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.

摘要：动态可塑性中的多维问题该跨学科建议解决了有关颗粒流动动力学的三个广泛的科学问题：（1）不稳定性，包括后稳定性状态中的模式形成，（2）波动，（2）计算具有多个尺度的颗粒状流量。 当前和计划的实验包括：（a）使用双轴设备的组成型测试，能够测量声音速度并连续监测X射线的变形，（b）进一步研究孔隙率波，（c）实验，用于隔离易于策略的概览的概览的概览的原因（d），（C）和1/f噪声。 基于以下事实：非社交可塑性的管理PDE在适度的压力下变得不符合，目前的分析工作寻求（a）概括以前的一维工作，这是由于数学上的考虑因素而驱动的，并且需要建立一个合理的理论框架来建立一个合理的理论框架，以进行两种自由的现象和（b）的数值模拟，以实验和（b）相关的现象，以实验性现象，以实验性现象，以实验性现象。乐队。 金属可塑性中的相关问题也正在分析研究。 数值工作包括（a）连续体和（b）分子动力学（MD）计算。 前者的关键努力是完成模拟剪切带形成和传播的代码，尤其是在双轴测试中。该代码包括剪切带的前跟踪和网状细化。 MD计算的直接目标是收集有关颗粒流中波动的定量信息，尤其是长度尺度的这种波动的变化。 在远距离的情况下，计划开发一个混合代码，该代码求解解决方案平稳的区域中的连续方程，并在快速变化区域中调用MD。 应用工程师的许多领域都受益于该项目中解决的基本问题的进展，包括（1）粒子处理和运输，（2）土壤力学，（3）形成材料，以及（4）岩土工程。 以下详细说明区域（1）。 化学工业添加的值估计有40％或610亿美元与粒子技术有关。 兰德公司（Rand Corporation）的一项研究发现，由于无法准确预测粉末行为，生产固体生产工厂平均以设计能力的63％进行制造厂，而产生液体的植物为84％。 从经济角度来看，这种差异令人震惊。 （关于未来的竞争力，美国应注意，德国和日本在粒子技术研究中领导着世界。）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，以及（b）开发新的，更高效的工业过程。 为了说明（a）：颗粒流的困难之一是，显然相同的情况可能会导致截然不同的行为，尤其是在涉及扩大规模的情况下（例如，从实验室规模的实验到工业筒仓）。 大多数现有的理论都试图仅以平均数量来描述流量，而忽略了与这些平均值的偏差。 该项目对波动和长度尺度的重点提供了能够预测和设计真实材料处理系统的全部行为的可能性。 为了说明（b）：该项目中使用摇晃的颗粒材料进行的实验为两种计划的专利应用带来了想法，一种是获得多尺寸颗粒的均匀混合，另一个是将大型表面积暴露于周围气体的大型表面积（如流体床中，但不需要流体流动）。 这些应用程序正在与行业研究人员共同探索。