Background:
Peridynamics (PD) represents a generalization of classical continuum mechanics. Instead of partial differential equations (PDEs), the field equations are formulated in the form of integral equations.
This approach is particularly advantageous for modeling processes with discontinuities, as classical PDEs cannot be directly applied at singularities (e.g., crack surfaces or interface layers).
Assignment:
Our research group develops peridynamic models for simulating corrosion processes and material degradation. In collaboration with the Institute for Geotechnics and Construction Management of
Prof. Dr. Jürgen Grabe, a peridynamic corrosion model is to be implemented as a nonlocal diffusion-advection equation and tested using selected benchmarks. The student will first conduct a literature review on peridynamics and its application in corrosion modeling. Subsequently, a numerical model will be developed that can be used for the simulation of corrosion in load-bearing structures in geotechnical or medical applications. The modeling should consider an efficient numerical implementation of nonlocal diffusion and advection processes. Finally, the implementation is to be validated using suitable benchmark problems.
Requirements:
- Good programming skills in modern C++ / MATLAB / Python or Julia
- Knowledge of continuum mechanics and material mechanics
- Interest in scientific research and numerical modeling
- Beneficial: knowledge of numerical methods for integral equations
Start: anytime Duration: 6 months
Contact for further questions: Dr.-Ing. Alexander Hermann alexander.hermann(at)hereon(dot)de