Mechanical Performance of Multidirectional Buckling-Based Negative Stiffness Metamaterials: An Analytical and Numerical Study.

Chenhui Ren,Deqing Yang,Haoxing Qin

doi:10.3390/ma11071078

Abstract

Unidirectional, bidirectional and tridirectional Buckling-based Negative Stiffness (BNS) lattice metamaterials are designed by adding prefabricated curved beams into multidimensional rigid frames. Finite Element Analysis models are built, and their mechanical performance is investigated and discussed. First, geometric parameters of the curved beam were systematically studied with numerical analyses and the results were validated by theoretical solutions. Next, within unidirectional designs of different layer numbers, the basic properties of multilayer BNS metamaterials were revealed via quasi-static compressions. Then, the bidirectional and tridirectional designs were loaded on orthogonal axes to research both the quasi-static and dynamic behaviors. For dynamic analysis conditions, simulation scenarios of different impact velocities were implemented and compared. The results demonstrate that the proposed numerical analysis step has accurately predicted the force-displacement relations of both the curved beam and multilayer designs and the relations can be tuned via different geometric parameters. Moreover, the macroscopic performance of the metamaterials is sensitive to the rigidity of supporting frames. The shock force during impact is reduced down below the buckling thresholds of metamaterial designs and sharp impact damage is avoided. The presented metamaterials are able to undergo multiaxial stress conditions while retaining the negative stiffness effect and energy-absorbing nature and possess abundant freedom of parametric design, which is potentially useful in shock and vibration engineering.

Highlights

Unlike homogeneous natural materials, metamaterials are products of human ingenuity and their properties depend largely on internal construction rather than on parent materials [1]
As the constructions of the bi/tridirectional based Negative Stiffness (BNS) lattice metamaterials stem from the study on the unidirectional case, mechanical behaviors are investigated for the unidirectional design first
Curved beams are assembled row by row toward one, two and three different directions respectively, to ensure that they are loaded laterally at the midpoints, negative stiffness effect can be utilized for multiaxial stress conditions

Summary

Introduction

Metamaterials are products of human ingenuity and their properties depend largely on internal construction rather than on parent materials [1]. In the field of mechanical metamaterials, negative stiffness effect has been exploited to obtain innovative properties. Materials 2018, 11, 1078 piezoelectricity and pyroelectricity, can be achieved in composite materials with an appropriately tuned negative-stiffness phase. Negative stiffness is usually achieved from beams undergoing both compression and bending [17,18,19], linear springs under rotation [20,21], and specific material distributions [22,23]. With increasing displacement or deformation, these systems experience unloading in the applied force (or provide decreasing resistance). Among these systems, bistable beams are widely used as basic elements in microstructures, and several scholars have been working on them. Later Qiu et al [25,26] presented a bistable mechanism of “pre-fabricated curved beams” that did not rely on compressional residual stress for its bistability

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