Presidential Young Investigator Award: Foundation and Special Reference of Inelasticity

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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.