Presidential Young Investigator Award: Foundation and Special Reference of Inelasticity

这项研究涉及现代非线性连续介质力学的几何和计算方面，特别强调非弹性。从根本上讲：(I)研究将进一步探索非线性弹性、板和壳的哈密顿结构；(Ii)建立一个物理激励的、数学上良好的、适合于大规模非弹性计算的非线性塑性的一般框架。在数字方面，一个基本目标是开发适合超级计算环境的计算方法。特别是，(Iii)开发新的非弹性的算法处理方法，绕过目前的限制，如所谓的增量目标算法的必要性。最后，(Iv)本研究将把这一方法应用于分叉和局部化问题。

The research is concerned with geometric and computational aspects of modern nonlinear continuum mechanics, with special emphasis on inelasticity. From a fundamental standpoint: (i) the research will further explore the Hamiltonian structure of nonlinear elasticity, plates and shells; (ii) develop a general framework for nonlinear plasticity, which is physically motivated, mathematically well-posed and suitable for large-scale inelastic computation. On the numerical side, a basic objective is to develop computational methodologies suitable for a supercomputing environment. In particular, (iii) development of new algorithmic treatments for inelasticity which by-pass current limitations, such as the necessity for so-called incrementally objective algorithms. Finally, (iv) the research will use this methodology in applications concerned with bifurcation and localization problems.