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国际多尺度计算工程期刊
影响因子: 1.016 5年影响因子: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN 打印: 1543-1649
ISSN 在线: 1940-4352

国际多尺度计算工程期刊

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

ABSTRACT

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.

REFERENCES

  1. Bangerth, W., Hartmann, R., and Kanschat, G., deal.II - Ageneral-purpose object-oriented finite element library. DOI: 10.1145/1268776.1268779

  2. Bonet, J. and Wood, R. D., Nonlinear Continuum Mechanics for Finite Element Analysis.

  3. Bruce, D. M., Mathematical modelling of the cellular mechanics of plants. DOI: 10.1098/rstb.2003.1337

  4. Chen, W. and Fish, J., A generalized space-time mathematical homogenization theory for bridging atomistic and continuum scales. DOI: 10.1002/nme.1630

  5. Chen, W. and Fish, J., A mathematical homogenization perspective of virial stress. DOI: 10.1002/nme.1622

  6. Cundall, P. A. and Strack, O. D. L., A discrete numerical model for granular assemblies. DOI: 10.1680/geot.1979.29.1.47

  7. Feyel, F. and Chaboche, J. L., FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. DOI: 10.1016/S0045-7825(99)00224-8

  8. Fish, J., Chen, W., and Li, R., Generalized mathematical homogenization of atomistic media at finite temperatures in three dimensions. DOI: 10.1016/j.cma.2006.08.001

  9. Gear, C. W., Kaper, T. J., Kevrekidis, I. G., and Zagaris, A., Projecting to a slow manifold: Singularly perturbed systems and legacy codes. DOI: 10.1137/040608295

  10. Gear, C. W. and Kevrekidis, I. G., Constraint-defined manifolds: a legacy code approach to low-dimensional computation. DOI: 10.1007/s10915-004-4630-x

  11. Ghysels, P., Samaey, G., Tijskens, B., Van Liedekerke, P., Ramon, H., and Roose, D., Multi-scale simulation of plant tissue deformation using a model for individual cell mechanics. DOI: 10.1088/1478-3975/6/1/016009

  12. Hairer, E., Norsett, S. P., andWanner, G., Solving Ordinary Differential Equations I: Nonstiff Problems.

  13. Kevrekidis, I. G., Gear, C.W., Hyman, J. M., Kevrekidis, P. G., Runborg, O., and Theodoropoulos, C., Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level analysis.

  14. Kevrekidis, I. G. and Samaey, G., Equation-free multiscale computation: Algorithms and applications. DOI: 10.1146/annurev.physchem.59.032607.093610

  15. Khisaeva, Z. F. and Ostoja-Starzewski, M., On the size of RVE in finite elasticity of random composites. DOI: 10.1007/s10659-006-9076-y

  16. Kouznetsova, V., Brekelmans, W. A. M., and Baaijens, F. P. T., An approach to micro-macro modeling of heterogeneous materials. DOI: 10.1007/s004660000212

  17. Kouznetsova, V., Geers, M. G. D., and Brekelmans, W. A. M., Multi-scale second-order computational homogenization of multi-phase materials: A nested finite element solution strategy. DOI: 10.1016/j.cma.2003.12.073

  18. Kouznetsova, V., Geers, M. G. D., and Brekelmans, W. A. M., Size of a representative volume element in a second-order computational homogenization framework. DOI: 10.1615/IntJMultCompEng.v2.i4.50

  19. Liu, M. B., Smoothed Particle Hydrodynamics: A Meshfree Particle Method.

  20. Lu, R. and Puri, V. M., Characterization of nonlinear creep behavior of two food products. DOI: 10.1122/1.550172

  21. Malkus, D. S. and Hughes, T. J. R., Mixed finite element methods- Reduced and selective integration techniques–A unification of concepts. DOI: 10.1016/0045-7825(78)90005-1

  22. Massart, T. J., Peerlings, R. H. J., and Geers, M. G. D., An enhanced multi-scale approach for masonry wall computations with localization of damage. DOI: 10.1002/nme.1799

  23. Miehe, C., Schroder, J., and Schotte, J., Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. DOI: 10.1016/s0045-7825(98)00218-7

  24. Miller, R. E. and Tadmor, E. B., The quasicontinuum method: Overview, applications and current directions. DOI: 10.1023/A:1026098010127

  25. Mittal, J. P., Mohsenin, N. N., and Sharma, M. G., Rheological characterization of apple cortex. DOI: 10.1111/j.1745-4603.1987.tb00570.x

  26. Monaghan, J. J., Smoothed particle hydrodynamics. DOI: 10.1146/annurev.aa.30.090192.002551

  27. Morris, J. P., Fox, P. J., and Zhu, Y., Modeling low Reynolds number incompressible flows using SPH. DOI: 10.1006/jcph.1997.5776

  28. Taylor, G. I., Plastic strain in metals.

  29. Van Liedekerke, P., Tijskens, E., Ghysels, P., Samaey, G., Roose, D., and Ramon, H., A particle based model to simulate the micromechanics of single plant cells and aggregates. DOI: 10.1088/1478-3975/7/2/026006

  30. Van Liedekerke, P., Tijskens, E., Ramon, H., Ghysels, P., Samaey, G., and Roose, D., A particle based model to simulate plant cells dynamics.

  31. Zienkiewicz, O. C. and Taylor, R. L., The Finite Element Method for Solid and Structural Mechanics.


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