A NEW CRITERION OF STABILITY FOR THE VISCOUS SOLIDS: DISPLACEMENT FIELD APPROACH
Résumé
This study deals with the stability problems encountered in the strain-rate-dependent solids and structures. The absence of equilibrium state in these viscous solids leads us to study the stability of their quasi-static evolutions. This concept of stability in the sense of trajectories thus generalises the stability of an equilibrium state but leads to more complex problems because of the non-autonomous character. Once the problem of evolution is set in the form of a non-autonomous differential equation, the method of linearisation will be used to obtain results concerning the stability. The criterion of stability thus obtained is equivalent to study the sign of the eigenvalues of a certain time-dependent operator. Note that the approach presented here consists to eliminate the internal variables to write the problem of evolution as a differential equation in the displacement field. This approach in displacement will be compared with that in internal variables recently proposed by the same author.
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