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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]

High damping and high stiffness (HDHS) viscoelastic materials, which exhibit desired energy‐dissipating capability and structural integrity, may be achieved by using negative‐stiffness inclusions, such as ferroelastic particles, in composite materials. However, stability has long been questioned for such composites to be realistic. Wang and Ko (pp. 2070–2079) examine a two‐dimensional, two‐phase, negative‐stiffness viscoelastic composite under partial displacement loading by time–domain analysis with the finite element method. It was found that force responses may be stable or unstable, depending on the amount of negative stiffness. A small amount of negative stiffness in the viscoelastic composites may not deteriorate their stability, but is insufficient to trigger HDHS. Through examining the existing stability criteria of three‐dimensional composites, the softening anomaly in the overall viscoelastic stiffness may be in the stability range, indicating stable damping enhancement. However, simultaneously enhancing damping and stiffness violates ellipticity requirements, hence the system is unstable/metastable. The cover image shows stress distributions around the inclusion of the two‐dimensional composite in the background and stiffness/damping anomalies, as well as divergent force responses, deviating from expected sinusoidal responses. [ABSTRACT FROM AUTHOR]