Journal
MATHEMATICS AND MECHANICS OF SOLIDS
Volume 25, Issue 3, Pages 838-865Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1081286519891769
Keywords
Nonlinear elasticity; residual stress; electro-elastic; preferred direction; constitutive equation
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In this communication, a spectral model is developed for a residually stressed electro-elastic body with a preferred direction. The model uses a total energy function that depends on the right stretch tensor, the residual stress tensor, a preferred direction structural tensor and one of the electric variables. The proposed spectral invariants have a clear physical meaning; using these invariants, we prove that only 13 of the 37 classical invariants in the corresponding minimal integrity basis are independent. A method for exclusion or partial exclusion of compressed fibres is proposed. Some boundary value problems with cylindrical symmetry are studied. Results for the inflation of a hollow sphere, where the residual stress is assumed to depend only on the radial position, are also given. The spectral constitutive formulation is useful in a rigorous construction of a specific form of the total energy function via appropriate experiments.
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