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

目的：在大多数固体经受大的 变形，变形主要是不均匀的，伴随着 材料对称性的变化和残余应力的发展 和永久变形。 对自然的理解 材料对称性和残余应力程度的变化可 在制造的设计和性能方面发挥着重要作用， 产品. 为了确定材料对称性的变化以及 各向异性由于非均匀变形，以及基本的 非线性弹性非均匀变形力学 材料，并没有得到很好的理解。 在这项提案中，主要研究者K.R.博士Rajagopol概述 非线性弹性非均匀变形的详细研究 材料. 他计划确定本构方程的类别 对于这种情况，保持一定的变形。 他还将 研究特定本构关系的可能的普遍解 方程 将研究的一个相关问题是 这样的解决方案。 此外，对材料对称性变化的研究 由于施加非均匀变形，将产生非均匀变形。 Rajagopal博士将与M.海耶斯 都柏林大学学院数学物理系。 海斯博士在非线性弹性领域的专业知识将 为这一合作项目的成功做出了巨大贡献。 相关性：这是美国的目标-爱尔兰合作科学 促进互利研究合作计划， 使美国科学家能够利用特殊研究 机会该奖项通过使K.R.博士 Rajagopal将与爱尔兰科学家合作两年， 补充专业知识。 优点：本研究具有良好的前景， 对科学知识做出了重大贡献。 的 首席研究员是一个受人尊敬的，多产的科学家，谁将是 与这一领域的另一位国际专家合作。 工作计划 是合理的，预算是合理的。 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.