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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i4.50
pages 411-422

Coarse Implicit Time Integration of a Cellular Scale Particle Model for Plant Tissue Deformation

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

ABSTRACT

We describe a multiscale method to simulate the deformation of plant tissue. At the cellular scale we use a combination of smoothed particle hydrodynamics and discrete elements to model the geometrical structure and basic properties of individual plant cells. At the coarse level, the material is described by the standard continuum approach without explicitly constructing a constitutive equation. Instead, the coarse scale finite element model uses simulations with the fine (cellular) scale model in small subdomains, called representative volume elements (RVEs), to determine the necessary coarse scale variables, such as stress and the elasticity and viscosity tensors. We present an implicit time integration scheme for the coarse finite element model, allowing much larger time steps than possible with explicit methods. Computation of the Cauchy stress from an RVE is straightforward by volume averaging over the RVE. In this work, we use forward finite differencing of the objective Truesdell stress rate to estimate both the fourth-order elasticity and viscosity tensors. These tensors are then used to construct the coarse scale stiffness and damping matrices required for implicit integration.

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