Stability of viscoelastic continuum with negative‐stiffness inclusions in the low‐frequency range

Abstract

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.