Project Details
Projekt
Adaptive isogeometric modeling of discontinuities in complex-shaped heterogeneous solids
Subject Area
Mechanics
Term
from 2014 to 2021
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 255853920
The development of innovative products demands multi-material lightweight designs with complex heterogeneous local material structures. Their computer-aided engineering relies on the constitutive modelling and, in particular, the numerical simulation of propagating cracks. The underlying numerical techniques have to account for the failure of interfaces and bulk material as well as their interaction in the form of crack branching and coalescence. In order to provide realistic predictions by simulation, the true 3D nature of the problem has to be captured.For this purpose, this project develops new numerical models and methods that combine adaptive spline-based approximations from Isogeometric Analysis (IGA) with phase-field models for crack propagation. The phase-field approach significantly relaxes the necessary resolution of interfaces and cracks and, hence, avoids the critical problem of re-meshing. The IGA framework bridges the gap to the computer aided design (CAD) of complex structures and, when combined with adaptivity, allows the accurate representation of diffuse interfaces in the context of phase-field modeling.This proposal concerns the enhancement of this promising approach to the computational modeling of failure in complex-shaped heterogeneous 3D solids. The key idea is to connect an exact, continuous surface description with a non-conforming structured volume mesh that represents the local material structure in an implicit, diffuse manner. The benefits of the approach, will be demonstrated by the numerical analysis of contact induced damage and fracture. Equally important are the underlying mathematics to foresee and assess its efficiency and reliability in practice. The main goals of this project are linked to fundamental challenges in the fields of Computational Mechanics, Numerical Analysis and Material Sciences, e.g., the representation and adaptive refinement of unstructured (water-tight) spline surfaces, the feasible coupling of spline surfaces with structured bulk meshes, the regularized modeling of heterogeneous materials, and the rigorous error analysis and control in pre-asymptotic regimes. The implementation of these goals will build upon the collaboration of engineers and mathematicians established during the first funding period that lead to exciting developments such as the characterization of analysis-suitable meshes and optimal adaptive mesh refinement in IGA, its efficient algorithmic realization via Bézier extraction as well as its application to phase-field models for brittle and ductile fracture. Further fundamental results regard the competitiveness of the envisioned approach, in particular, the mathematical justification of the conjectured spectral superiority of IGA when compared with standard finite elements.
DFG Programme
Priority Programmes
