Résumé
We consider hyperelastic problems and their numerical solution using a conforming nite element discretization and iterative linearization algorithms. For these problems, we present equilibrated, weakly symmetric, Hpdivq-conforming stress tensor reconstructions, obtained from local problems on patches around vertices using the ArnoldFalkWinther nite element spaces. We distinguish two stress reconstructions, one for the discrete stress and one representing the linearization error. The reconstructions are independent of the mechanical behavior law. Based on these stress tensor reconstructions, we derive an a posteriori error estimate distinguishing the discretization, linearization, and quadrature error estimates, and propose an adaptive algorithm balancing these dierent error sources. We prove the eciency of the estimate, and conrm it on a numerical test with analytical solution for the linear elasticity problem. We then apply the adaptive algorithm to a more application-oriented test, considering the HenckyMises and an isotropic damage models.