Novel Extreme Composite Materials due to Constituents of Negative Stiffness

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

Novel extreme composite materials due to constituents of negative stiffness R. S. Lakes, R. W. Carpick, R. F. Cooper*, W. J. Drugan Department of Engineering Physics and *Department of Materials Science University of Wisconsin-Madison Madison, WI 53706 The proposed research is directed toward the attainment of extreme material properties by relaxing some of the assumptions commonly held about constituent behavior in a composite material. A composite material combines two or more constituent phases of different material properties to achieve a new material with enhanced mechanical/transport properties. Effective mechanical properties of composites are determined primarily by the properties of the materials being combined, the interface behavior, and the spatial arrangement of the phases in the composite. Traditionally, the design variables associated with composites include (i) the choice of constituent materials, (ii) the volume fraction of the constituents, and (iii) the geometry of the phases. Recently, one of the writers (Lakes) and co-workers showed that several classes of composites can exhibit extreme behavior if one constituent has negative stiffness. An analysis of the possibilities in viscoelastic composite systems was reported in Physical Review Letters. Peak damping and large stiffness anomalies are possible even with a dilute concentration of inclusions, provided matrix damping is small. An experimental illustration of the behavior of a lumped unit cell was reported in Philosophical Magazine Letters. It disclosed singular mechanical damping tan(delta) [where tan(delta) is the tangent of the phase angle between stress and strain] in a system containing post-buckled tubes. A further experimental illustration of extreme behavior in a particulate composite was reported in Nature. Composites prepared with a dilute concentration of ferroelastic inclusions exhibited large peaks in tan(delta). The inclusions are more effective than diamond in increasing the composite stiffness at selected temperatures. These results point to the possibility of achieving extreme behavior in designed composites, and exceeding conventional bounds based on the assumption of positive constituent stiffness. The goal of this research is to explore the effects of constituents of negative stiffness in composite materials. We hypothesize on the basis of some initial theoretical analyses and experiments that if one phase has negative stiffness, the overall stiffness of the composite can be made large. Moreover, we hypothesize that extreme mechanical damping effects can occur if one phase has negative stiffness. Multiple methods of achieving inclusion negative stiffness are to be examined. Also, the question of stability of materials and composites is to be examined in new theoretical developments. For a composite with extremely high stiffness to be useful, it must be stable. Composites with inclusions of negative stiffness are of scientific interest in that current understanding of heterogeneous media is predicated on an assumption of each phase to have positive stiffness. Our preliminary theoretical and experimental results indicate extreme effects in stiffness and damping when that assumption is relaxed, so we anticipate that the present work will facilitate the development of new classes of materials with extreme properties, even materials stiffer than diamond.