Elasticity Approach to Predict Shape Transformation of Functionally Graded Mechanical Metamaterial under Tension

Mohammad Javad Khoshgoftar,Sajjad Seifoori,Ali Barkhordari,Mohammad Javad Mirzaali

doi:10.3390/ma14133452

Mohammad Javad Khoshgoftar, Sajjad Seifoori + Show 2 more

Open Access

https://doi.org/10.3390/ma14133452

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Abstract

The re-entrant structures are among the simple unit cell designs that have been widely used in the design of mechanical metamaterials. Changing the geometrical parameters of these unit cell structures, their overall elastic properties (i.e., elastic stiffness and Poisson’s ratio), can be simultaneously tuned. Therefore, different design strategies (e.g., functional gradient) can be implemented to design advanced engineering materials with unusual properties. Here, using the theory of elasticity and finite element modeling, we propose a fast and direct approach to effectively design the microarchitectures of mechanical metamaterials with re-entrant structures that allow predicting complex deformation shapes under uniaxial tensile loading. We also analyze the efficiency of this method by back calculating the microarchitectural designs of mechanical metamaterials to predict the complex 1-D external contour of objects (e.g., vase and foot). The proposed approach has several applications in creating programmable mechanical metamaterials with shape matching properties for exoskeletal and soft robotic devices.

Highlights

IntroductionCellular materials (e.g., bone, wood, and cork) can be extensively found in nature. These natural cellular materials have been sources of inspiration for engineers for many decades to create bioinspired lattice structures [1], for instance, those with low density and high stiffness [2] or high energy absorption properties [3]
Cellular materials can be extensively found in nature
Here, the functionally graded mechanical metamaterials made from reentrant structures under uniaxial tensile load were modeled using the elasticity theory and FEM

Summary

Introduction

Cellular materials (e.g., bone, wood, and cork) can be extensively found in nature. These natural cellular materials have been sources of inspiration for engineers for many decades to create bioinspired lattice structures [1], for instance, those with low density and high stiffness [2] or high energy absorption properties [3]. By a rational combination of re-entrant unit cells with different values of Poisson’s ratios, one can control the local (e.g., action-at-a-distance [16]) or global deformation (e.g., shape-matching mechanical metamaterials [17]) of the lattice structures under uniaxial far-field loading. This can lead to the design of programmable mechanical materials with shape morphing or shape transformation properties with numerous applications in the fields of architecture, sports, soft robotics, mechanical and biomedical engineering, and aeronautical industries [18,19,20,21,22,23,24]. The proposed method has several applications in designing programmable mechanical metamaterials with shape matching properties for exoskeletal and soft robotic devices

Modeling Approach

Finite Element Modeling

Results and Design

Variable Porosity Modeling

Conclusions