Speaker
Description
Nematic elastomers are cross-linked polymer networks where rod-like mesogens, described by a director field, determine the material’s internal structure. Standard theories in soft elasticity assume macroscopic isochoricity (incompressibility) and the mesogens’ inextensibility. These conditions can be enforced as internal constraints, thereby aligning with thermodynamically compatible frameworks [1, 2]. Yet, inspired by recent investigations [3], we addressed in [4] the possibility of “extending” the inextensibility condition to hold explicitly also on the boundary of the elastomer via an appropriate boundary Lagrange multiplier. In this presentation, we report the main outcomes of our study, which involve potential computational advantages, alternative interpretations of known stability results, and the use of gauge relations in nematic elastomers.
References
[1] Anderson, D.R., Carlson, D.E., Fried, E., “A continuum-mechanical theory for nematic elastomers”, J. Elast. 56, 33–58 (1999).
[2] Chen, Y., Fried, E., “Uniaxial nematic elastomers: constitutive framework and a simple application”, Proc. R. Soc. Lond. A 462, 1295–1314 (2006).
[3] Steigmann, D.J.: Lagrange multipliers at the boundary in the inextensional bending theory of thin elastic shells. Math. Mech. Solids 30(2), 211–217 (2023).
[4] Pastore, A., Grillo, A., Fried, E., “Internal constraints and gauge relations in the theory of uniaxial nematic elastomers”, Journal of Elasticity, 158, 10 (2026).