Novel Extreme Composite Materials due to Constituents of Negative Stiffness

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Novel extreme composite materials due to constituents of negative stiffnessR. S. Lakes, R. W. Carpick, R. F. Cooper*, W. J. DruganDepartment of Engineering Physics and *Department of Materials ScienceUniversity of Wisconsin-MadisonMadison, WI 53706 The proposed research is directed toward the attainment of extremematerial properties by relaxing some of the assumptions commonly held aboutconstituent behavior in a composite material. A composite materialcombines two or more constituent phases of different material properties toachieve a new material with enhanced mechanical/transport properties.Effective mechanical properties of composites are determined primarily bythe properties of the materials being combined, the interface behavior, andthe spatial arrangement of the phases in the composite. Traditionally, thedesign variables associated with composites include (i) the choice ofconstituent 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 thatseveral classes of composites can exhibit extreme behavior if oneconstituent has negative stiffness. An analysis of the possibilities inviscoelastic composite systems was reported in Physical Review Letters.Peak damping and large stiffness anomalies are possible even with a diluteconcentration of inclusions, provided matrix damping is small. Anexperimental illustration of the behavior of a lumped unit cell wasreported in Philosophical Magazine Letters. It disclosed singularmechanical damping tan(delta) [where tan(delta) is the tangent of the phaseangle between stress and strain] in a system containing post-buckled tubes.A further experimental illustration of extreme behavior in a particulatecomposite was reported in Nature. Composites prepared with a diluteconcentration of ferroelastic inclusions exhibited large peaks intan(delta). The inclusions are more effective than diamond in increasingthe composite stiffness at selected temperatures. These results point tothe possibility of achieving extreme behavior in designed composites, andexceeding conventional bounds based on the assumption of positiveconstituent stiffness. The goal of this research is to explore the effects of constituentsof negative stiffness in composite materials. We hypothesize on the basisof some initial theoretical analyses and experiments that if one phase hasnegative stiffness, the overall stiffness of the composite can be madelarge. Moreover, we hypothesize that extreme mechanical damping effects canoccur if one phase has negative stiffness. Multiple methods of achieving inclusion negative stiffness are tobe examined. Also, the question of stability of materials and compositesis to be examined in new theoretical developments. For a composite withextremely high stiffness to be useful, it must be stable. Composites with inclusions of negative stiffness are of scientificinterest in that current understanding of heterogeneous media is predicatedon an assumption of each phase to have positive stiffness. Our preliminarytheoretical and experimental results indicate extreme effects in stiffnessand damping when that assumption is relaxed, so we anticipate that thepresent work will facilitate the development of new classes of materialswith extreme properties, even materials stiffer than diamond.