Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures

Bertoldi, Katia; Boyce, Mary C.; Deschanel, Stéphanie; Prange, Sharon M.; Mullin, T.

doi:10.1016/j.jmps.2008.03.006

Cited by 299 publications

(241 citation statements)

References 48 publications

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“…A structure which forms the basis of many auxetic materials is that of a cellular solid and research into the deformation these materials is a relatively mature field [19] with primary emphasis on the role of buckling phenomena on load carrying capacity and energy absorption under compressive loading. Very recently, the results of a combined experimental and numerical investigation demonstrated that mechanical instabilities in 2D periodic porous structures can trigger dramatic transformations of the original geometry [20,21] . Specifically, uniaxial loading of a square array of circular holes in an elastomeric matrix is found to lead to a pattern of alternating mutually orthogonal ellipses.…”

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confidence: 99%

“…Details of the method are provided elsewhere [21] and here we highlight some of the parts of the numerical procedure which are specific to the current investigation. Each mesh was constructed using six-node, quadratic, hybrid, plane strain elements (ABAQUS element type CPE6H) and the accuracy was checked by mesh refinement.…”

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confidence: 99%

“…Each mesh was constructed using six-node, quadratic, hybrid, plane strain elements (ABAQUS element type CPE6H) and the accuracy was checked by mesh refinement. The material was modeled using a two-term I1-based Rivlin model, which was modified to include compressibility with a high bulk modulus [21] where the material properties were determined by fitting the model to experimental calibration data (see Experimental Details Section). The instabilities were initially investigated using a linear perturbation procedure and the results confirmed that the observed pattern transformation arose from an elastic instability, since it corresponds to the lowest eigenmode of the structure.…”

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confidence: 99%

“…Moreover, practical applications are likely to involve samples of a large spatial extent. Consideration of both of these points, directed our focus to considering infinite periodic structures using Representative Volume Elements (RVEs) and numerically convenient periodic boundary conditions [21] . Two different types of instability may occur [21] in infinite periodic solids under compression on periodic domains: microscopic instabilities with a finite wavelength and macroscopic instabilities characterized by a wavelength much larger than the scale of the microstructure.…”

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confidence: 99%

“…Consideration of both of these points, directed our focus to considering infinite periodic structures using Representative Volume Elements (RVEs) and numerically convenient periodic boundary conditions [21] . Two different types of instability may occur [21] in infinite periodic solids under compression on periodic domains: microscopic instabilities with a finite wavelength and macroscopic instabilities characterized by a wavelength much larger than the scale of the microstructure. Although microscopic instabilities alter the original periodicity of the solid, here they are investigated on the primitive cell using Bloch wave analysis [21] which provides both the point on loading path where instability occurs and the periodicity of the new structure.…”

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Negative Poisson's Ratio Behavior Induced by an Elastic Instability

et al. 2010

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When materials are compressed along a particular axis they are most commonly observed to expand in directions orthogonal to the applied load. The property that characterizes this behavior is the Poisson's ratio which is defined as the ratio between the negative transverse and longitudinal strains. The majority of materials are characterized by a positive Poisson's ratio which is approximately 0.5 for rubber and 0.3 for glass and steel. Materials with a negative Poisson's ratio will contract (expand) in the transverse direction when compressed (stretched) and, although they can exist in principle, demonstration of practical examples is relatively recent. Discovery and development of materials with negative Poisson's ratio, also called auxetics, was first reported in the seminal work of Lakes in 1987. [1] There is significant interest in the development of auxetic materials because of tremendous potential in applications in areas such the design of novel fasteners [2] , prostheses [3] , piezocomposites with optimal performance [4] and foams with superior damping and acoustic properties [5] . The results of many investigations [6][7] suggest that the auxetic behavior involves an interplay between the microstructure of the material and its deformation. Examples of this are provided by the discovery that metals with a cubic lattice [8] , natural layered ceramics [9] , ferroelectric polycrystalline ceramics [10] and zeolites [11] may all exhibit negative Poisson's ratio behavior. Moreover, several geometries and mechanisms have been proposed to achieve negative values for the Poisson's ratio, including foams with reentrant structures [1] , hierarchical laminates [12] , polymeric and metallic foams [13] , microporous polymers [14] , molecular networks [15] and manybody systems with isotropic pair interactions [16] . Negative Poisson's ratio effects have also been demonstrated at the micron scale using complex materials which were fabricated using soft lithography [17] and at the nanoscale with sheets assemblies of carbon nanotubes [18] .A significant challenge in the fabrication of materials with auxetic properties is that it usually involves embedding structures with intricate geometries within a host matrix. As such, the manufacturing process has

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confidence: 99%

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confidence: 99%

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Negative Poisson's Ratio Behavior Induced by an Elastic Instability

et al. 2010

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Stability of Lattice Materials

Casadei

Wang

Bertoldi

2017

Dynamics of Lattice Materials

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Perforated Sheets Exhibiting Negative Poisson's Ratios

2010

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Sheets made from readily available conventional materials containing diamond or star shaped perforations are shown to exhibit various Poisson's ratio values which could also be negative (auxetic). This behavior may be exhibited in both tension and compression and can be explained through models based on “rotating rigid units.” This provides an easy manner for the manufacture of auxetic or conventional systems at any scale which can be tailor made to exhibit particular values of the Poisson's ratio.

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Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures

Cited by 299 publications

References 48 publications

Negative Poisson's Ratio Behavior Induced by an Elastic Instability

Negative Poisson's Ratio Behavior Induced by an Elastic Instability

Stability of Lattice Materials

Perforated Sheets Exhibiting Negative Poisson's Ratios

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