There is an open question, namely Chien’s question, in construction of a generalized functional in elasticity, i.e., why the stress-strain relation can still be derived from the Hu-Washizu generalized variational principle while the Lagrangian multiplier method is applied in vain? This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics. This investigation finds that as long as the functional has one of the combinations (A(εij)-σijεij) or (B(σij)-σijεij), its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method. This research proves that the Hu-Washizu functional ΠHW(uij, εij; σij) is real three-field functional, and resolves the historic academic controversy on the issue of constructing a three-field functional.
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