A Phenomenological Model for the Adaptative Biomechanical Response of Growing Tree
DOI:
https://doi.org/10.11145/97Abstract
Modelling the shape evolution of growing trees requires to account for the interaction between growth and adaptative biomechanical response to its environment. Trees develop growth strategies to ensure light and nutrient capture as stability. These strategies are linked with the branching process and shape evolution of the exisiting branches or stem. Unlike growth of bones and soft tissues where the change in volume originates from the insertion of new particles within the continuum, growth in trees is modeled by the addition of new material points on an existing deformed structure. Most of the existing models adopt an incremental approach and propose the equilibrium of the growing structure to be reached at each time after growth has occured, thus separating growth and mechanical effects. Guillon et al. [1, 2] have origninally proposed a new formalism to model the time-space continuous growth of rod with applications to tree-like structures. The purpose of this work is to advance some thermodynamically consistent constitutive relations describing the biomechanical response of the continuously radially growing section. In particular, we introduce an internal variable which aims at accounting for the adaptative structure of the (growing) woody stem section. We present an existence analysis for both the constitutive relation problem and the quasi-static evolution problem.
В References
[1] T. Guillon, Y. Dumont, T. Fourcaud, A new mathematical framework for modelling the biomechanics of growing trees with rod theories, Mathematical and Computer Modelling, 55, 2061-2077.
[2] T. Guillon, Y. Dumont, T. Fourcaud,Numerical methods for the biomechanics of growing trees , Computers andВ Mathematics with Applications, 64, 289-309.
Downloads
Published
Issue
Section
License
The journal Biomath Communications is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
