caa a22 4500 605515964 CHVBK 20210128100712.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s00205-015-0871-0 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0871-0 Effective Behavior of Nematic Elastomer Membranes [Elektronische Daten] [Pierluigi Cesana, Paul Plucinsky, Kaushik Bhattacharya] We derive the effective energy density of thin membranes of liquid crystal elastomers as the $${\Gamma}$$ Γ -limit of a widely used bulk model. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic membranes and due to oscillations in the nematic director that one expects in liquid crystal elastomers. We provide an explicit characterization of the effective energy density of membranes and the effective state of stress as a function of the planar deformation gradient. We also provide a characterization of the fine-scale features. We show the existence of four regimes: one where wrinkling and microstructure reduces the effective membrane energy and stress to zero, a second where wrinkling leads to uniaxial tension, a third where nematic oscillations lead to equi-biaxial tension and a fourth with no fine scale features and biaxial tension. Importantly, we find a region where one has shear strain but no shear stress and all the fine-scale features are in-plane with no wrinkling. Springer-Verlag Berlin Heidelberg, 2015 Cesana Pierluigi Mathematical Institute, Woodstock Road, OX26GG, Oxford, England aut Plucinsky Paul California Institute of Technology, 91125, Pasadena, CA, USA aut Bhattacharya Kaushik California Institute of Technology, 91125, Pasadena, CA, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 863-905 0003-9527 218:2<863 2015 218 205 https://doi.org/10.1007/s00205-015-0871-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0871-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cesana Pierluigi Mathematical Institute, Woodstock Road, OX26GG, Oxford, England aut NATIONALLICENCE 700 1- Plucinsky Paul California Institute of Technology, 91125, Pasadena, CA, USA aut NATIONALLICENCE 700 1- Bhattacharya Kaushik California Institute of Technology, 91125, Pasadena, CA, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 863-905 0003-9527 218:2<863 2015 218 205