Mathematical Sciences: Multidimensional Problems in DynamicPlasticity

数学科学：动态塑性中的多维问题

• 批准号: 9201062
• 负责人: E Bruce Pitman
• 金额: $ 6.07万
• 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: 1992
• 资助国家: 美国
• 起止时间: 1992-12-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201062&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multidimensional; Problems; DynamicPlasticity

The central goal of this interdisciplinary, continuing project is to develop fundamental understanding of phenomena involving the slow flow of dry granular materials. Part I of the research, the first of two parts, focuses on a biaxial constitutive test with two additional, innovative, features: (i) the capacity to continuously measure the speed of sound in deforming granular material as a function of the accummulated deformation in the sample and the direction of propagation of the waves and (ii) the capacity of continuously measure density changes and particle velocities with sophisticated X-ray imaging equipment. The goals of Part I include (i) experimentally, to construct and operate the apparatus and (ii) computationally, to simulate deformation of a sample in the apparatus, including superimposed acoustic waves, up to and beyond the formation of shear bands. Mathematical analysis has a major supporting role to play in extracting constitutive information from the experimental data and in developing an appropriate numerical scheme. Part II of the research consists of several subprojects which probe more deeply phenomena discovered in the previous grant period. These include (i) to study the flutter instability as a possible cause of vibrations in silos, (ii) to further investigate experimentally and to understand analytically porosity waves in a discharging silo, (iii) to characterize more fully and to explain the power spectra of time-dependent stresses in a discharging silo, and (iv) to explore "scale-invariant" initial value problems as a possible paradigm problem in elastoplasticity (analogous to the Riemann problem in gas dynamics). Regarding applications, this project has been most closely associated with the flow of granular materials inside silos. However, there are many geophysical occurrences of granular materials, and the rich supply of constitutive information on sound propagatioyn to be gathered from this project will be relevant for these. Moreover, the simulation of shear banding has implications far beyond this project - mathematically because shear banding involves PDE which change type and scientifically because shear banding is a widespread mechanism leading to failure in many materials.

这个跨学科的持续项目的核心目标是发展对涉及干颗粒材料缓慢流动的现象的基本理解。 这项研究的第一部分（两个部分中的第一部分）着重于双轴构型测试，具有两个其他创新的特征：（i）能够连续测量样品中的变形颗粒材料中的声音速度，这是样品中实现的变形的函数，并且波浪的传播方向以及（ii）持续测量粒子的能力和（ii）与粒度范围的不断变化的能力。 第一部分的目标包括（i）实验，以构建和操作设备和（ii）计算，以模拟设备中样品的变形，包括叠加的声波，直至剪切带的形成。 数学分析在从实验数据中提取本构信息以及开发适当的数值方案中起着重要的支持作用。 该研究的第二部分由几个副标题组成，这些副标题更深入地探讨了上一批赠款期间发现的现象。 这些包括（i）将扑动的不稳定性作为孤岛振动的可能原因，（ii），（ii）在实验中进一步研究并理解排放筒仓中的分析孔隙率波，（iii）以更充分的表征，并解释了在排放式的s salo中依赖时间依赖性的压力，以探索“尺度上的质量数量”，以探索“最初的价值问题”（iv）。气体动力学中的Riemann问题）。 关于应用，该项目与筒仓内的颗粒材料流动最密切相关。 但是，颗粒状材料有许多地球物理发生，并且从该项目中收集的有关声音宣传的本构信息丰富的信息与这些信息有关。 此外，剪切带的模拟远远超出了该项目 - 从数学上讲，因为剪切带涉及PDE，它会改变类型，并且科学上是因为剪切带是一种广泛的机制，导致许多材料失败。