Computability of Material Instabilities - New Methods and Case Study

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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.