Elastic composite with negative stiffness inclusions in antiplane strain

Dyskin, Arcady; Pasternak, Elena

doi:10.1016/j.ijengsci.2012.03.024

Cited by 36 publications

(24 citation statements)

References 57 publications

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“…Stability of the negative compressibility from the thermodynamics viewpoints have been demonstrated . In addition, effects of negative stiffness in elastic composites in the antiplane strain setting has been analyzed . Although stability of purely elastic, negative‐stiffness composites cannot be statically stable, as has recently been proven in the framework of elasticity theory , stability of the systems that are not purely elastic, nor in statics, may yet require more studies for possible stabilizing agents, such as driving frequency, multi‐physics interactions, or other deformation processes, for example, geometric nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Anomalous effective viscoelastic, thermoelastic, dielectric, and piezoelectric properties of negative‐stiffness composites and their stability

Wang

Chang

2015

Physica Status Solidi (b)

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Composite materials containing negative‐stiffness inclusions embedded in positive‐stiffness matrix may exhibit unconventional (anomalous) effective coupled‐field properties through interactions of the two phases. Effective coupled‐field properties are calculated with the finite element methods under the quasi‐static assumption. Stability boundaries are determined by applying 10 Hz sinusoidal loading on boundary surfaces, and the system is unstable if its energy becomes divergent for a chosen inclusion Young's modulus ratio (λE) or bulk modulus ratio (λK). Effective viscoelastic properties and their stability are studied for negative λE at 10 Hz, while the Poisson's ratio of the purely elastic inclusion is kept constant. For small inclusion volume fractions, their stability boundary is at λE ∼ –0.3, and extreme large effective damping and viscoelastic modulus are in the unstable regime. Furthermore, in the viscoelastic case, inclusion shapes have no effects on stability. As for the effective coupled‐field properties, all anomalous peaks are in the unstable regime for negative λE or λK, except for an anomalous peak in effective thermal expansion coefficient with electrically insulated inclusions. Insulated inclusions may cause charge accumulation at the inclusion‐matrix interface and boundary surface effects may serve as stabilizing agents to the composite system.

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Section: Introductionmentioning

confidence: 99%

Anomalous effective viscoelastic, thermoelastic, dielectric, and piezoelectric properties of negative‐stiffness composites and their stability

Wang

Chang

2015

Physica Status Solidi (b)

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“…This transitional negative stiffness should be distinguished form the quasi-static negative stiffness whereby the material or structure exhibits descending stress-strain dependence under displacement-controlled loading in a sufficiently stiff load frame (see examples and conditions of stability in Refs. [69][70][71][72][73][74][75]). On the other hand, we assume that it is insufficiently short to make dynamic effects important.…”

Section: Damage Accumulation As Instantaneous Appearance Of Negative mentioning

confidence: 99%

Behavior of Extreme Auxetic and Incompressible Elastic Materials

Dyskin

Pasternak

2017

Physica Status Solidi (b)

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We investigate auxetic isotropic elastic materials with the Poisson's ratio of exactly −1 and isotropic materials with the Poisson's ratio of near 0.5 (incompressible). In both cases the energy is not positive definite, which can lead to the material instability. In incompressible materials, the instability manifests itself in the emergence of non‐uniform displacement distribution. Investigation of the behavior of such materials with respect to damage or crack accumulation is based on the notion that during the instantaneous process of fracture formation, the fracture acts as a negative stiffness element; after the fracture is formed, it immediately turns into a conventional fracture with usual positive stiffness. We demonstrate that the cracks formed due to tensile or combined tensile and shear fracturing of the material are capable of momentarily bringing the Poisson's ratio of nearly incompressible material to 0.5, which instantaneously turns the material into unstable. On the other hand, the formation of shear cracks leads to reduction in the Poisson's ratio bringing the material away from the point of instability. Opposite to this, cracks of all kinds do not change the Poisson's ratio in extreme auxetics (the Poisson's ratio equal to −1). Thus the auxetic materials remain stable with respect to fracture formation.

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“…Lee and Goverdovskiy [26] demonstrated that negative-stiffness elements can be used to improve vibration isolation systems. Elastic composite materials with negative stiffness inclusions can have extreme overall stiffness and mechanical damping [27,28].…”

Section: Lattice With Nearest-neighbor and Next-nearest-neighbor Intementioning

confidence: 99%

Lattice Model with Nearest-Neighbor and Next-Nearest-Neighbor Interactions for Gradient Elasticity

Tarasov

2015

DNC

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Lattice models for the second-order strain-gradient models of elasticity theory are discussed. To combine the advantageous properties of two classes of secondgradient models, we suggest a new lattice model that can be considered as a discrete microstructural basis for gradient continuum models. It was proved that two classes of the second-gradient models (with positive and negative sign in front the gradient) can have a general lattice model as a microstructural basis. To obtain the secondgradient continuum models we consider a lattice model with the nearest-neighbor and next-nearest-neighbor interactions with two different coupling constants. The suggested lattice model gives unified description of the second-gradient models with positive and negative signs of the strain gradient terms. The sign in front the gradient is determined by the relation of the coupling constants of the nearestneighbor and next-nearest-neighbor interactions.

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Elastic composite with negative stiffness inclusions in antiplane strain

Cited by 36 publications

References 57 publications

Anomalous effective viscoelastic, thermoelastic, dielectric, and piezoelectric properties of negative‐stiffness composites and their stability

Anomalous effective viscoelastic, thermoelastic, dielectric, and piezoelectric properties of negative‐stiffness composites and their stability

Behavior of Extreme Auxetic and Incompressible Elastic Materials

Lattice Model with Nearest-Neighbor and Next-Nearest-Neighbor Interactions for Gradient Elasticity

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