Arbitrary Lagrangian-Eulerian (ALE) finite element formulations in finite strain elasto-plasticity.

다국어 초록 (Multilingual Abstract)

This dissertation presents a new implicit Arbitrary Lagrangian-Eulerian (ALE) finite element method for large deformation plasticity problems in solid mechanics. An extension to fluid dynamics is also included. The proposed formulation is based on a composition of mappings which does not appear to have been fully investigated or developed in previous works in this area.
The first part of the dissertation presents the necessary background information on Lagrangian continuum mechanics and it's mixed finite element implementation. Both finite strain elasticity and multiplicative plasticity are considered. The latter includes constitutive models of inelastic solids based on the multiplicative decomposition <bold>F</bold> = <bold>F</bold><italic><super> e</super></italic><bold>F</bold><italic><super>p</super></italic> of the deformation gradient into an elastic and a plastic part, with the elastic response of the material given in terms of an elastic potential. These Lagrangian methods are to be extended to the ALE setting. Next, an existing ALE method is implemented and evaluated for reference and comparison purposes. The focus of this work is on implicit methods, with explicit schemes considered as a particular case.
The second part of the dissertation focuses on the newly developed implicit ALE method. The proposed schemes are discussed first in the context of finite elasticity. They include both coupled and staggered solution strategies. The staggered scheme, in particular, involves a separate solution of the advection phase, leading to more computationally efficient procedures. The extension to plasticity problems is presented next. The advection of the internal variables is discussed in detail.
The third part of the dissertation presents the extension of the new ALE method to solid dynamics. Furthermore, a viscous fluid can be viewed as a special case of a rigid-viscoplastic solid. This crucial observation leads to an easy extension of these developments to fluid dynamics problems. The interest in this work focuses on applications involving a contained fluid, typically with free surfaces or fluid/solid interfaces to be modeled accurately.
The dissertation concludes with a discussion of the possible future lines of research after the identification of some outstanding issues in this area of computational mechanics. (Abstract shortened by UMI.).