Mathematical Sciences: Some Studies in Nondestructive Evaluation of Prestressed Media

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The principal investigator will study how the general theory of linear elasticity with initial stress can be used as the basis for new techniques in the nondestructive evaluation of stress. In particular, he will study the well-posedness of certain boundary value problems, an extension of the elastic theory to visco-elastic media, the use of Rayleigh waves as stress-evaluators, and the use of certain waves in the nondestructive evaluation of lung parenchyma. The nondestructive evaluation of stress in elastic and visco-elastic media is an important area of research that has far-reaching technological ramifications. As an illustration, the nondestructive evaluation of lung parenchyma could lead to advances in the diagnosis and treatment of various forms of lung disease.