Two-Scale Model for Mechanical Analysis of Nastic Materials and Structures

Abstract

Nastic actuators are high energy density active materials that mimic the working processes in the plant kingdom to produce large deformation through the conversion of chemical energy inside the materials. In these actuators, the transport of the charge and fluid across a selectively permeable membrane is controlled to achieve bulk deformation. The permeable membrane may contain biological ion pumps, ion channels, and ion exchangers surrounding fluid-filled cavities embedded within a matrix. To study the working mechanism of the nastic actuators, the coupled process of ion transport and matrix response in nastic materials is characterized at two-scales by developing and solving biological transport models at one scale that are coupled with a finite element model of the matrix at a much larger scale. The emphasis is mainly focused on the mechanical analysis of the multi-actuators array structures. To increase the computational efficiency, the analysis of a nastic structure with multi-actuators is performed using an appropriate homogeneous method. A two-scale model is developed to simulate the mechanical response of the structure composed of multi-actuators. Numerical results are shown to illustrate the validity and efficiency of the proposed method.

Keywords

nastic material ion transport coupled model multi-actuators two-scale model.

Get full access to this article

View all access options for this article.

References

Berger, H. , Kari, S. , Gabbert, U. , Rodriguez-Ramos., Guinovart, R.A. , Otero, J. and Bravo-Castillero , J. 2005 . ‘‘An Analytical and Numerical Approach for Calculating Effective Material Coefficients of Piezoelectric Fiber Composites,’’ International Journal of Solids and Structure, 42:5692-5714.

Brown, W.H. 1916. ‘‘The Mechanism of Movement and the Duration of the Effect of Stimulation in the Leaves of Dionaea, ’’ American Journal of Botany, 3:68-90.

Endresen, L.P. 1997. ‘‘Chaos in Weakly-Coupled Pacemaker Cells ,’’ Journal of Theoretical Biology, 184:41-50.

Endresen, L.P. , Hall, K. , Høye, J.S. and Myrheim, J. 2000. ‘‘A Theory for the Membrane Potential of Living Cells,’’ European Biophysics Journal , 29:90-103.

Forterre, Y. , Skotheim, J.M. , Dumais, J. and Mahadevan, L. 2005. ‘‘How the Venus Flytrap Snaps, ’’ Nature, 433:421-425.

Freeman, E. and Weiland, L.M. 2009. ‘‘ High Energy Density Nastic Materials : Parameters for Tailoring Active Response ,’’ Journal of Intelligent Material Systems and Structures, 20:233-243.

Hill, B.S. and Findlay, G.P. 1981. ‘‘The Power of Movement in Plants: the Role of Osmotic Machines,’’ Quarterly Review of Biophysics , 14:173-222.

Hohe, J. 2003. ‘‘A Direct Homogenization Approach for Determination of the Stiffness Matrix for Microheterogeneous Plates with Application to Sandwich Panels,’’ Composites: Part B, 34:615-626.

Homison , 2006, Coupled Transport/Hyperelastic Model for High Energy Density Nastic Materials , MS Thesis, University of Pittsburgh, Pittsburgh, PA.

10.

Homison, C. and Weiland, L.M. 2006. Coupled Transport/ Hyperelastic Model for Nastic Materials , In: Proceedings of the SPIE, March, San Diego, CA.

11.

Ken-ichiro, M. , Kozo, O. and Masanori, S. 1991. ‘‘Finite Element Modelling of Forming Process of Solid Metal with Liquid Phase,’’ Journal of Materials Processing Technology, 27:111-118.

12.

Martin, O. 1999. ‘‘Scale Effects in Materials with Random Distributions of Needles and Cracks,’’ Mechanics of Materials , 31:883-893.

13.

Matthews, L. , Sundaresan, V.B. , Giurgiutiu, V. and Leo, D.J. 2006. ‘‘Bioenergetics and Mechanical Actuation Analysis with Membrane Transport Experiments for Use in Biomimetic Nastic Structures ,’’ Journal of Materials Research , 21:2058-2067.

14.

Morillon, R. , Lienard, D. , Chrispeels, M.J. and Lassalles, J.P. 2001. ‘‘Rapid Movements of Plants Organs Require Solute-Water Cotransporters or Contractile Proteins, ’’ Plant Physiology, 127:720-723.

15.

Pecullan, S. , Gibiansky, L.V. and Torquato, S. 1999. ‘‘Scale Effects on the Elastic Behavior of Periodic and Hierarchical Two-Dimensional Composites,’’ Journal of the Mechanics and Physics of Solids, 47:1509-1542.

16.

Sundaresan, V.B. and Leo, D.J. 2006a. ‘‘Chemo-Mechanical Model for Actuation Based on Biological Membranes,’’ Journal of Intelligent Material Systems and Structures, 17:863-870.

17.

Sundaresan, V.B. and Leo, D.J. 2006b. Protein-Based Microhydraulic Transport for Controllable Actuation, In: Proceedings of the SPIE Smart Structures and Materials, 26 February to 2 March, 6168, San Diego, CA.

18.

Sundaresan, V.B. and Leo, D.J. 2008. ‘‘Modeling and Characterization of a Chemomechanical Actuator using Protein Transporter,’’ Sensors and Actuators B, 131:384-393.

19.

Sundaresan, V.B. , Leo, D.J. , Homison, C. and Weiland, L.M. 2007a. ‘‘Biological Transport Processes for Microhydraulic Actuation,’’ Sensors and Actuators B: Chemical , 123:685-695.

20.

Sundaresan, V.B. , Sarles, S.A. and Leo, D.J. 2007b. ‘‘Chemoelectrical Energy Conversion of Adenosine Triphosphate,’’ Proceedings of the SPIE, 6525: 65250.

21.

Suquet, P. 1987. ‘‘Elements of Homogenization Theory for Inelastic Solid Mechanics,’’ In: Sanchez-Palencia, E. and Zaoui, A. (eds), Homogenization Techniques for Composite Media , pp. 194-275, Springer-Verlag , Berlin.

22.

Terada, K. , Hori, M. , Kyoya, T. and Kikuchi, N. 2000. ‘‘Simulation of the Multi-Scale Convergence in Computational Homogenization Approaches,’’ International Journal of Solids and Structures, 37:2285-2311.

23.

Volkov, A.G. , Adesina, T. , Markin, V.S. and Jovanov, E. 2008. ‘‘Kinetics and Mechanism of Dionaea Muscipula Trap Closing,’’ Plant Physiology, 146:694-702.

24.

Williams, S.E. and Bennett, A.B. 1982. ‘‘Leaf Closure in the Venus Flytrap: an Acid Growth Response,’’ Science, 218:1120-1122.