TY - JOUR

T1 - A finite element method for simulating soft active non-shearable rods immersed in generalized Newtonian fluids

AU - Ausas, Roberto Federico

AU - Gebhardt, Cristian Guillermo

AU - Buscaglia, Gustavo Carlos

N1 - Funding Information: Roberto Federico Ausas and Gustavo Carlos Buscaglia gratefully acknowledge financial support from the São Paulo Research Foundation FAPESP and from the Conselho Nacional de Desenvolvimento Científico e Tecnológico (grants CEPID-CeMEAI 2013/07375-0 and INCT-MACC ). Funding Information: Roberto Federico Ausas and Gustavo Carlos Buscaglia gratefully acknowledge financial support from the S?o Paulo Research Foundation FAPESP and from the Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico (grants CEPID-CeMEAI 2013/07375-0 and INCT-MACC). The authors acknowledge as well the University of Bergen for the open access funding. Finally, the authors thank to D. Ham and K. Sagiyama from the Firedrake project and P. Farrell for giving some guidelines in the initial stages of the development.

PY - 2022/5

Y1 - 2022/5

N2 - We propose a finite element method for simulating one-dimensional solid models with finite thickness and finite length that move and experience large deformations while immersed in generalized Newtonian fluids. The method is oriented towards applications involving microscopic devices or organisms in the soft-bio-matter realm. By considering that the strain energy of the solid may explicitly depend on time, we incorporate a mechanism for active response. The solids are modeled as Cosserat rods, a detailed formulation being provided for the planar non-shearable case. The discretization adopts one-dimensional Hermite elements for the rod and two-dimensional low-order Lagrange elements for the fluid's velocity and pressure. The fluid mesh is boundary-fitted, with remeshing at each time step. Several time marching schemes are studied, of which a semi-implicit scheme emerges as most effective. The method is demonstrated in very challenging examples: the roll-up of a rod to circular shape and later sudden release, the interaction of a soft rod with a fluid jet and the active self-locomotion of a sperm-like rod. The article includes a detailed description of a code that implements the method in the Firedrake library.

AB - We propose a finite element method for simulating one-dimensional solid models with finite thickness and finite length that move and experience large deformations while immersed in generalized Newtonian fluids. The method is oriented towards applications involving microscopic devices or organisms in the soft-bio-matter realm. By considering that the strain energy of the solid may explicitly depend on time, we incorporate a mechanism for active response. The solids are modeled as Cosserat rods, a detailed formulation being provided for the planar non-shearable case. The discretization adopts one-dimensional Hermite elements for the rod and two-dimensional low-order Lagrange elements for the fluid's velocity and pressure. The fluid mesh is boundary-fitted, with remeshing at each time step. Several time marching schemes are studied, of which a semi-implicit scheme emerges as most effective. The method is demonstrated in very challenging examples: the roll-up of a rod to circular shape and later sudden release, the interaction of a soft rod with a fluid jet and the active self-locomotion of a sperm-like rod. The article includes a detailed description of a code that implements the method in the Firedrake library.

KW - Finite element method

KW - Fluid–structure interaction

KW - Freely available Firedrake implementation

KW - Generalized Newtonian fluids

KW - One-dimensional solids with finite thickness and finite length

KW - Soft active bio-matter realm

UR - http://www.scopus.com/inward/record.url?scp=85122539977&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2021.106213

DO - 10.1016/j.cnsns.2021.106213

M3 - Article

AN - SCOPUS:85122539977

VL - 108

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 106213

ER -