Negative-stiffness composite systems and their coupled-field properties

Abstract

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 $$\lambda _E = E_{\text {inc}}/E_{\text {matrix}}$$ 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 $$\lambda _K=K_{\text {inc}}/K_{\text {matrix}}$$ . 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 $$\lambda _E \approx -0.3$$ in 0.3 s under 10 Hz driving frequency. For $$V_i = 5.1 \%$$ case, its stability boundary is around $$\lambda _E \approx 0$$ . 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.