Negative stiffness in ZrW2O8 inclusions as a result of thermal stress

Abstract

Materials with negative stiffness, although inherently unstable in isolation, can be stabilized by external constraints, for example, by inclusion within a material with positive stiffness. We have identified ZrW2O8, a material with negative thermal expansion, as a candidate negative-stiffness material arising from its negative bulk modulus during a ferroelastic cubic–orthorhombic pressure-induced phase transition (PIPT). A hyperelastic constituent equation for this transition was developed and implemented in a finite-element model of ZrW2O8 inclusions in positive stiffness, positive thermal expansion matrices. In these matrices, thermal stress during cooling, originating from thermal expansion mismatch, would be sufficient to initiate the PIPT after small temperature drops. The subsequent progress of the PIPT depends strongly on the thermoelastic properties of the matrix, with stiff, low thermal expansion matrices stabilizing the transition state over broad temperature ranges, indicating that ZrW2O8 or materials with similar properties could be used as versatile negative-stiffness inclusion materials. The models were used to understand previous experiments on composites that include ZrW2O8.

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

“…It was theorized that in a constrained system (such as particles embedded in a matrix), negative stiffness can be stabilized as derived theoretically [96,98,107,134]. Negative stiffness was detected in unconstrained phases by special nanoindentation techniques [156], and it was also reported in phase-transforming systems such as ZrW 2 O 8 during a ferroelastic cubic-orthorhombic pressureinduced phase transition [157]. Ferroelectric switching in perovskite ceramics is another mechanism that induces instability (by applied electric fields).…”

Composition, Response to Pressure, and Negative Thermal Expansion in MIIBIVF6 (M = Ca, Mg; B = Zr, Nb)

“…Although most materials expand upon heating, a growing number are known to contract. − Such negative thermal expansion (NTE) can, in principle, be used to compensate for the response of positive thermal expansion (PTE) solids, either by preparing composites of the PTE and NTE materials or by assembling devices containing parts made from separate NTE and PTE components. There is a significant body of work examining the fabrication and performance of metal matrix-ceramic composites, polymer ceramic composites, and ceramic–ceramic composites containing NTE materials for various applications. − When NTE and PTE solids are used together in a composite, there can be considerable stresses within the composite due to differential thermal expansion. These stresses can lead to phase transitions and other unwanted phenomena, , as open framework NTE solids typically display quite rich behavior at low pressure. − …”

Effects of Cracks on Anomalous Mechanical Behavior and Energy Dissipation of Negative‐Stiffness Plates

“…Enhanced damping in such composites has also been demonstrated with neutron scattering . A recent experiment has exemplified the existence of negative stiffness in inclusions due to thermal stress …”