Mathematical Sciences: Multidimensional Problems in Dynamic Plasticity

数学科学：动态塑性的多维问题

• 批准号: 9504433
• 负责人: E Bruce Pitman
• 金额: $ 9万
• 依托单位: SUNY at Buffalo
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504433&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multidimensional; Problems; Dynamic

ABSTRACT: MULTIDIMENSIONAL PROBLEMS IN DYNAMIC PLASTICITY This interdisciplinary proposal addresses three broad scientific issues regarding the dynamics of granular flow: (1) instability, including pattern formation in the post-instability regime, (2) fluctuations, and (3) computation of granular flows with multiple scales. Current and planned experiments include: (a) constitutive tests using a biaxial apparatus with the capability of measuring the speed of sound and of continuously monitoring the deformation with x-rays, (b) further study of porosity waves, (c) experiments directed toward isolating the causes of the instabilities of shaken granular material, and (d) experiments probing various aspects of fluctuations in granular flow, including stress chains and 1/f noise. Based on the fact that the governing PDE of nonassociative plasticity become ill-posed at moderate strains, current analytical work seeks (a) to generalize previous one-dimensional work, driven by both mathematical considerations and the need to establish a sound theoretical framework for numerical simulations of two-and-three-dimensional phenomena and (b) to relate ill-posedness to various experimental phenomena such as porosity waves and shear banding. Related problems in metal plasticity are also being studied analytically. Numerical work includes both (a) continuum and (b) molecular-dynamics (MD) computations. The key effort in the former is to complete a code for simulating shear-band formation and propagation, especially in the biaxial test; this code includes front tracking and mesh refinement at the shear band. MD computations have the immediate goal of gathering quantitative information about fluctuations in granular flow, particularly the variation of such fluctuations with length scale. In the long range, it is planned to develop a hybrid code that solves continuum equations in regions where the solution is smooth and invokes MD in regions of rapid change. Many areas of applied engineer ing stand to benefit from progress on the fundamental questions addressed in this project, including (1) particle handling and transport, (2) soil mechanics, (3) materials forming, and (4) geotechnical engineering. The following elaborates on area (1). An estimated 40%, or $61 billion, of the value added by the chemical industry is linked to particle technology. A study by the Rand Corporation found that, because of inability to accurately predict powder behavior, solids-producing manufacturing plants performed on average at 63% of design capacity, compared to 84% for liquids-producing plants. In economic terms, this difference is staggering. (Regarding future competitiveness, the U.S. should note that Germany and Japan lead the world in particle-technology research.) Fundamental understanding of the flow of granular materials would help (a) in finding ways to control industrial problems and (b) in developing new, more efficient industrial processes. To illustrate (a): one of the difficulties of granular flow is that quite different behavior may result from apparently identical circumstances, especially when scale-up is involved (e.g., from laboratory-scale experiments to an industrial silo). Most existing theories attempt to describe the flow only in term of average quantities, ignoring deviations from these averages. The focus in this project on fluctuations and length scales offers the possibility of being able to predict, and design for, the full range of behavior of real materials-handling systems. To illustrate (b): the experiments in this project with shaken granular material have led to ideas for two planned applications for patents, one in obtaining uniform mixing of multi-sized particles and the other in exposing a large surface area to the surrounding gas (as in a fluidized bed but not requiring fluid flow). These applications are being explored in concert with researchers in industry.

动态塑性力学中的多维问题 这个跨学科的建议解决了关于颗粒流动力学的三个广泛的科学问题：（1）不稳定性，包括不稳定后制度中的模式形成，（2）波动，以及（3）多尺度颗粒流的计算。 目前和计划进行的实验包括：（a）使用能够测量声速和用X射线连续监测变形的双轴装置的本构试验，（B）孔隙率波的进一步研究，（c）针对分离振动粒状材料的不稳定性的原因的实验，和（d）探测粒状流中波动的各个方面的实验，包括应力链和1/f噪声。 基于这样的事实，即非缔合塑性偏微分方程成为不适定在适度的应变，目前的分析工作旨在（a）推广以前的一维工作，驱动的数学考虑和需要建立一个良好的理论框架的数值模拟的二维和三维现象和（B）与不适定的各种实验现象，如孔隙波和剪切带。 金属塑性的相关问题也在分析研究中。 数值工作包括（a）连续介质和（B）分子动力学（MD）计算。 在前者的关键努力是完成一个代码，用于模拟剪切带的形成和传播，特别是在双轴测试，这个代码包括前跟踪和网格细化剪切带。 MD计算的直接目标是收集有关颗粒流波动的定量信息，特别是这种波动随长度尺度的变化。 在长期的范围内，计划开发一个混合代码，解决连续方程的解决方案是顺利的地区，并调用MD在快速变化的地区。 应用工程的许多领域都将从本项目所解决的基本问题的进展中受益，包括（1）颗粒处理和运输，（2）土壤力学，（3）材料形成，以及（4）岩土工程。 下文详细阐述领域（1）。 据估计，化学工业增加值的40%或610亿美元与颗粒技术有关。 兰德公司的一项研究发现，由于无法准确预测粉末的行为，固体生产制造厂的平均生产能力为设计能力的63%，而液体生产厂的平均生产能力为84%。 从经济角度来看，这种差异是惊人的。 （关于未来的竞争力，美国应该注意到德国和日本在粒子技术研究方面处于世界领先地位。） 对颗粒材料流动的基本了解将有助于（a）找到控制工业问题的方法和（B）开发新的、更有效的工业过程。 举例说明（a）：颗粒流的困难之一在于，完全不同的行为可能由表面上相同的情况导致，特别是当涉及按比例放大时（例如，从实验室规模的实验到工业筒仓）。 大多数现有的理论试图描述流量的平均数量，忽略了这些平均值的偏差。 在这个项目的波动和长度尺度的重点提供了能够预测和设计的可能性，真实的材料处理系统的行为的全方位。 为了说明（B）：在该项目中，用摇动的粒状材料进行的实验产生了两个计划的专利申请的想法，一个是获得多尺寸颗粒的均匀混合，另一个是将大的表面积暴露于周围气体（如在流化床中，但不需要流体流动）。 目前正在与工业界的研究人员共同探讨这些应用。