Reliable Simulation in the Mechanics of Materials and Structures

   

Topics

• Verification, validation and prediction: general definitions within the field of Computational Mechanics.
• Abstraction and idealization of a physical problem: based on examples, the processes of abstraction and idealization from a real world problem into a mathematical model (depending on the aim of simulation) will be clarified. The influence of faulty idealization will be thoroughly discussed.
• Verification of a model: to ensure the accuracy of the numerical implementation of the mathematical model, the results will be compared with a reference solution (e.g. analytical solution).
• Factors affecting the FEM implementation: time integration scheme (explicit or implicit) , time step size, element type, static or dynamic model, linear or non-linear model geometric non-linearity, etc. .
• Validation of a model: by comparison of a numerical model with reality (e.g. experimental results, complete systems).
• Solving coupled problems: suitable solution strategies for weakly and strongly coupled problems. Example: differential equations of a coupled spring, damper and mass system.
• Example of strongly coupled problems: multiphase porous media.
• Introduction to multi-scale modeling: Effect of the time scale and space dimensions on the choice of the modeling method (nano- to micro- to macro-scale).
  Example: applying the molecular-dynamics simulation to solve problems on the nano-scale.