A new variational principle in linear elasticity (Q1339419)

It is known that the rotation field can be determined uniquely except for a rigid-body rotation by the Kirchhoff stress tensor or the Jaumann stress tensor, if the corresponding stress compatibility condition is considered. Hence a type of variational principles in nonlinear theory of elasticity which involve only the stress field as the unique independent argument can be obtained. The counterpart of these principles in linear theory of elasticity is a new variational principle which differs from the classical complementary energy principle. Since the relation between stress and strain in linear theory is simple, in this paper we can write the explicit form of this principle and give a straightforward proof and some remarks.