具有负刚度相的复合材料和非均匀体有效模量的严格界
Rigorous bounds on the effective moduli of composites and inhomogeneous bodies with negative-stiffness phases
摘要：
我们审查的有效性质的线弹性非均匀固体（包括复合材料）的成分具有非正定的弹性模量（所谓的负刚度相）的存在下的理论界限。我们表明，静态稳定机构的经典位移为基础的变分原理的Dirichlet和Neumann边界问题举行，但对偶变分原理的牵引边界问题不适用。我们说明了我们的研究结果的例子，涂层球形夹杂的稳定性条件得到的变分原理。我们进一步表明，在多相非均匀体和复合材料的线弹性模量的经典Voigt上限适用，它施加了一个稳定性条件：整体稳定性要求的有效模量不超过Voigt上限。这特别意味着，虽然复合材料中组分之间的几何约束可以稳定负刚度相，但稳定不足以允许极端的总体静态弹性模量（超过组分的静态弹性模量）。从Hashin-Shtrikman变分不等式可以得到各向同性复合材料的有效弹性模量的更强的界限，这也被证明是在负刚度的存在下举行。
英文摘要：
We review the theoretical bounds on the effective properties of linear elastic inhomogeneous solids (including composite materials) in the presence of constituents having non-positive-definite elastic moduli (so-called negative-stiffness phases). We show that for statically stable bodies the classical displacement-based variational principles for Dirichlet and Neumann boundary problems hold but that the dual variational principle for traction boundary problems does not apply. We illustrate our findings by the example of a coated spherical inclusion whose stability conditions are obtained from the variational principles. We further show that the classical Voigt upper bound on the linear elastic moduli in multi-phase inhomogeneous bodies and composites applies and that it imposes a stability condition: overall stability requires that the effective moduli do not surpass the Voigt upper bound. This particularly implies that, while the geometric constraints among constituents in a composite can stabilize negative-stiffness phases, the stabilization is insufficient to allow for extreme overall static elastic moduli (exceeding those of the constituents). Stronger bounds on the effective elastic moduli of isotropic composites can be obtained from the Hashin-Shtrikman variational inequalities, which are also shown to hold in the presence of negative stiffness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
