A quasi-inextensible and quasi-incompressible finite element formulation for transversely anisotropic hyperelastic solids and soft biological tissues

2017-09-07
The contribution presents a novel finite element formulation for quasi-inextensible and quasi-incompressiblefinite hyperelastic behaviour of transeversely anisotropic materials and addresses its computational aspects.The formulation is presented in purely Eulerian setting and based on the additive decomposition of the freeenergy function into isotropic and anisotropic parts where the former is further decomposed into isochoricand volumetric parts. For the quasi-incompressible response the Q1P0 element formulation is outlinedbriefly where the pressure-type Lagrange multiplier and its conjugate enter the variational formulationas anextended set of variables. Using the similar argumentation an extended Hu-Washizu-type mixedvariational potential is introduced where the volume averaged fiber stretch and fiber stress are additional fieldvariables. Within this context, the resulting Euler-Lagrange equations and the element formulation resultingfrom the extended variational principle are derived[1]. The numerical implementation exploits the underlyingvariational structure leading to a canonical symmetric structure.The efficiency of the proposed approachedis demonstrated through representative boundary value problems. The superiority of the proposed elementformulation 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-reinforcedelastomers in the inextensibility limit.We demonstrate the performance of the proposed formulationin terms of representative boundaryvalue problems applied to (i)fiber-reinforced elastomeric solidsand (ii)soft biological tissues.
XIV International Conference on Computational Plasticity. Fundamentals and Applications (05 - 07 September 2017 )

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Citation Formats
H. Dal, “A quasi-inextensible and quasi-incompressible finite element formulation for transversely anisotropic hyperelastic solids and soft biological tissues,” presented at the XIV International Conference on Computational Plasticity. Fundamentals and Applications (05 - 07 September 2017 ), Barcelona, Spain, 2017, Accessed: 00, 2021. [Online]. Available: http://congress.cimne.com/complas2017/Admin/Files/FileAbstract/a400.pdf.