804 Novel Mathematical Models and Computational Methods

N.R. Aluru, University of Illinois at Urbana-Champaign
J.N. Reddy, Texas A&M University
Karan Surana, University of Kansas
The mini-symposium on “Novel Mathematical Models and Computational Methods” focuses on recent advances and progress in the development of new mathematical models and non-conventional computational methods for problems in mechanics and beyond. Classical mathematical models often fail to accurately describe physical phenomena at small scales and new mathematical models are necessary. In addition, classical computational methods may not be adequate to accurately solve mathematical models describing non-local and non-classical phenomena. This symposium aims to bring together researchers and scientists who are developing novel mathematical models and/or computational methods to solve relevant engineering problems. Some of the topics of interest for this symposium are:

- Non-local and non-classical continuum mechanics (e.g., gradient elasticity, couple-stress theories, internal polar theories, Cosserat theories, peridynamics, and others)
- Constitutive theories for non-classical continua, including internal polar and Cosserat solids and fluids
- Non-classical mathematical models for complex interfaces involving mechanics
- New mathematical formulations of problems (including constitutive theories) in mechano-biology and micro and nanomechanics
- Non-conventional computational methods (e.g., beyond C0 finite elements)
- Particle methods for non-classical phenomena
- Multiphysics and multiscale approaches for non-classical physical phenomena
- Other mathematical formulations and numerical approaches as appropriate for mechanics problems

Key Words: non-local mechanics, novel mathematical models, non-conventional computational methods