Mathematical Sciences: Nonlinear Elasticity and the Calculusof Variations

有了这个奖项，首席研究员将研究模型， 非线性弹性力学描述了 材料在中等到大变形。 相比 线性模型非线性模型通常要求其解 更复杂的数学分析 上 理论方面，首席研究员将研究弱者 雅可比行列式的连续性和空间的选择 允许的变形。 在应用方面，他将学习 弹性复合材料如泡沫橡胶的稳定性， 他将分析弹性力学中的固-固相变 晶体 大量的日常现象涉及弹性材料 可以用线弹性理论来解释。 这种线性理论涉及弹性材料在 对微小变形的反应。 然而，当变形 是中等到大规模的线性理论必须取代 一个更复杂的非线性理论。 非线性理论是 如果材料是复合材料，如泡沫橡胶， 或纤维增强橡胶。 凭借这一奖项， 研究人员将使用数学分析来研究 非线性弹性材料

With this award the principal investigator will study models of nonlinear elasticity that describe the behavior of elastic materials at moderate to large deformations. In contrast to linear models nonlinear models usually require for their solution more sophisticated types of mathematical analysis. On the theoretical side the principal investigator will study the weak continuity of the Jacobian determinant and the choice of a space of admissible deformations. On the applied side he will study the stability of elastic composite materials such as foam rubber, and he will analyze solid-solid phase transitions in elastic crystals. A goodly number of everyday phenomena involving elastic materials can be explained using what is called linear elasticity theory. This linear theory concerns the behavior of elastic materials in response to small deformations. However when the deformations are moderate to large in size the linear theory must be replaced with a more complicated nonlinear theory. A nonlinear theory is also required if the material is a composite, such as foam rubber or fibre-reinforced rubber. With this award the principal investigator will use mathematical analysis to study models of nonlinear elastic materials.