Computability of Material Instabilities - New Methods and Case Study

提出的工作的目的是检查在破坏模拟固体力学问题的可计算性。这个问题是在边坡、基础和挖掘破坏的背景下解决的，但我们也将研究破坏模拟的其他领域的可计算性。并以土体承载力计算为例进行了研究。这样的计算在大型工程中已经变得司空见惯，其中与支撑开挖相关的地面运动是主要设计参数。例如，波士顿的中央动脉/隧道项目估计耗资160亿美元，其中很大一部分费用用于临时支持挖掘工作。这些问题的模拟是困难的，因为这些问题的失败通常是由于材料的不稳定性引起的。材料的不稳定性对问题的模型和数据非常敏感，目前尚不清楚它们如何准确地模拟或如何约束行为。在提议的工作中，将开发提取可能响应带的方法。将开发非均匀数据建模技术，并通过反优化方法获得响应的极值。作为这项工作的一部分，将开发用于模拟任意不连续面的新有限元。在这些方法中，函数及其导数的不连续可以独立于网格对齐进行建模，从而可以模拟任意剪切带和裂缝。这项工作的结果将适用于大量的模拟问题。在制造业中，诸如钣金成形、挤压和金属切割等过程都受到材料不稳定性的影响。材料的不稳定性在地震分析中也很重要，它们表现为液化和结构的断裂。

The objective of the proposed work is to examine the computability of solid mechanics problems in the simulation of failure. The issue is addressed in the context of the failure of slopes, foundations and excavations but we will also examine computability in other areas of failure simulation. The computation of the bearing capacity of soils is considered as a case study. Such computations have become commonplace for large projects where the ground movements associated with a supported excavation are a primary design parameter. For example, in the Central Artery/Tunnel Project in Boston, which is estimated to cost $16 billion, a significant percentage of the cost is in the temporary support of excavations.The simulation of these problems is difficult because failure in these problems usually arises due to material instabilities. Material instabilities are very sensitive to the models and data of the problem, and it is not understood how accurately they can be simulated or how to bound the behavior.In the proposed work, methods for extracting bands of likely response will be developed. Techniques will be developed for modeling inhomogeneous data and obtaining the extremes in responses via anti-optimization methods. As part of this work, new finite elements for modeling arbitrary discontinuities will be developed. In these methods, discontinuities in functions and their derivatives can be modeled independent of mesh alignment so that arbitrary shear bands and cracks can be modeled.The results of this work will be applicable to a large class of simulation problems. In manufacturing, processes such as sheet-metal forming, extrusion, and metal cutting are subject to material instabilities. Material instabilities are also important in seismic analysis, where they are manifested as liquefaction, and in the fracture of structures.