Problems in Anisotropic Nonlinear Elasticity

9500642 Polignone这项工作得到了女性科学家和工程师研究规划奖的支持。将对各向异性材料的非线性弹性变形问题进行初步研究。将考虑几个研究领域。第一个问题是确定在对称载荷条件下描述非径向对称变形（各向同性和各向异性）固体的不稳定性。数学上，非线性常微分和偏微分的边值问题 将研究平衡方程。第二相关 问题是研究载荷扰动对描述径向对称空化不稳定性（固体中的空穴成核和生长）的分叉解的影响。第三个重点是确定（i）非线性各向异性材料的广义弹性模量，（ii）它们与相应线性模量的关系，以及（iii）描述超弹性材料物理合理响应的本构不等式。最后，将考虑各向异性（横观各向同性）方向不恒定的问题，并对势感兴趣。 在生物力学中的应用，例如心脏建模。 国家科学基金会的任务是确保国家科学事业的活力，包括关注科学和工程人力资源基础的质量、组成、分布和有效性。 在此背景下，基金会致力于提高目前妇女在科学和工程职业中的总体参与率，并积极参与其所有方案。 研究规划补助金的颁发是为了：（1）帮助增加参加国家科学基金会研究方案的新的妇女研究人员的人数;（2）促进与以前没有独立的联邦研究基金的妇女制定竞争性研究方案和建议有关的初步研究和其他活动。 研究规划赠款是一次性奖励，可用于初步工作，以确定拟议的可行性 调查线，和/或其他活动，将促进提案的发展。

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.