Higher order stabilized finite element method for hyperelastic finite deformation

✍ Scribed by Antoinette M. Maniatty; Yong Liu; Ottmar Klaas; Mark S. Shephard

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 1001 KB
• Volume: 191
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00335-8

✦ Synopsis

This paper presents a higher order stabilized ®nite element formulation for hyperelastic large deformation problems involving incompressible or nearly incompressible materials. A Lagrangian ®nite element formulation is presented where mesh dependent terms are added element-wise to enhance the stability of the mixed ®nite element formulation. A reconstruction method based on local projections is used to compute the higher order derivatives that arise in the stabilization terms, speci®cally derivatives of the stress tensor. Linearization of the weak form is derived to enable a Newton±Raphson solution procedure of the resulting non-linear equations. Numerical experiments using the stabilization method with equal order shape functions for the displacement and pressure ®elds in hyperelastic problems show that the stabilized method is eective for some non-linear ®nite deformation problems. Finally, conclusions are inferred and extensions of this work are discussed.