Understanding Explicit Solid Dynamics: Theory

The course "Understanding Explicit Solid Dynamics" is divided into three separate modules: Introduction, Theory and Practice. The Theory module builds upon the foundations provided in the Introduction module, which gave a broad overview of explicit solid dynamics technology and its applications. In this module, we will dive deeper into the fundamental concepts of explicit solid dynamics, providing students with the necessary knowledge to start simulating and analyzing dynamic events using numerical methods.The module is divided into two main sections, each covering an essential aspect of explicit solid dynamics simulation.In the first section, we will review the key concepts of nonlinear solid mechanics, focusing on the kinematics of moving solids. We will study the deformation gradient, stress and strain measures and an introduction to Lagrangian formulations. Equilibrium and conservation properties of dynamic systems will be discussed, along with the concepts of stress waves in solids. These topics will be covered in detail, and have complementary lecture notes to consolidate the concepts.The second section explores the numerical aspects of explicit solid dynamics, specifically, the topic of time integrators. We will compare and contrast Implicit and Explicit methods and explore the stability properties of explicit schemes. The concept of critical time step and the Courant–Friedrichs–Lewy condition will be covered in detail.By the end of the Theory module, students will have a solid understanding of the fundamental concepts of nonlinear solid mechanics, stress waves in solids, and the differences between explicit and implicit methods. They will gain notions of what is behind explicit dynamics simulations, understand the influence of meshing, material properties, and time integrator parameters. This knowledge will be crucial for successfully completing the final module of the course, Practice, which focuses on diverse aspects of practical simulations.