US-Ireland Cooperative Science: An Investigation Into FiniteDeformation of Solids

目的：在大多数固体发生大变形的技术应用中，变形主要是非均匀的，伴随着材料对称性的变化以及残余应力和永久变形的发展。了解材料对称性变化的本质和残余应力的程度可以在制造产品的设计和性能中发挥很大的作用。迄今为止，由于非均匀变形引起的材料对称性和诱导各向异性的变化，以及非线性弹性材料非均匀变形的基本力学，都没有得到很好的理解。在本提案中，首席研究员Dr. K.R. Rajagopol概述了非线性弹性材料的非均匀变形的详细研究。他计划确定一类本构方程，其中某些变形是可维持的。他还将研究特定本构方程的可能的通用解。要研究的一个相关问题是这种解的稳定性。此外，还将研究由于非均匀变形的应用而引起的材料对称性的变化。Rajagopal博士将与都柏林大学数学物理系M. Hayes教授合作进行这项研究。海斯博士在非线性弹性领域的专业知识将大大有助于这个联合项目的成功。相关性：美国-爱尔兰合作科学项目的目标是促进互利的研究合作，使美国科学家能够利用特殊的研究机会。该奖项使K.R. Rajagopal博士能够与具有互补专业知识的爱尔兰科学家合作两年，从而实现了这一目标。优点：所提出的研究将对科学知识作出重大贡献，前景良好。首席研究员是一位受人尊敬、富有成效的科学家，他将与该领域的另一位国际专家合作。工作计划合理，预算合理。资助：该奖项不会重复其他资助。

Objective: In most technical applications wherein solids undergo large deformations, the deformation is primarily non-homogeneous, accompanied by changes in material symmetry and the development of residual stresses and permanent deformations. An understanding of the nature of the changes in material symmetry and the extent of the residual stresses can play a great role in the design and performance of manufactured products. To date the changes in material symmetry and the induced anisotropies due to non-homogeneous deformations, as well as the basic mechanics of non-homogeneous deformations of non-linearly elastic materials, are not well understood. In this proposal the principal investigator Dr. K.R. Rajagopol outlines a detailed study of non-homogeneous deformations of non-linearly elastic materials. He plans to determine the class of constitutive equations for which certain deformations are maintainable. He will also investigate the possible universal solutions for specific constitutive equations. A related question which will be studied is the stability of such solutions. In addition a study of the changes in material symmetry due to the application of non-homogeneous deformations will be made. Dr. Rajagopal will collaborate in this research with Professor M. Hayes, Department of Mathematical Physics, University College, Dublin. Dr. Hayes expertise in the field of non-linear elasticity will contribute greatly to the success of this joint project. Relevance: It is the objective of the U.S.-Ireland Cooperative Science Program to promote mutually beneficial research cooperation and to enable U.S. scientists to take advantage of special research opportunities. This award fulfills that objective by enabling Dr. K.R. Rajagopal to spend two years in collaboration with Irish scientists with complementary expertise. Merit: There is an excellent prospect that the proposed research will result in a significant contribution to scientific knowledge. The principal investigator is a respected, productive scientist, who will be working with another international expert in this field. The work plan is sound and the budget is reasonable. Funding: This award will not duplicate other funding.