Macroscopic Response of¶Nematic Elastomers via Relaxation of¶a Class of SO(3)-Invariant Energies

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Quasiconvex functions incorporating volumetric constraints are rank-one convex (2008, background): “This leads to considerable simplifications in the proof of relaxation results with volumetric constraints, as for example those obtained for nematic and smectic elastomers and for models in plasticity [ 9 , 1, 12].”
On the Theory of Relaxation in Nonlinear Elasticity with Constraints on the Determinant (2014, background): “In the physically relevant situation n = 3 a similar expression is analytically known and turns out to be polyconvex for all p ≥ 1 [20].”