Three-Dimensional-Printed Multistable Mechanical Metamaterials With a Deterministic Deformation Sequence

Multistable mechanical metamaterials are materials that have multiple stable configurations. The geometrical changes caused by the transition of the metamaterial from one stable state to another, could be exploited to obtain multifunctional and programmable materials. As the stimulus amplitude is varied, a multistable metamaterial goes through a sequence of stable configurations. However, this sequence (which we will call the deformation sequence) is unpredictable if the metamaterial consists of identical unit cells. This paper proposes to use small variations in the unit cell geometry to obtain a deterministic deformation sequence for one type of multistable metamaterial that consists of bistable unit cells. Based on an analytical model for a single unit cell and on the minimization of the total strain energy, a rigorous theoretical model is proposed to analyze the nonlinear mechanics of this type of metamaterials and to inform the designs. The proposed theoretical model is able to accurately predict the deformation sequence and the stress–strain curves that are observed in the finite-element simulations with an elastic constitutive model. A deterministic deformation sequence that matches the sequence predicted by the theory and finite-element simulations is obtained in experiments with 3D-printed samples. Furthermore, an excellent quantitative agreement between simulations and experiments is obtained once a viscoelastic constitutive model is introduced in the finite-element model. [DOI: 10.1115/1.4034706]

[1]  C. Sun,et al.  An elastic metamaterial with simultaneously negative mass density and bulk modulus , 2011 .

[2]  S. Kota,et al.  Synthesis of Multistable Equilibrium Compliant Mechanisms Using Combinations of Bistable Mechanisms , 2009 .

[3]  N. Fang,et al.  Ultrasonic metamaterials with negative modulus , 2006, Nature materials.

[4]  P. Pai,et al.  Acoustic metamaterial plates for elastic wave absorption and structural vibration suppression , 2014 .

[5]  K. Bertoldi,et al.  Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures , 2008 .

[6]  Damiano Pasini,et al.  Snapping mechanical metamaterials under tension. , 2015, Advanced materials.

[7]  J. R. Raney,et al.  Multistable Architected Materials for Trapping Elastic Strain Energy , 2015, Advanced materials.

[8]  Jongmin Shim,et al.  Harnessing instability-induced pattern transformation to design tunable phononic crystals , 2015 .

[9]  Guoliang Huang,et al.  On the negative effective mass density in acoustic metamaterials , 2009 .

[10]  Harley T Johnson,et al.  Optical properties of two-dimensional polymer photonic crystals after deformation-induced pattern transformations , 2009 .

[11]  Katia Bertoldi,et al.  Effects of geometric and material nonlinearities on tunable band gaps and low-frequency directionality of phononic crystals , 2013 .

[12]  D. Hodges,et al.  Fundamentals of Structural Stability , 2006 .

[13]  E. Thomas,et al.  Micro‐/Nanostructured Mechanical Metamaterials , 2012, Advanced materials.

[14]  M. Boyce,et al.  Enhanced energy dissipation in periodic epoxy nanoframes. , 2010, Nano letters.

[15]  Katia Bertoldi,et al.  Amplifying the response of soft actuators by harnessing snap-through instabilities , 2015, Proceedings of the National Academy of Sciences.

[16]  J. Lang,et al.  A curved-beam bistable mechanism , 2004, Journal of Microelectromechanical Systems.

[17]  Razvan Udroiu,et al.  Experimental determination of surface roughness of parts obtained by rapid prototyping , 2009 .

[18]  R. Lakes.  Foam Structures with a Negative Poisson's Ratio , 1987, Science.

[19]  C. Seepersad,et al.  Mechanical design of negative stiffness honeycomb materials , 2015, Integrating Materials and Manufacturing Innovation.

[20]  K. Bertoldi,et al.  Harnessing buckling to design tunable locally resonant acoustic metamaterials. , 2014, Physical review letters.

[21]  L. Valdevit,et al.  Multistable Shape‐Reconfigurable Architected Materials , 2016, Advanced materials.

[22]  Jie Li,et al.  Switching periodic membranes via pattern transformation and shape memory effect , 2012 .

[23]  C. Sun,et al.  Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density , 2009 .

[24]  Rigoberto Burgueño,et al.  Buckling-induced smart applications: recent advances and trends , 2015 .

[25]  Michael R. Haberman,et al.  A nonlinear negative stiffness metamaterial unit cell and small-on-large multiscale material model , 2013 .

[26]  Mary C Boyce,et al.  Transforming wave propagation in layered media via instability-induced interfacial wrinkling. , 2014, Physical review letters.

[27]  Chunyin Qiu,et al.  Metamaterial with simultaneously negative bulk modulus and mass density. , 2007, Physical review letters.

[28]  Christopher B. Williams,et al.  EXAMINING VARIABILITY IN THE MECHANICAL PROPERTIES OF PARTS MANUFACTURED VIA POLYJET DIRECT 3 D PRINTING , 2012 .

[29]  P. Frank Pai,et al.  Metamaterial-based Broadband Elastic Wave Absorber , 2010 .

[30]  P. Sheng,et al.  Membrane-type acoustic metamaterial with negative dynamic mass. , 2008, Physical review letters.

[31]  Brian Boswell,et al.  An Investigation of Dimensional Accuracy of Parts Produced by Three-Dimensional Printing , 2013 .

[32]  M. van Hecke,et al.  Programmable mechanical metamaterials. , 2014, Physical review letters.

[33]  Jongmin Shim,et al.  3D Soft Metamaterials with Negative Poisson's Ratio , 2013, Advanced materials.

[34]  Nilesh D. Mankame,et al.  Phase transforming cellular materials , 2015 .