The theory of plane stress for infinitesimal deformations of elastic membranes commonly yields solutions that are unstable with respect to out-of-plane perturbations. This can be remedied by replacing the elastic strain energy by a certain relaxed energy density. This procedure yields tension field theory when it is appropriate. Minimum energy and minimum complementary energy theorems, based on the relaxed energy density, are proved.
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A. C. Pipkin (1993) studied this question.
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