The quasiconvex envelope of conformally invariant planar energy functions in isotropic hyperelasticity

par Prof. Patrizio Neff (Université de Duisburg-Essen)

jeudi 14 mars 2019, 14:30 → 15:30 Europe/Paris

RAPP (Bât. L de Vinci - INSA-Lyon)

We consider conformally invariant energies W on the group GL+(2) of 2 × 2-matrices with positive
determinant, i.e. W : GL+(2) → R such that W(AFB) = W(F) for all A,B ∈ {aR ∈ GL+(2)|a ∈ (0,∞), R ∈ SO(2)},
where SO(2) denotes the special orthogonal group, and provide an explicit formula for the (notoriously
difficult to compute) quasiconvex envelope of these functions. Our results, which are based on the
representation W(F) = h(λ1 ) of W in terms of the singular values λ1, λ2 of F, are applied to a number of λ2.