A variational model for plastic reorientation in fibrous material: numerical experiments on phase segregation
Andrea Rodella, Antonino Favata, Stefano Vidoli
download PDFAbstract. We propose a continuum model of fibrous material that may undergo an internal reorganization, which turns out in a plastic change of the orientation of the fibers when the remodeling torque achieves a threshold. We have recently found that the reorientation may induce a complex scenario in the response of such materials. In a traction test, we show that the most general transversely isotropic material may evolve in three different ways; in particular, the fibers asymptotically tend (regularly or with jumps): (A) to a given angle; (B) to align perpendicularly to the load direction; (C) to align with the load direction if their initial orientation is less than a given value otherwise perpendicularly. We focus on the latter material response (C) which has all the ingredients to manifest a phase transition phenomenon. Finally, we provide a numerical investigation to demonstrate phase segregation.
Keywords
Phase Segregation, Fibrous Material, Plastic Remodeling, FEniCS
Published online 3/17/2022, 6 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Andrea Rodella, Antonino Favata, Stefano Vidoli, A variational model for plastic reorientation in fibrous material: numerical experiments on phase segregation, Materials Research Proceedings, Vol. 26, pp 17-22, 2023
DOI: https://doi.org/10.21741/9781644902431-3
The article was published as article 3 of the book Theoretical and Applied Mechanics
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] G. Grekas, M. Proestaki, P. Rosakis, J. Notbohm, C. Makridakis, and G. Ravichandran, Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix, Journal of the Royal Society Interface, vol. 18, no. 175, p. 20200823, (2021). https://doi.org/10.1098/rsif.2020.0823
[2] E. Ban, J. M. Franklin, S. Nam, L. R. Smith, H. Wang, R. G. Wells, O. Chaudhuri, J. T. Liphardt, and V. B. Shenoy, Mechanisms of Plastic Deformation in Collagen Networks Induced by Cellular Forces, Biophysical Journal, vol. 114, no. 2, pp. 450–461, (2018). https://doi.org/10.1016/j.bpj.2017.11.3739
[3] B. Buchmann, L. Engelbrecht, P. Fernandez, et al., Mechanical plasticity of collagen directs branch elongation in human mammary gland organoids, Nature Communication, vol. 12, no. 2759, (2021). https://doi.org/10.1038/s41467-021-22988-2
[4] B. Halphen and Q. Nguyen, Sur les matériaux standards généralisés, Journal de Mécanique, vol. 14, pp. 39–63, 01 (1975).
[5] J.-J. Marigo, Constitutive relations in plasticity, damage and fracture mechanics based on a work property, Nuclear Engineering and Design, vol. 114, pp. 249–272, (1989). https://doi.org/10.1016/0029-5493(89)90105-2
[6] A. Favata, A. Rodella, and S. Vidoli, An internal variable model for plastic remodeling in fibrous materials, European Journal of Mechanics – A/Solids, p. 104718, (2022). https://doi.org/10.1016/j.euromechsol.2022.104718
[7] B. Coleman and M. Gurtin, Thermodynamics with internal state variables, The Journal of Chemical Physics, vol. 47, no. 2, pp. 597–613, (1967). https://doi.org/10.1063/1.1711937
[8] P. Germain, The method of virtual power in continuum mechanics. Part 2: Microstructure, SIAM Journal on Applied Mathematics, vol. 25, no. 3, pp. 556–575, (1973). https://doi.org/10.1137/0125053
