NEW CLASSES OF SIMPLICIAL AND NON-SIMPLICIAL CONFORMAL MIXEDFINITE ELEMENT METHODS FOR NONLINEAR ELASTICITY

New classes of stabilized mixed finite element methods are introduced. New mixed formulations for compressible nonlinear elasticity have been derived based on dis-placement, displacement gradient, and stress as independent unknowns. By adding a pressure-like field to the three-field mixed formulation, a mixed formulation for incompressible nonlinear elasticity is introduced. The novelty of these formulations arises from choosing proper solution spaces for each unknown.H1-,Hc-,Hd-, andL2-spaces are chosen respectively for displacement, displacement gradient, stress, and pressure. The set of test and trial spaces satisfy Hadamard jump conditions and the continuity of traction. Two types of inf-sup conditions are obtained to investigate the stability of the new mixed formulations. After recognizing unstable choices of finite elements, two stabilization techniques, bubble functions, and perturbation methods, are employed to stabilize unstable cases. By solving different benchmark problems, the performance of new stabilized mixed methods in 2D and 3D are studied. New mixed formulations showed good performance for problems with complex geometries, bending problems, and near-incompressible and incompressible regimes. Numerical instabilities such as hourglass instability and shear-locking were not observed in numerical analysis.

Author

• Gerami Matin, Ali

Language

• en

Keyword

• Mixed Methods
• Finite Element Methods
• Nonlinear Elasticity
• Inf-sup Conditions
• Stabilization

Date created

• 2022

Type of Work

• Dissertation

License

• All rights reserved

Rights statement

• In Copyright

GW Unit

• Civil & Environmental Engineering

Degree

• Ph.D.

Advisor

• Manzari, Majid
• Angoshtari, Arzhang

Committee Member(s)

• Manzari, Majid
• Angoshtari, Arzhang
• Ren, Xiaofeng
• Silva, Pedro
• Li, Tianshu

Persistent URL

•  https://scholarspace.library.gwu.edu/etd/6t053g751