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Composite materials consisting of negative-stiffness inclusions in positive-stiffness matrix may exhibit anomalous effective coupled-field properties through the interactions of the positive and negative phases, giving rise to extremely large or small effective properties. In this work, effective viscoelastic properties of a continuum composite system under the effects of negative inclusion Young's modulus ratio λ E = E inc / E matrix are studied with the finite element method. Furthermore, effective coupled-field properties, such as thermal expansion coefficient, dielectric constants and piezeoelectric constants, are numerically calculated under the effects of negative inclusion bulk modulus ratio λ K = K inc / K matrix . Stability boundaries are determined by applying small dynamic perturbation to the systems through boundary surfaces, and the system is unstable if its field variables become divergent in time. For viscoelastic composite systems containing small volume fractions, less than V i = 1.5 % , the systems can be stable up to λ E ≈ - 0.3 in 0.3 s under 10 Hz driving frequency. For V i = 5.1 % case, its stability boundary is around λ E ≈ 0 . Larger inclusion volume fraction reduces allowable negative stiffness in the viscoelastic system. All anomalous peaks found in the coupled-field properties are in the unstable regime, except for the piezoelectric and thermal-expansion anomalies in the composite system with electrically insulated inclusions and large inclusion volume fraction V i = 26.81 % . Insulated inclusions may cause charge accumulation at the inclusion–matrix interface and boundary surface effects may serve as stabilizing agents to the composite system. Since it is known that negative-stiffness composite is unstable in the purely elastic system in statics, stability enhancement found here in the negative-stiffness systems with viscoelastic and coupled-field effects may be considered as multiphysics-induced stabilization. [ABSTRACT FROM AUTHOR]

Chiral materials may exhibit negative Poisson's ratio and deformation‐mode coupling phenomena. The finite element numerical method is adopted to analyze a class of 2D chiral and nonchiral materials and to show the effects of microstructural geometry on their effective elastic properties and coupling between tension/compression and bending. With the same area fraction (AF), nonchiral samples show larger effective moduli than chiral ones. The number of unit cells may reduce negativity in effective Poisson's ratio of the chiral samples due to nonuniform lateral deformation under uniaxial straining. Increasing AF in a hierarchical pattern in the chiral samples makes their Poisson's ratio more negative. Bending occurs in the chiral samples when they are under uniform, uniaxial, tensile, or compressive straining due to the coupling of deformation modes. The sensibility of tension–bending coupling may be controlled by the chiral microstructure. Optimization of the coupling sensitivity may help develop novel mechanical sensors. [ABSTRACT FROM AUTHOR]

Honeycombs or foams with reentrant microstructures exhibit effective negative Poisson's ratio. Although they are light weight due to inherently empty space, their overall stiffness and damping are somewhat limited. With judiciously chosen filler material to fill the voids in star‐shaped honeycomb, it is numerically demonstrated its auxeticity may be enhanced. By combining the filler and skeleton, the hierarchical composite materials are constructed. The magnitude of the enhancement depends on inner and outer filler's modulus mismatch, as well as the types of filling. Filler's auxeticity also largely enhances overall auxeticity of the outer‐ and all‐filled honeycomb. In addition, for outer‐filled honeycomb, its effective viscoelastic modulus and damping are significantly increased, while maintaining relatively light weight, due to local stress concentration. [ABSTRACT FROM AUTHOR]

Microstructured plates, consisting of various conventional and re-entrant cells, are numerically constructed and analyzed for their effective elastic properties under in-plane deformation. The finite element numerical method is adopted. The calculated effective Poisson's ratios of the plates are found to be in the range between −1 and 1, in consistency with the theory of two-dimensional elasticity. Auxetic angles need to be greater than about 20° in order to obtain negative Poisson's ratio. Increasing the auxetic angles reduces the effective pure shear modulus. Elastically anisotropic characteristics of the homogenized plate are analyzed with the calculated effective Young's modulus, Poisson's ratio, and pure shear modulus. [ABSTRACT FROM AUTHOR]

The dynamic mechanical responses of the ferroelastic materials under uniaxial straining and temperature cycling are studied via the Landau-type phase field model in two dimensions. The model may exhibit a single-well (doublewell) energy profile when temperature is greater (less) than the critical temperature. Effective negative stiffness in the vicinity of the temperature-induced solid-solid phase transformation is numerically demonstrated through monotonic uniaxial straining on a single-domain ferroelastic under temperature cycling around the Curie temperature. Under sinusoidal uniaxial straining, the effective Young's modulus and damping, as indicated by the enclosed area of the stress-strain curve, may be largely increased due to the phase transition. Our calculated responses here are consistent with experimental data reported in the literature, as well as theoretical results based on the composite theory with inclusions assumed to have negative modulus. No negative stiffness values are directly assigned in our phase field model as the underlying physics of the order parameters, i.e., spontaneous strains, provides effective negative stiffness into the systems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The stability of viscoelastic composites with negative stiffness (NS) inclusions and their associated extreme mechanical properties are studied with time-domain finite element analysis and composite theory. In the finite element analysis, the stability of the plane-strain, two-phase NS composite is evaluated by monitoring the stress divergence under uniaxial straining. In addition, 2D and 3D two-phase NS composites are studied by using composite theories and the elastic-viscoelastic correspondence principle. Effective stiffness and damping anomalies are observed, and the stability of the composites is evaluated. In the low frequency regime, stability conditions for purely elastic systems are suitable to estimate the stability of the viscoelastic composites. This is verified with the finite element analysis. For the 2D problem, the finite element analysis and composite theory agree well with each other in terms of the overall properties and stability. For the 3D problem, only the results obtained from the composite theory are presented. Our analysis shows that the extreme mechanical properties for both of the 2D and 3D cases are located near the strong ellipticity boundary. When the matrix modulus is suitably chosen to satisfy all stability conditions, the effective stiffness softening anomaly (i.e., damping enhancement) may be in the stability range. The effective stiffness enhancement locates in the non-elliptic range of the negative inclusion bulk modulus parameter space. [ABSTRACT FROM AUTHOR]