Multi-Scale Material Modelling techniques Part-I

Multi-scale materials modelling is a powerful tool in bridging the gap between the different length scale and time scale of material ranging from subatomic scale to the macroscopic scale. The theoretical foundations and numerical methods of handling the multiscale modelling in solid mechanics, from atomistic techniques all the way up to the macroscopic continuum scale have been discussed. In the part-I of this course, students will learn the basic principles of Finite Element Method, discretization of the domain, and numerical solution techniques for solid mechanics problems. Emphasis is placed on solving boundary value problems, developing element matrices, and implementing various solution methods. Practical applications of FEM in engineering design and material behavior prediction are discussed. The method of handling the material behaviour at a lower scale is different from its large scale behaviour and is dealt with under a separate section on molecular dynamics. It will  cover Molecular Dynamics (MD) simulations, where students will explore atomistic models and their applications to materials science. The course introduces the principles of MD, including interatomic potentials, time integration algorithms, and system initialization. By the end of the course, students will be proficient in applying FEM for macroscopic modelling and MD for atomistic simulations, enabling them to approach complex multi-scale problems in materials engineering with a deeper understanding of both methods and their integration.