Mechanics of sandwich panels with a buckling-dominated lattice core: The effects of the initial rod curvatures

Abstract

The mechanical behavior of sandwich panels with a buckling-dominated lattice core (SPBLC) are studied in this work. Based on an analysis of the structural force, deformation, yield point, plastic limit, and bifurcation buckling, the formulas for predicting the structural stiffness and strength are established and then validated by experimental tests and numerical simulations. The negative effects of the initial rod curvatures on the structural stiffness and strength are investigated for SPBLCs with different relative densities, different initial rod curvatures, and different cross-section shapes. Moreover, a comparative study on the energy absorption ability of SPBLCs and traditional sandwich panels with stretching-dominated lattice cores (SPSLCs) is conducted, which shows that a better energy absorption performance can be achieved by rationally designing the initial rod curvature. This work provides a theoretical model and design criteria for sandwich panels with buckling-dominated lattice cores, and it is instructive for the design of other buckling-dominated structures.

Introduction

Configuring lightweight materials or structures with the periodic arrangement of rods [1], [2], [3], [4], [5], [6], [7], [8], [9], shells [10], [11] or blocks [12], [13], [14], [15], [16] is a common approach in recent research. A representative example is lattice materials [1], [2], [3], [4], [17], [18], [19], [20], [21]. By rationally designing the direction, length, and cross-section of rods and utilizing the stretching-dominated mechanism [22], lattice materials can achieve optimal specific mechanical properties (i.e., a specific strength and stiffness), which is demonstrated in both periodic lattice materials [23], [24], [25] and sandwich panels with lattice cores [26]. Utilizing these advantages, these materials and structures are widely used in aerospace engineering and other fields that require the material to have a light weight but high mechanical performance [20]. In addition, the lattice materials are also reported to exhibit other potential applications including energy-absorbing device in impacting [6], [27], [28], vibration control [29], sound insulation [30], heat exchangers [31], biological applications [32] and multifunctional applications [18], [33].

However, these materials or structures, which are composed of straight rods, were found to have some disadvantages such as an uncontrollable stress–strain curve shape and poor energy-absorbing ability [34], [35], [36], [37], [38], which is because the buckling path of a straight rod is uncontrollable. Previous work has revealed many advantages of using rods with initial curvatures in design. Xu et al. [39], [40] proposed and studied a metamaterial composed of curved rods in DNA shapes, and demonstrated the high designability and recoverability of the metamaterial. Wang et al. [41] reported a 3D architected lattice structure composed of curved rods, which exhibited a negative Poisson’s ratio over a wide range of deformation values. Yang et al. [42] investigated a 3D double-U auxetic structure composed of curved rods, showing that curved configurations could enhance the auxetic behavior and increase the static collapse stress of the rods. DiPalma and Gandhi [43] compared hexagonal cellular lattice structures with straight and curved inclined walls, and the results showed that structures with curved walls had more favorable stress distributions at the junctions than those with straight walls. In addition, beam with initial curvature have been widely used for designing negative stiffness metamaterials [44], [45], [46], [47].

Sandwich panels with a buckling-dominated lattice core (SPBLC) is a new type of sandwich structures whose cores are composed of curved rods. By experimental investigation, previous work [36] has demonstrated that such structures have better energy-absorbing abilities than traditional sandwich panels with stretching-dominated lattice cores (SPSLCs). However, essentially, the initial curvature of the rods, as an initial defect, have negative effects on the strength and stiffness of the SPBLC. A difficulty in evaluating the effects is that such effects are affected by multiple structural parameters (e.g., initial curvature of the rod, cross-section of the rod, and structural relative density) and different failure mechanisms (e.g., buckling and yielding). Another problem is how to control the deformation path of SPBLCs by using initial curvature. Therefore, theoretical research on such structures is urgently needed to solve this difficulty.

In this work, SPBLCs are mainly investigated by theoretical methods. In Section 2, the geometry and fabrication of SPBLCs are introduced. In Section 3, based on the analysis of the force–deformation relationship for a small deformation, the plastic behavior (plastic yield and plastic limit analyses), and the bifurcation buckling behavior, formulas for predicting the structural stiffness and strength are obtained. In Section 4, to verify the correctness of the theoretical results, experimental and simulative tests are conducted. Based on the above results, in Section 5, the effects of the initial rod curvature on the structural stiffness and strength are investigated for structures with different relative densities, initial rod curvatures, and cross-section shapes. Moreover, the controllability of the large structural deformation and the positive effects of the initial curvature on the energy absorption are also studied.