Mathematical Sciences: Viscoelastic Shocks, QuasiconvexifiedTheories

数学科学：粘弹性冲击、拟凸理论

• 批准号: 9002745
• 负责人: Allen Pipkin
• 金额: $ 18万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-15 至 1993-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002745&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Viscoelastic; Shocks; QuasiconvexifiedTheories

In this proposal the principal investigator plans to continue his studies of the formation and propagation of shock waves in stiff polymeric materials and to develop a mathematical theory of finite deformations of membranes. The latter theory is useful in providing better estimates of the errors incurred when employing stress analysis to wrinkled membranes. The principal investigator will also study the mathematical properties of certain idealized materials that have applications to the twinning of crystals and the behavior of shape-memory alloys. Materials scientists very often study the properties of materials by testing their responses to applied stresses; one could call this the experimental approach. Mathematicians interested in the behavior of materials usually take a different approach which involves the theoretical analysis of mathematical models of materials. In this proposal the principal investigator will use advanced mathematics to try to understand twinning in crystals, necking in polymers and the behavior of shape-memory alloys.

在本提案中，主要研究者计划 继续研究激波的形成和传播 波在刚性聚合物材料，并制定了一个数学 薄膜有限变形理论 后一种理论是 有助于更好地估计在以下情况下发生的错误： 对褶皱膜进行应力分析。 校长 研究人员还将研究数学性质的 某些理想化的材料， 晶体的孪生和形状记忆合金的行为。 材料科学家经常研究 通过测试材料对施加应力的反应;一个 可以称之为实验方法。 数学家 对材料行为感兴趣的人通常会采取不同的 方法，涉及数学的理论分析， 材料的模型。 在这份提案中，首席研究员 我会用高等数学来尝试理解 聚合物的颈缩与形状记忆行为 合金.