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Negative-stiffness composite systems and their coupled-field properties
Continuum Mechanics and Thermodynamics ( IF 2.6 ) Pub Date : 2021-05-08 , DOI: 10.1007/s00161-021-01021-3
Yun-Che Wang , Chih-Chin Ko , Keng-Wei Chang , Tsai-Wen Ko

Composite materials consisting of negative-stiffness inclusions in positive-stiffness matrix may exhibit anomalous effective coupled-field properties through the interactions of the positive and negative phases, giving rise to extremely large or small effective properties. In this work, effective viscoelastic properties of a continuum composite system under the effects of negative inclusion Young’s modulus ratio \(\lambda _E = E_{\text {inc}}/E_{\text {matrix}}\) are studied with the finite element method. Furthermore, effective coupled-field properties, such as thermal expansion coefficient, dielectric constants and piezeoelectric constants, are numerically calculated under the effects of negative inclusion bulk modulus ratio \(\lambda _K=K_{\text {inc}}/K_{\text {matrix}}\). Stability boundaries are determined by applying small dynamic perturbation to the systems through boundary surfaces, and the system is unstable if its field variables become divergent in time. For viscoelastic composite systems containing small volume fractions, less than \(V_i = 1.5 \%\), the systems can be stable up to \(\lambda _E \approx -0.3\) in 0.3 s under 10 Hz driving frequency. For \(V_i = 5.1 \%\) case, its stability boundary is around \(\lambda _E \approx 0\). Larger inclusion volume fraction reduces allowable negative stiffness in the viscoelastic system. All anomalous peaks found in the coupled-field properties are in the unstable regime, except for the piezoelectric and thermal-expansion anomalies in the composite system with electrically insulated inclusions and large inclusion volume fraction \(V_i = 26.81 \%\). Insulated inclusions may cause charge accumulation at the inclusion–matrix interface and boundary surface effects may serve as stabilizing agents to the composite system. Since it is known that negative-stiffness composite is unstable in the purely elastic system in statics, stability enhancement found here in the negative-stiffness systems with viscoelastic and coupled-field effects may be considered as multiphysics-induced stabilization.



中文翻译:

负刚度复合系统及其耦合场特性

在正刚度矩阵中由负刚度夹杂物组成的复合材料可能会通过正负相的相互作用而显示出异常有效的耦合场特性,从而产生非常大或很小的有效特性。在这项工作中,通过负夹杂物杨氏模量比\(\ lambda _E = E _ {\ text {inc}} / E _ {\ text {matrix}} \},研究了连续复合材料系统在负夹杂物作用下的有效粘弹性。有限元法。此外,在负夹杂物体积模量比\(\ lambda _K = K _ {\ text {inc}} / K _ {\文字{matrix}} \)。稳定边界是通过对系统通过边界表面施加小的动态扰动来确定的,并且如果系统的场变量随时间变化,则该系统将变得不稳定。对于体积分数小于\(V_i = 1.5 \%\)的粘弹性复合材料系统,在10 Hz的驱动频率下,该系统在0.3 s内可稳定至\(\ lambda _E \ approx -0.3 \)。对于\(V_i = 5.1 \%\)情况,其稳定性边界在\(\ lambda _E \ approx 0 \)附近。较大的夹杂物体积分数降低了粘弹性体系中允许的负刚度。除具有电绝缘夹杂物和较大夹杂物体积分数\(V_i = 26.81 \%\)的复合系统中的压电和热膨胀异常外,所有在耦合场性质中发现的异常峰均处于不稳定状态。绝缘的夹杂物可能会在夹杂物-基体界面处引起电荷积聚,边界表面效应可能会成为复合系统的稳定剂。由于已知负刚度复合材料在纯弹性系统的静力学中是不稳定的,因此在此处出现的具有粘弹性和耦合场效应的负刚度系统中的稳定性增强可被视为多物理场诱导的稳定。

更新日期:2021-05-08
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