evidence. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state of the art of this problem, and provide pertinent results that are instrumental in the design of advanced sandwich shells operating in a dynamic environment. Moreover, the closed-form solutions developed in the paper, can serve as excellent references for comparison with numerical based solutions.     

One-dimensional response of sandwich plates to underwater shock loading

The one-dimensional shock response of sandwich plates is investigated for the case of identical face sheets separated by a compressible foam core. The dynamic response of the sandwich plates is analysed for front face impulsive loading, and the effect of strain hardening of the core material is determined. For realistic ratios of core mass to face sheet mass, it is found that the strain hardening capacity of the core has a negligible effect upon the average through-thickness compressive strain developed within the core. Consequently, it suffices to model the core as an ideally plastic-locking solid. The one-dimensional response of sandwich plates subjected to an underwater pressure pulse is investigated by both a lumped parameter model and a finite element (FE) model. Unlike the monolithic plate case, cavitation does not occur at the fluid-structure interface, and the sandwich plates remain loaded by fluid until the end of the core compression phase. The momentum transmitted to the sandwich plate increases with increasing core strength, suggesting that weak sandwich cores may enhance the underwater shock resistance of sandwich plates.     

Higher-order dynamic response of composite sandwich panels with flexible core under simultaneous low-velocity impacts of multiple small masses

Small mass impactors, such as runway debris and hailstones may result in a wave controlled local response, which is essentially independent of boundary conditions. The higher-order impact model of sandwich beams presented by Mijia and Pizhong [Mijia, Y., Pizhong, Q., 2005. Higher-order impact modeling of sandwich structures with flexible core. International Journal of Solids and Structures 42 (10), 5460–5490] is developed and enhanced to impact analysis of sandwich panels with transversely flexible cores. Therefore, an improved fully dynamic higher-order impact theory is developed to analyze the low-velocity impact dynamic of a system which consists of a composite sandwich panel with transversely flexible core and multiple small impactors with small masses. Impacts are assumed to occur normally and simultaneously over the top face-sheet with arbitrary different masses and initial velocities of impactors. The contact forces between the panel and the impactors are treated as the internal forces of the system. First shear deformation theory (FSDT) is used for the face-sheets while three-dimensional elasticity is used for the soft core. The fully dynamic effects of the core layer and the face-sheets are considered in this study. Contact area can be varied with contact duration. The results in multiple mass impacts over sandwich panels that are hitherto not reported in the literature are presented based on proposed improved higher-order sandwich plate theory (IHSAPT). Finally, for the case study of the single mass impact, the numerical results of the analysis have been compared either with the available experimental results or with some theoretical results. As no literature could be found on the impact of multiple impactors over sandwich panels, the present formulation is validated indirectly by comparing the response of two cases of double small masses and single small mass impacts. Also, in order to demonstrate the applicability of the validation, the analytical relation of minimum distance between two impactors is derived based on Olsson’s wave control principle in this paper.     

Effect of Facesheet Thickness on Dynamic Response of Composite Sandwich Plates to Underwater Impulsive Loading

The response of sandwich structures to underwater blast loading is analyzed. The analysis focuses on the effect of varying structural attributes on energy dissipation and deformation. The structures analyzed are planar sandwich plates with polymer foam cores and fiber-reinforced polymer composite facesheets. The thickness of the facesheets is varied under the conditions of constant material properties and core dimensions. The fully three-dimensional finite-element simulations carried out account for underwater blast loading through the use of the Mie-Gruneisen equation-of-state of a linear Hugoniot form and a modified Drucker-Prager core crushing model. The impulse imparted to the panels is varied from 4 to 42 kPa·s. The results show that there exists an optimal thickness of the facesheets which maximizes energy absorption in the core and minimizes the overall deflection of the structure.     

Dynamic response of anisotropic sandwich flat panels to underwater and in-air explosions

The problem of the dynamic response of flat rectangular sandwich panels subjected to underwater and in-air explosions is analyzed. The study is carried out in the framework of a geometrically non-linear model of sandwich structures featuring anisotropic laminated face sheets and an orthotropic core, in conjunction with the unsteady pressure generated by an explosion. Effects of the core and of the orthotropy of its material, as well as those related to the ply-thickness, directional material property and stacking sequence of face sheets, geometrical non-linearities and of the structural damping ratio are investigated, and their implications upon the dynamic response are highlighted. To the best of the authors’ knowledge, the specialized literature addressing the dynamic response of sandwich structures to underwater and in-air explosions is rather scanty. This work is likely to fill a gap in the specialized literature on this topic.     

Special behavior of unidirectional sandwich panels with transversely flexible core under statical loading

Special features inherent in the response of ordinary (fully bonded) and delaminated sandwich panels with a transversely flexible (“soft”) core subjected to external in-plane and vertical statical loads are analyzed. The analytical formulation is based on a higher-order theory for sandwich panels with non-rigid bond layers between the face sheets and the core. The central finite difference scheme is used for discretizing the continuous formulation. The deflated iterative Arnoldi scheme for solution of a large-scale generalized eigenvalue problem is employed, as well as the quasi-Newton global framework for the natural parameter and the arc-length continuation procedures. The numerical higher-order analysis reveals that the ordinary sandwich panel behaves as a compound structure in which the local/localized, overall or interactive forms of the response can take place depending on the geometry, mechanical properties, and boundary conditions of the structure. The non-sinusoidal modes confined to the support zones of the panel may occur at critical loads much lower than those predicted on the basis of presumed sinusoidal modes. Soft-core sandwich panels possess a complex branching behavior with limit points and secondary bifurcations. The thin-film-delamination approach used in the field of the composite plates is unsuitable for the analysis of delaminated sandwich panels and consideration of the interaction between the face sheets and the core is required. The complex response of the soft-core sandwich panels can be predicted only with the aid of the enhanced higher-order theory.     

Influence of imperfections on the performance of metal foam core sandwich panels

Sandwich panels and beams are used in bending and compression dominated components. The retention of their load capacity in the presence of imperfections is a central consideration. To address this issue, sandwich beams with metallic foam cores have been tested in four-point bending following the introduction of imperfections, created by impressing the face sheets. Limit load expressions for face yielding, core shear, and indentation failure have been developed and used to construct failure mechanism maps. From these maps, specimen designs were determined. Imperfections were introduced by indenting to varying penetrations. The indents were located on both the compressive and tensile side of bending configurations. Experimental measurements of the load/deflection response are obtained and compared with finite element results.     

Study on the Collapse of Pin-Reinforced Foam Sandwich Panel Cores

New fabrication technologies now allow for hybrid sandwich structures, known as X-core, to be manufactured. The X-core panels consist of a pin reinforced polymer foam core with carbon fiber face sheets. Carbon fiber or metallic (Titanium/Steel) pins are inserted into the foam core in the out-of-plane direction and extend from face sheet to face sheet. The through thickness three-point simply supported bending behavior of these panels is used to evaluate the collapse characteristics of the panels. Explicit experimental observations are used to calibrate analytical energy balance models describing the panel collapse as a function of geometry and properties. The mechanical response of X-core sandwich panels is compared to current sandwich materials for material selection.     

Elastica of sandwich panels with a transversely flexible core—A high-order theory approach

The elastica behavior of an extensional sandwich panel with a “soft” core when subjected to in-plane compressive loads is presented and it is compared with the response of its extensional equivalent single layer (ESL) with shear deformations model. The field equations along with the appropriate boundary conditions for the sandwich and the ESL panels have been derived through a variational approach following the High-order SAndwich Panel Theory (HSAPT) approach that takes into account the vertical flexibility of the core. The governing equations include the effects of the extension of the mid-surfaces of the face sheets of the sandwich panel or the mid-plane of the ESL model which the classical elastica approach misses. The results of the elastica response of a clamped-simply-supported sandwich panel and its ESL counterpart are presented and compared. They include the response along the panel, deformed shapes and equilibrium curves of in-plane loads versus structural quantities such as displacements and internal stress resultants and stresses. These results reveal that the predicted buckling load of the ESL panel is larger than that of the sandwich panel and that deep in the non-linear range the upper face sheet wrinkles with increasing overall and edge displacements and a release of the load. Hence, the use of an equivalent single layer panel especially when a sandwich panel with a compliant core is considered may lead to unsafe and unreliable predictions when large displacements and large rotations are considered.