Exploring Nonlinearities in Buckling of Solids

当压缩充分时，直梁通过向一侧鼓起或屈曲而变形。在几千年的人类文明中，我们一直在努力避免这种类型的不稳定，最明显的是在建筑方面。然而，我们思考屈曲问题的方式发生了范式转变--我们现在将这种现象视为改变材料功能的一种手段。一个完美的例子是屈曲在机械超材料设计中的作用，例如孔梁(具有规则孔线的梁)，一旦屈曲，就会表现出伸展行为(它们收缩，而不是像普通的固体材料梁那样膨胀)。这种特殊的性质是由于结构的几何形状而出现的，但当变形的几何形状与本构非线性相结合时，会出现更有趣的性质。例如，由金属制成的开孔梁在屈曲后会软化(尽管相应的金属没有应变软化行为)。在这个项目中，我们将使用包括孔梁在内的几个模型系统来探索屈曲过程中几何非线性和本构非线性之间的相互作用。这些相互作用将通过理论建模和定量实验相结合的方式进行研究。

When compressed sufficiently, a straight beam deforms by bulging to one of its sides, or buckling. For thousands of years of human civilization, we were trying to avoid this type of instability, most notably in construction of building. However, there is a paradigm shift in how we think about the buckling problems - we now embrace this phenomenon as a means of changing material functionality. A perfect example is the role buckling has in designing mechanical metamaterials, such as holey beams (beams with a regular line of holes), which, once buckled, show auxetic behaviours (they contract instead of expanding like regular beam of solid material would). This particular property emerges as a consequence of geometry of the structure, but even more interesting properties arise when geometry of the deformation combines with constitutive nonlinearities. For example, holey beams made from metals soften post-buckling (although the corresponding metals do not have strain-softening behaviour). During this project we will explore the interplay between geometrical and constitutive nonlinearities during buckling using a handful of model systems, including the holey beams. These interactions will be studied by combining theoretical modelling with quantitative experiments.