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International Journal for Multiscale Computational Engineering
Fator do impacto: 1.016 FI de cinco anos: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i4.30
pages 379-396

Multiscale Modeling of Viscoelastic Plant Tissue

P. Ghysels
K.U. Leuven, Department of Computer Science, Celestijnenlaan 200A, bus 2402, B-3001 Heverlee, Belgium
G. Samaey
K.U. Leuven, Department of Computer Science, Celestijnenlaan 200A, bus 2402, B-3001 Heverlee, Belgium
P. Van Liedekerke
K.U. Leuven, Department of Biosystems, Kasteelpark Arenberg 30, bus 2456, B-3001 Heverlee, Belgium
E. Tijskens
K.U. Leuven, Department of Biosystems, Kasteelpark Arenberg 30, bus 2456, B-3001 Heverlee, Belgium
H. Ramon
K.U. Leuven, Department of Biosystems, Kasteelpark Arenberg 30, bus 2456, B-3001 Heverlee, Belgium
D. Roose
K.U. Leuven, Department of Computer Science, Celestijnenlaan 200A, bus 2402, B-3001 Heverlee, Belgium

RESUMO

We present a multiscale method for the simulation of large viscoelastic deformations and show its applicability to biological tissue such as plant tissue. At the microscopic level we use a particle method to model the geometrical structure and basic properties of individual cells. The cell fluid, modeled as a viscoelastic fluid by means of smoothed particle hydrodynamics (SPH), is enclosed in an elastic cell wall, modeled by discrete elements. The macroscopic equation and stress tensor are derived from the SPH model by means of the generalized mathematical homogenization (GMH) technique. The macroscopic domain is discretized using standard finite elements, where the stress tensor is evaluated from microscopic simulations in small sub-domains, called representative volume elements (RVEs). Our emphasis is on reconstructing the microscopic state inside the RVE for a given macroscopic deformation and velocity gradient. We propose a scheme to initialize the RVE consistently, not only with the macroscopic variables, but also with the microscopic dynamics.

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