具有可逆图案变换的非线性周期材料中的尺寸效应
Size effects in nonlinear periodic materials exhibiting reversible pattern transformations
摘要：
本文重点研究了由于微结构中的局部弹性屈曲不稳定性而引起的可逆图案变换驱动的周期性机械超材料的尺寸效应。研究了两种不同的加载情况：压缩和弯曲，其中材料在整个结构或仅部分结构中表现出图案变换。样品的高度与晶胞的尺寸之间的比率被定义为尺度比。一个家庭的移位的微观结构，对应于所有可能的安排的微观结构相对于外部边界，被认为是为了确定合奏平均的解决方案计算每个比例。在压缩情况下，试样的顶部和底部边缘被完全约束，这引入了具有受限模式转换的边界层。在弯曲的情况下，顶部和底部边缘是自由边界，导致顺应性边界层，而附加的尺寸效应出现从施加的应变梯度。为了比较，经典的均匀化解决方案的计算和匹配以及合奏平均数值解只有非常大的比例。对于较小的比例，尺寸效应占主导地位，经典的均匀化不再适用。
英文摘要：
This paper focuses on size effects in periodic mechanical metamaterials driven by reversible pattern transformations due to local elastic buckling instabilities in their microstructure. Two distinct loading cases are studied: compression and bending, in which the material exhibits pattern transformation in the whole structure or only partially. The ratio between the height of the specimen and the size of a unit cell is defined as the scale ratio. A family of shifted microstructures, corresponding to all possible arrangements of the microstructure relative to the external boundary, is considered in order to determine the ensemble averaged solution computed for each scale ratio. In the compression case, the top and the bottom edges of the specimens are fully constrained, which introduces boundary layers with restricted pattern transformation. In the bending case, the top and bottom edges are free boundaries resulting in compliant boundary layers, whereas additional size effects emerge from imposed strain gradient. For comparison, the classical homogenization solution is computed and shown to match well with the ensemble averaged numerical solution only for very large scale ratios. For smaller scale ratios, where a size effect dominates, the classical homogenization no longer applies.
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。
