Problems in Anisotropic Nonlinear Elasticity

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9500642 Polignone This work is supported by a Research Planning Grant for Women Scientists and Engineers Award. Preliminary work on problems involving nonlinearly elastic deformations of anisotropic materials will be conducted. Several areas of research will be considered. The first concerns the determination of instabilities describing non- radially symmetric deformations (of both isotropic and anisotropic) solids under symmetric loading conditions. Mathematically, boundary value problems for nonlinear ordinary and partial differential equations governing equilibrium will be studied. A second related issue is to examine the effects of loading perturbations on bifurcation solutions describing radially symmetric cavitation instabilities (void nucleation and growth in solids). The third focus will be on the determination of (i) generalized elastic moduli for nonlinear anisotropic materials, (ii) their connection to the corresponding linear moduli, and (iii) constitutive inequalities to describe physically reasonable response of hyperelastic materials. Finally, problems in which the direction of anisotropy (transverse isotropy) is non- constant will be considered, with interest toward potential applications in biomechanics, such as modeling of the heart. The National Science Foundations mandate to ensure the vitality of the Nations scientific enterprise includes concern for the quality, composition, distribution and effectiveness of the human resource base in science and engineering. Within this context, the Foundation is committed to enhancing the current rate of participation of women in science and engineering careers, in general, and as active participants in all of its programs. Research Planning Grant awards are made: (1) to help increase the number mf new women investigators participating in NSFs research programs; and, (2) to facilitate preliminary studies and other activities related to the development of competitive research p rojects and proposals by women who have not previously had independent Federal research funding. Research Planning Grants are one-time awards that may be used for preliminary work to determine the feasibility of a proposed line of inquiry, and/or for other activities that will facilitate proposal development.