论文标题
有效的二级弹性和手性弹性的理论
Effective medium theory for second-gradient elasticity with chirality
论文作者
论文摘要
我们从异质的二级非线性弹性材料中得出有效的，简约的模型，这些弹性材料考虑了手性尺寸的效果。我们对有效方程式的分类取决于四个特征长度的层次结构：异质性$ \ ell $的大小，组成部分的内在长度$ \ ell _ {\ rm sg} $和$ \ ell _ {\ ell _ {\ rm chiral} $，以及domain $ lm lm的$ lm lm rm rm lm rm l i}取决于$ \ ell _ {\ rm sg} $，$ \ ell _ {\ rm phiral} $，$ \ ell $和$ {\ rm l} $之间的不同比例相互作用。工作技术将缩放参数与周期性均匀化渐差程序相结合。均质化极限的通过和校正器结构的揭幕都取决于适当使用定期展开和相关操作员。
We derive effective, parsimonious models from a heterogeneous second-gradient nonlinear elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four characteristic lengths: The size of the heterogeneities $\ell$, the intrinsic lengths of the constituents $\ell_{\rm SG}$ and $\ell_{\rm chiral}$, and the overall characteristic length of the domain ${\rm L}$. Depending on the different scale interactions between $\ell_{\rm SG}$, $\ell_{\rm chiral}$, $\ell$, and ${\rm L}$ we obtain either an effective Cauchy continuum or an effective second-gradient continuum. The working technique combines scaling arguments with the periodic homogenization asymptotic procedure. Both the passage to the homogenization limit and the unveiling of the correctors' structure rely on a suitable use of the periodic unfolding and related operators.
