Microstructural Modeling and Probabilistic Prediction of Micro-Electro-Mechanical Systems Response (REU Supplement)

这是一个研究项目，旨在根据材料的微观结构，提高对用于制造微机电系统（MEMS）的材料和结构元件（梁、板、膜）的行为的理解。目的是评估这类系统的性能可靠性。有效的（整体）物理性能，主要是弹性和强度；并且将评估相关的结构响应，认识到有许多微观结构效应在与MEMS相关的长度尺度上很重要，但在更大的长度尺度上不重要。这些包括材料中晶体的典型线性尺寸与薄膜厚度在同一数量级上，晶粒尺寸和形状在厚度上的实质性变化，晶粒（纹理）的相当大的排列导致响应的各向异性，以及制造MEMS的过程中产生的大量残余应力。这种效应可能使经典理论无法直接应用于结构元件，因此需要发展新的理论。此外，微结构固有的可变性很大程度上取决于工艺条件，因此需要对材料行为和结构响应进行概率描述，以评估MEMS的性能可靠性。为此，本研究将研究：(1)材料强度和有效性能的数学建模；(2)微结构对MEMS结构响应的影响；(3)利用随机有限元方法对MEMS进行可靠性分析。

This is a research project aimed at developing an improved understanding of the behavior of materials and structural elements (beams, plates, membranes) employed in the manufacture of micro-electro-mechanical systems (MEMS), on the basis of the microstructure exhibited by the materials, with the goal of assessing the performance reliability of such systems. Effective (overall) physical properties, primarily elasticity and strength, and the associated structural response will be evaluated with the recognition that there are a number of microstructural effects that are important at the length scales associated with MEMS but which are unimportant at larger length scales. These include the typical linear dimension of a crystallite within the material being on the same order of magnitude as the thickness of the film, substantial through-thickness variations in grain size and shape, the presence of considerable alignment of the grains (texture) leading to anisotropy of response, and large levels of residual stress arising form the processes used to create may MEMS. Such effects may preclude direct application of classical theories for structural elements, thus necessitating the development of new theories. Furthermore, the variability inherent in the microstructure, which depends strongly on the process conditions, requires a probabilistic description of the material behavior and structural response evaluation aimed at assessing the performance reliability of MEMS. To this end, this research will address: (1) mathematical modeling of material strength and effective properties, (2) influence of microstructure on the structural response of MEMS, and (3) reliability analysis of MEMS using stochastic finite-element methods.