On Gradient Theory: What is Next?

关于梯度理论：下一步是什么？

• 批准号: 9978758
• 负责人: Elias Aifantis
• 金额: $ 10万
• 依托单位: Michigan Technological University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-15 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9978758&HistoricalAwards=false
• 关键词: Gradient; Theory; What; Next

Gradient Theory Phase I: Fundamental AspectsE.C. Aifantis: Center for the Mechanics of Material Instabilities and Manufacturing Processes, Michigan Technological University, Houghton, MI 49931, USAAbstract: Gradient theory, i.e. a theory equipped with an internal length in the form of higher-order gradients for the constitutive variables, has been introduced by Aifantis and co-workers in the early 1980's in order to address the problem of dislocation patterning, to provide estimates of shear band thickness, and to settle the issue of mesh-size dependence in finite element calculations in the strain softening regime. An additional problem that was possible to address within the setting of gradient theory was concerned with the bridging of length scales by providing a mechanism for capturing the occurrence of material instabilities at the microscale and investigating their effect on the macroscopic response. Various authors have made significant contributions on the subject along the original second-order "symmetric stress" theory mentioned above (e.g. Zbib, Muhlhaus, Vardoulakis, de Borst, Tomita, etc.) or along the first-order "asymmetric stress" theory introduced by Fleck and Hutchinson in the early 1990's (e.g. Shu, Stolken, Huang, Gao, Nix, etc.). The main objective of this project is to revisit previously employed gradient models of elasticity, dislocation dynamics, and plasticity with respect to their physical origin, the nature of the gradient coefficients, and the form of the pertinent boundary conditions. A comparison between the aforementioned "symmetric stress" strain gradient theory and the "asymmetric stress" strain gradient theory on all these aspects will be provided and an assessment will be made on their advantages and shortcomings. Particular examples selected for this comparison will be simple shear / pure bending configurations, nanoidentation problems, and solid interfaces.

梯度理论第一阶段：基本方面艾凡提斯：美国密歇根理工大学材料不稳定性和制造过程力学中心，霍顿，MI 49931摘要：梯度理论，即配备有用于本构变量的高阶梯度形式的内部长度的理论，已经由Aifantis及其同事在20世纪80年代早期引入，以便解决位错图案化的问题，提供剪切带厚度的估计，并解决应变软化区有限元计算中网格尺寸依赖性的问题。在梯度理论的背景下，可以解决的另一个问题是通过提供一种机制来捕获微观尺度上材料不稳定性的发生并研究它们对宏观响应的影响，从而实现长度尺度的桥接。许多作者沿着上述原始二阶“对称应力”理论，对该主题做出了重大贡献（例如Zbib、Muhlhaus、Vardoulakis、de Borst、Tomita等）或者沿着Fleck和哈钦森在20世纪90年代早期提出的一阶“非对称应力”理论（例如，Shu、Stolken、Huang、Gao、Nix等）。本项目的主要目标是重新审视以前采用的弹性，位错动力学和塑性梯度模型，其物理起源，梯度系数的性质，以及相关的边界条件的形式。对上述“对称应力”应变梯度理论和“非对称应力”应变梯度理论在这些方面进行了比较，并对它们的优缺点进行了评价。选择用于此比较的特定示例将是简单剪切/纯弯曲配置、纳米压痕问题和固体界面。