We determine the relaxation of some transversally-isotropic energy densities, i.e. functions W : R^{3×3} → [0,∞] with the property W(QFR) = W(F) for all Q ∈ SO(3) and all R ∈ SO(3) such that Rn0 = n0, where n0 is a fixed unit vector. One physically relevant example is a model for smectic A elastomers. We discuss the implications of our result for the computation of macroscopic stress–strain curves for this material and compare with experiment.
Relaxation of some transversally isotropic energies and applications to smectic A elastomers / Adams, J; Conti, S; De Simone, Antonio; Dolzmann, G.. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 18:1(2008), pp. 1-20. [10.1142/S0218202508002693]
Relaxation of some transversally isotropic energies and applications to smectic A elastomers
De Simone, Antonio;
2008-01-01
Abstract
We determine the relaxation of some transversally-isotropic energy densities, i.e. functions W : R^{3×3} → [0,∞] with the property W(QFR) = W(F) for all Q ∈ SO(3) and all R ∈ SO(3) such that Rn0 = n0, where n0 is a fixed unit vector. One physically relevant example is a model for smectic A elastomers. We discuss the implications of our result for the computation of macroscopic stress–strain curves for this material and compare with experiment.| File | Dimensione | Formato | |
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