EAPSI:EAPSI: Investigation of the Wrinkling and Buckling Behavior of Layered Soft Materials with Applications in the Developing Brain

在怀孕的最后三个月，人类的大脑从光滑的表面进化成成人大脑特有的“褶皱”外观。这是如何发生的，为什么有时会出错？几十年来，力学界一直对这些问题感兴趣，试图将大脑建模为一个薄、硬、不断增长的层（灰质）附着在更厚、更软的层（白质）上。然而，最近的机械测试表明，灰质实际上比潜在的白质稍微不那么坚硬，这挑战了许多先前的模型和假设。通过与中国北京清华大学的冯锡乔博士合作，他是软膜起皱和屈曲方面的专家，该项目将探索在类似刚度的基底上薄生长层的行为。根据这些最近的发现，这项研究将导致对大脑发育的更好理解。对于软基板上的刚性生长层，预计会形成正弦波，而在较硬的基板上的软层的生长将导致具有压缩谷的折痕。波形和折痕之间的转换在脑组织感兴趣的区域逐渐发生。采用解析和数值方法，本研究将探索具有接近统一刚度比的软层状材料的行为。数值模拟将在有限元软件Abaqus中进行，使用内置的线性扰动分析以及用户定义的模拟体积增长的材料模型。该奖项由国家科学基金会与中国科技部共同资助。

During the third trimester of gestation, the human brain evolves from having a mostly smooth surface to the characteristic 'wrinkled' appearance of the adult brain. How does this happen, and why does it sometimes go wrong? The mechanics community has been interested in these questions for decades, attempting to model the brain as a thin, stiff, growing layer (gray matter) attached to a thicker, softer layer (white matter). Recent mechanical tests, however, have revealed that gray matter is actually slightly less stiff than the underlying white matter, challenging many prior models and assumptions. Through collaboration with Dr. Feng Xi-Qiao of Tsinghua University in Beijing, China, an expert in the wrinkling and buckling of soft films, this project will explore the behavior of thin growing layers on substrates of a similar stiffness. This research will lead to a greater understanding of brain development in light of these recent findings.For a stiff growing layer on a soft substrate, the formation of sinusoidal waves is expected, while the growth of a soft layer on a stiffer substrate will lead to creases with pinched valleys. The transition between waves and creases happens gradually in the region of interest for brain tissue. Using both analytical and numerical approaches, this research will explore the behavior of soft layered materials with stiffness ratios close to unity. Numerical simulations will be performed in the finite element software Abaqus, using the built-in linear perturbation analysis as well as user-defined material models that simulate volumetric growth. This NSF EAPSI award is funded in collaboration with the Chinese Ministry of Science and Technology.