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

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 (λ_E) or bulk modulus ratio (λ_K). Effective viscoelastic properties and their stability are studied for negative λ_E 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 λ_E ∼ –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 λ_E or λ_K, 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.