Numerical and experimental investigation of FDM fabricated re-entrant auxetic structures of ABS and PLA materials under compressive loading
Authors: Vyavahare Swapnil , Kumar Shailendra 
Published: February 2021

Purpose
Auxetic structures are one type of mechanical meta-materials mainly used for energy absorption applications because of their unique negative Poisson’s ratio. This study is focused on numerical and experimental investigations of fused deposition modeling (FDM) fabricated re-entrant auxetic structures of acrylonitrile butadiene styrene (ABS) and poly-lactic acid (PLA) materials under compressive loading. Influence of geometric parameters, namely, re-entrant angle, height and arm-length on strength, stiffness and specific energy absorption (SEA) of auxetic structures under compressive loading. Optimization of significant parameters is also performed to maximize these responses and minimize weight and time of fabrication. Further, efforts have also been made to develop predictive models for strength, stiffness and SEA of auxetic structures.

Design/methodology/approach
A full factorial design of experiment is used for planning experiments. Auxetic structures of ABS and PLA are fabricated by FDM technique of additive manufacturing within the constrained range of geometric parameters. Analysis of variance is performed to identify the influence of geometric parameters on responses. To optimize the geometric parameters Gray relational analysis is used. Deformation of auxetic structures is studied under compressive loading. A numerical investigation is also performed by building nonlinear finite element models of auxetic structures.

Findings
From the analysis of results, it is found that re-entrant angle, height and arm-length with their interactions are significant parameters influencing responses, namely, strength, stiffness and SEA of the auxetic structures of ABS and PLA materials. Based on the analysis, statistical nonlinear quadratic models are developed to predict these responses. Optimal configurations of auxetic structure of ABS and PLA are determined to maximize strength, stiffness, SEA and minimize weight and time of fabrication. From the study of deformation of auxetic structures, it is found that ABS structures have higher energy absorption, whereas PLA structures have better stiffness. Results of finite element analysis (FEA) are found in good agreement with experimental results.

Research limitations/implications
The present study is limited to re-entrant type of auxetic structures of ABS and PLA materials only under compressive loading. Also, results from the present study are valid within the selected range of geometric parameters. The findings of the present study are useful in maximizing strength, stiffness and SEA of auxetic structures that have wide applications in the automotive, aerospace, sports and marine sector.

Originality/value
No literature is available on studying the influence of geometric parameters, namely, re-entrant angle, height and arm-length of auxetic structure on strength, stiffness and SEA under compressive loading. Also, a comparative study of feedstock materials, namely, ABS and PLA, is also not reported. The present work attempts to fulfill the above research gaps.