Introduction to Elasticity/Hellinger-Reissner principle

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Hellinger-Prange-Reissner Variational Principle[edit | edit source]

In this case, we assume that the elasticity field is invertible and is smooth on . We also assume that is the set of all admissible states that satisfy the strain-displacement relations, the traction-stress relations and the balance of angular momentum.

Let denote the set of all admissible states and let be a functional on defined by

for every .

Then,

at an admissible state if and only if is a solution of the mixed problem.