Quasi-incompressible and quasi-inextensible element and material formulation for an isotropic medium

Rodoplu, Burak
The contribution presents a novel finite element formulation for quasi-inextensible and quasi-incompressible finite hyperelastic behavior of transversely anisotropic materialsandaddressesitscomputationalaspects. Theformulationispresentedinpurely Eulerian setting and based on the additive decomposition of the free energy function into isotropic and anisotropic parts where the isotropic part is further decomposed intoisochoricandvolumetricparts. Forthequasi-incompressibleresponse,theQ1P0 element formulation is outlined briefly where the pressure type Lagrange multiplier anditsconjugateenterthevariationalformulationasanextendedsetofvariables. Using the similar argumentation, an extended Hu-Washizu type potential is introduced where the average volume fiber stretch and fiber stress are additional field variables. Within this context, the resulting Euler-Lagrange equations and the element formulation resulting from the extended variational principle are derived. The numerical implementation exploits the underlying variational structure leading to a canonical symmetric structure. The efficiency of the proposed approached is demonstrated through representative boundary value problems. The superiority of the proposed element formulation over the standard Q1- and Q1P0-element formulation is studied through convergence analyses. The proposed finite element formulation is modular and shows excellent performance for fiber reinforced materials in the inextensibility limit. Moreover, performance of the proposed formulation is studied for representative boundary value problems applied to soft biological tissues such as human arterial wall.
Citation Formats
B. Rodoplu, “Quasi-incompressible and quasi-inextensible element and material formulation for an isotropic medium,” M.S. - Master of Science, Middle East Technical University, 2018.