We discuss numerical methods for solving initial boundary value problems in solid mechanics (static/dynamic elastic problems of solids and structures, thermal problems). Focus is on finite differences and on the finite element method, its theoretical foundation, the choices made when using it, its application for solving problems of engineering interest, and the interpretation of results.

This course introduces students to numerical methods commonly used in engineering with a focus on finite element (FE) analysis. Starting with finite differences and ending with static and dynamic FE problems, students will learn the fundamental concepts of finite elements as well as their implementation and application.

Dynamics of particles, rigid bodies, and deformable bodies: Motion of a single particle, motion of systems of particles, 2D and 3D motion of rigid bodies, vibrations, 1D waves.

Theoretical foundations and numerical applications of multiscale modeling in solid mechanics, from atomistics all the way up to the macroscopic continuum scale with a focus on scale-bridging methods (including the theory of homogenization, computational homogenization techniques, modeling by methods of atomistics, coarse-grained atomistics, mesoscale models, multiscale constitutive modeling).

Students develop and build a product from A-Z! They work in teams and independently, learn to structure problems, to identify solutions, system analysis and simulations, as well as presentation and documentation techniques. They build the product with access to a machine shop and state of the art engineering tools (Matlab, Simulink, etc).

This course addresses two major examples of phase transitions, namely solid-solid phase transformations and solidification. We focus on the modeling of the propagation of phase boundaries (surface of strain discontinuity or solidification front) in continuum media. Both the sharp-interface model and related numerical modeling techniques based on the phase-field method are introduced.