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Hyperelastic Membranes with Implicitly Defined, Continuously Embedded Fibers

Michael Wolfgang Kaiser, Thomas-Peter Fries

2024enhyperelasticitymembranesfibersanisotropyfinite element method

Abstract

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Anovelmechanicalmodelandcorrespondingfiniteelementmethodforanisotropic, hyperelastic, curved membranes are proposed. Hyperelastic fibers are embedded into the otherwise isotropic membrane, being relevant, for example, in reduced models for biological tissues and textiles. The geometrically nonlinear mechanics is formulated based on first principles of continuum mechanics (finite strain theory). The employed differential operators are formulated in a coordinate-free manner, through a framework known as tangential differential calculus. This enables a (semi-)implicit description of the fiber geometry through the intersection of level sets of some scalar function with the explicitly defined membrane surface. The mechanical model of the implicit fibers is then coupled to the mechanics of the membrane. For the numer-ical analysis, finite elements are applied such that the resulting scheme is a hybrid between classical Surface FEM and fictitious domain methods. For smooth physical fields, higher-order convergence rates are obtained and confirm the success of the nu-merical method.

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Cite This Work

@article{4e117b6e-8766-4a4f-b6f1-089c940856aa,
  title={Hyperelastic Membranes with Implicitly Defined, Continuously Embedded Fibers},
  author={Michael Wolfgang Kaiser and Thomas-Peter Fries},
  year={2024},
  language={en}
}
TY  - JOUR
TI  - Hyperelastic Membranes with Implicitly Defined, Continuously Embedded Fibers
AU  - Michael Wolfgang Kaiser
AU  - Thomas-Peter Fries
PY  - 2024
LA  - en
ER  -

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