Mesoscale Crystal Plasticity Based on Continuum Dislocation Dynamics

Explore a comprehensive lecture on mesoscale crystal plasticity based on continuum dislocation dynamics, delivered by Anter El-Azab at the Hausdorff Center for Mathematics. Delve into the mathematical formalism and numerical solutions of this cutting-edge approach to understanding plastic strength and failure in metals. Learn about the evolution from computationally intensive dislocation dynamics simulations to more tractable density-based models using statistical mechanics and non-equilibrium thermodynamics. Discover the first working model in this field, which employs a system of transport-reaction equations and linear elasticity to govern dislocation system evolution in crystals. Examine the novel Least Squares variational formalism and finite element method used to solve this complex problem, and witness the groundbreaking predictions of experimentally observed dislocation patterns. Gain insights into the collaborative work with Shengxu Xia and the implications for advancing dislocation theory and crystal plasticity theory.