Browsing by Author "Kienle, Daniel"

Now showing 1 - 2 of 2

Open Access
Phase-field modeling of multi-field problems with applications to hydraulic-elastic-plastic fracturing
(Stuttgart : Institute of Applied Mechanics, 2022) Kienle, Daniel; Keip, Marc-André (Prof. Dr.-Ing.)
The modeling of fracture, i.e. fracture initiation and fracture growth, has been the subject of intensive research in the field of continuum mechanics over the last decades. The overall goal is to use simulations to make the production or development process of new parts, materials or techniques cheaper and faster. These simulations are based on material models which are derived using fundamental concepts of continuum mechanics and thermodynamics. This includes the mathematical description of the motion and deformation of a body as well as the definition of mechanical stresses, heat and mass flows. In the present work, the above process of model conceptualization and numerical implementation is applied to ductile fracture in porous metals, fracture in ductile frictional materials, and ductile frictional materials at hydraulic fracture. With these three models, it is possible to treat ductile failure problems such as cup-cone failure surfaces, ductile fractures in soil materials, and hydraulically induced fractures in ductile soil materials. The latter aims at describing the ongoing processes in hydraulic fracturing. The models are mathematically derived and implemented based on an appropriate finite element description.
Open Access
Truncated nonsmooth Newton multigrid for phase-field brittle-fracture problems, with analysis
(2023) Gräser, Carsten; Kienle, Daniel; Sander, Oliver
We propose the truncated nonsmooth Newton multigrid method (TNNMG) as a solver for the spatial problems of the small-strain brittle-fracture phase-field equations. TNNMG is a nonsmooth multigrid method that can solve biconvex, block-separably nonsmooth minimization problems with linear time complexity. It exploits the variational structure inherent in the problem, and handles the pointwise irreversibility constraint on the damage variable directly, without regularization or the introduction of a local history field. In the paper we introduce the method and show how it can be applied to several established models of phase-field brittle fracture. We then prove convergence of the solver to a solution of the nonsmooth Euler-Lagrange equations of the spatial problem for any load and initial iterate. On the way, we show several crucial convexity and regularity properties of the models considered here. Numerical comparisons to an operator-splitting algorithm show a considerable speed increase, without loss of robustness.