A posteriori controllability of non-linear remodelling in linear elastic continua

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.