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

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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.