A posteriori controllability of non-linear remodelling in linear elastic continua
Abstract
We investigate the a posteriori controllability of remodelling within the framework of Geometric Control Theory applied to continuum systems. Remodelling is described through an isochoric Bilby--Kroner--Lee decomposition, where the internal structural transformation is represented by a remodelling tensor and its evolution is governed by a stress-driven constitutive law. Assuming infinitesimal deformation and remodelling stretches, while retaining finite rotations of the principal remodelling directions, we derive a nonlinear state-space representation in terms of principal remodelling stretches and orientation variables. This formulation allows the remodelling process to be interpreted as a finite-dimensional nonlinear control system parametrised by the material position. Equilibrium configurations are characterised, and under-actuated controllability problems are studied by means of the tools of Geometric Control Theory. The three-dimensional setting shows that the nonlinear coupling between remodelling stretches and orientations enables complete steering of the internal state through a reduced number of independent controls, while the planar reduction reveals a loss of controllability despite the presence of nonlinearity. The results provide a first systematic investigation of remodelling controllability and further support the development of Continuum Control Theory as a framework for the analysis and design of controlled internal structural transformations in continuous media.
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BibTeX
@misc{stefano2026posteriori,
title = {{A posteriori controllability of non-linear remodelling in linear elastic continua}},
author = {Salvatore Di Stefano and Marta Zoppello},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37411},
eprint = {2609.37411},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37411},
}
RIS
TY - UNPB
TI - A posteriori controllability of non-linear remodelling in linear elastic continua
AU - Salvatore Di Stefano
AU - Marta Zoppello
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37411
UR - https://arxiv.org/abs/2609.37411
AB - We investigate the a posteriori controllability of remodelling within the framework of Geometric Control Theory applied to continuum systems. Remodelling is described through an isochoric Bilby--Kroner--Lee decomposition, where the internal structural transformation is represented by a remodelling tensor and its evolution is governed by a stress-driven constitutive law. Assuming infinitesimal deformation and remodelling stretches, while retaining finite rotations of the principal remodelling directions, we derive a nonlinear state-space representation in terms of principal remodelling stretches and orientation variables. This formulation allows the remodelling process to be interpreted as a finite-dimensional nonlinear control system parametrised by the material position. Equilibrium configurations are characterised, and under-actuated controllability problems are studied by means of the tools of Geometric Control Theory. The three-dimensional setting shows that the nonlinear coupling between remodelling stretches and orientations enables complete steering of the internal state through a reduced number of independent controls, while the planar reduction reveals a loss of controllability despite the presence of nonlinearity. The results provide a first systematic investigation of remodelling controllability and further support the development of Continuum Control Theory as a framework for the analysis and design of controlled internal structural transformations in continuous media.
ER -