Steady-state and self-similar solution techniques in solid mechanics

Kristian Jørgensen Juul

Research output: Book/ReportPh.D. thesisResearch

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This thesis focuses on the development of spatial integration techniques that can be applied to history-dependent problems governed by specific properties. The main focus is on problems that are characterized by either a steady-state property, such as crack growth and manufacturing processes, or a self-similar property, such as indentation and void growth. It is explained how the spatial integration techniques are derived, how the history-dependent behavior is traced, and how the procedure is implemented in a finite element program. The spatial integration technique offers a number of advantages in terms of bringing out the desired solution directly, avoiding numerical issues related to the traditional incremental procedures, and the possibility for reducing the computation time, through mesh designs with fewer elements, without the loss of accuracy. The framework is generally applicable to any desired material model and the present work demonstrates how to include both rate-independent and rate-dependent models for both isotropic and anisotropic materials. Lastly, the capabilities of the framework are demonstrated through a number of studies including crack growth, wire drawing, rolling, and indentation. The numerical studies show high-resolution results, capturing features that are hard to obtain through traditional incremental methods either because of numerical issues or due to artifacts in the stationary solution, originating from the transient regime. Furthermore, high accuracy is demonstrated by comparison to analytical solutions whenever it is possible.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages301
ISBN (Electronic)978-87-7475-533-3
Publication statusPublished - 2018
SeriesDCAMM Special Report


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