Novel Extreme Composite Materials due to Constituents of Negative Stiffness

由于具有负硬度R的成分而产生的新型极端复合材料。威斯康星大学麦迪逊分校材料科学系，威斯康星大学麦迪逊分校53706拟议的研究旨在通过放松一些关于复合材料中组成行为的普遍假设来实现极端材料特性。复合材料将两种或两种以上不同材料性质的组成相结合，以获得具有增强的力学/传输性能的新材料。复合材料的有效力学性能主要由被结合材料的性质、界面行为以及复合材料中各相的空间排列决定。传统上，与复合材料相关的设计变量包括(I)组成材料的选择，(Ii)组分的体积分数，和(Iii)相的几何形状。最近，其中一位作者(莱克斯)和他的同事表明，如果一种成分具有负刚度，几类复合材料可以表现出极端的行为。在《物理评论快报》上报道了一项对非弹性复合材料系统可能性的分析。即使夹杂物稀疏集中，如果基质阻尼很小，也可能出现峰值阻尼和大刚度异常。《哲学杂志快报》上报道了一个集总单胞行为的实验图解。它揭示了包含后屈曲管的系统中的奇异机械阻尼tan(Delta)[其中tan(Delta)是应力和应变之间的相角的正切]。进一步的实验说明了颗粒复合材料中的极端行为。铁弹性夹杂物稀疏浓度下制备的复合材料具有较大的Intan(Delta)峰。在选定的温度下，夹杂物比金刚石更能有效地提高复合材料的刚性。这些结果指出了在设计的复合材料中实现极端行为的可能性，并基于正成分刚度的假设扩展了传统的界限。本研究的目的是探讨复合材料中负刚度分量的影响。在一些初步的理论分析和实验的基础上，我们假设，如果某一相具有负刚度，则复合材料的总刚度可以很大。此外，我们假设，如果一个相具有负刚度，则可能发生极端的机械阻尼效应。对实现夹杂负刚度的多种方法进行了研究。此外，材料的稳定性和组成的问题将在新的理论发展中加以研究。要使具有极高刚度的复合材料有用，它必须是稳定的。具有负刚度夹杂的复合材料具有科学意义，因为目前对非均质介质的理解是基于假设每个相都具有正刚度。我们的初步理论和实验结果表明，当这一假设放松时，在硬度和阻尼性方面会产生极端的影响，因此我们预计，本工作将促进具有极端性能的新型材料的发展，甚至是比钻石更硬的材料。

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.