Elastic response and Ward identities in stressed nematic elastomers

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 1, 2010, Pages

  Lubensky, T C ^a   Ye, Fangfu ^b,c  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b United States of America   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPLIED STRAIN; CRITICAL VALUE; CROSS-LINKING PROCESS; ELASTIC RESPONSE; EXTERNAL STRESS; NEMATIC ELASTOMERS; SIMPLE MODEL; WARD IDENTITIES;

ELASTOMERS; PLASTICS; RUBBER; STRESS-STRAIN CURVES;

ELASTIC MODULI;

EID: 77954346681     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.011704     Document Type: Article

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28. - 1 Λ i k σ k l Λ l j T, where σ i j is the second PK stress tensor of Eq., is symmetric. The energy associated with the application of σ i j C is Δ F ext = ∫ d d R σ i j C u i j C, where u i j C = (1 / 2) (∂ u i / ∂ R j + ∂ u j / ∂ R i). The strain u i j C is symmetric in i j because σ i j C is. To linear order in u i, it is identical to the Eulerian strain variable, but it lacks the nonlinear term - (1 / 2) (∂ u k / ∂ R i) (∂ u k / ∂ R j) required for rotational invariance. It is the absence of this nonlinear term in Δ F ext that encodes its preferred direction in the target space and that ultimately distinguishes it from the energy of Eq., which is linear in the strain u z z that is rotationally invariant in target space. For more details, see Ref.. A minus sign appears in Eq. because it is in reality contribution to the Legendre transformed free energy, which after putting u z z equal to its equilibrium value, depends on h and not u z z.