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

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2018

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Rodoplu, Burak

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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.

Subject Keywords

Elasticity., Anisotropy., Finite element method.

URI

http://etd.lib.metu.edu.tr/upload/12622007/index.pdf
https://hdl.handle.net/11511/27226

Collections

Graduate School of Natural and Applied Sciences, Thesis

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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.