First-and second-order shape sensitivity analyses in a fully nonlinear framework are presented in this paper. Using the fixed domain technique and the adjoint approach, integral expressions over the domain are obtained. The Guillaume-Masmoudi lemma allows these expressions to be rewritten as integrals over the domain boundary. The formalism is then applied to the steady creep of a bar in torsion, as an example of power-law nonlinearities that occur not only in creep problems but also in viscoplastic fluid flow. Finally, a problem with known analytical solution is presented in order to show the equivalence between exact differentiation and the shape sensitivity approach.
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