Ogden-type energies for nematic elastomers

Attainment results for nematic elastomers

“…Note that in (1.2) the power γi 2 refers to the matrix L −1/2 n F F T L −1/2 n . This is an energy density studied in [2] and can be considered as an "Ogden-type" generalization of the classical "Neo-Hookean" expression originally proposed by Bladon, Terentjev and Warner [4] to model an incompressible nematic elastomer. This is obtained from (1.2) by setting N = 1 and γ 1 = 2.…”

Dimension reduction via $$\Gamma $$ Γ -convergence for soft active materials

“…In particular, we focus our attention on nematic elastomers [1,2,5,14,15,28]. These are polymeric materials that, thanks to the coupling between elasticity and orientational nematic order, undergo spontaneous deformations as a consequence of a temperature-driven phase transformation.…”

Linear elasticity obtained from finite elasticity by $Γ$-convergence under weak coerciveness conditions

“…As shown in the proof of Theorem 2.4, the boundedness of {F (u j )} for every j sufficiently large implies that, up to a subsequence, the sequence {1 B j ∇u j } converges to ∇u weakly in L 2 …”

“…For simplicity, we focus on the homogeneous case. A common practice to pass from an incompressible model, with associated energy densityW defined on {F ∈ R 3×3 : det F = 1}, to a corresponding compressible model W (see, e.g., [2,7,9]) is to define …”