Year: 2025
Type: article
Abstract: We consider an elasto-plastic beam and address the following inverse problem: external forces have created some plastic strains in this beam, which therefore shows a residual observable deformation once the structure is load-free. Can we retrieve the loading history from this observation, or at least the plastic strains ? After proving the well-posedness of the forward problem, we show that the solution can be described in a semi-explicit way in the pure bending case, so that the forward problem amounts to a one dimensional non linear problem. Such problem is smooth enough for us to solve the inverse problem by using a classical least-square method, which is illustrated with the help of some numerical examples.
Source: Inverse Problems
Authors: Laurent Bourgeois, Jean-François Mercier
Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, École Nationale Supérieure de Techniques Avancées, Institut Polytechnique de Paris, POEMS: Propagation des Ondes : Etude Mathématique et Simulationan, École Nationale Supérieure de Techniques Avancées Paris
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414808101