|Address:||Institut für Angewandte Mathematik, Leibniz Universität Hannover|
|Phone:||+49 511 762 2337|
|Fax:||+49 511 762 3988|
DFG Priority Programme 1748:
Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretisation Methods, Mechanical and Mathematical Analysis
Adaptive isogeometric modeling of propagating strong discontinuities in heterogeneous materials
Cooperation with Dr.-Ing. Markus Kästner, TU Dresden
Multi-material lightweight designs and smart devices with characteristic microscopic material structures are the key features for the development of innovative products. In this context, an adaptive isogeometric framework for the modeling and simulation of crack propagation in heterogeneous materials is to be developed, implemented, and mathematically analyzed in this project. The mechanical modeling of interface failure will be based on increasing knot multiplicities driven by cohesive zone models for crack propagation along material interfaces. In addition, a phase-field model will account for propagating cracks in the bulk material including interaction phenomena such as crack branching and coalescence. The spline-based discretization used offers higher efficiency compared to Lagrangian polynomials, control of regularity, accurate approximation of strong gradients in the phase-field order parameter, as well as the possibility to discretize higher-order phase-field equations. Local mesh adaptivity required for the resolution of material interfaces and the phase-field variables will be provided by T-splines as well as hierarchical spline approximations. In addition to the physical modeling, open mathematical problems include a practicable characterization of T-meshes suitable for IGA in 3D and clear understanding of the role of increased regularity in the approximation.