ON FLUTTER INSTABILITY IN ELASTOPLASTIC CONSTITUTIVE MODELS

Two conditions of non-propagation of wave modes are analyzed: flutter instability as described by Rice (1976) and non propagation due to dif ferent algebraic and geometric multiplicity in the eigenvalues of the acoustic tenser. Explicit reference is made to elastoplastic constitut ive operators at finite strains. Both loading and unloading branches o f the constitutive operator are analyzed, but they are treated indepen dently (we disregard the interaction between loading and unloading). T he spectral analysis of Bigoni and Zaccaria (1994) is generalized to e xamine an unsymmetric acoustic tenser for the unloading branch of the constitutive operator. Two constitutive laws for finite-strain elastop lasticity are considered, one of which is widely in use (Rudnicki and Rice 1975). In both constitutive laws, unloading of the material follo ws a specific grade 1-hypoelasticity, lacking in any stress-rate poten tial. For these materials, we show that instabilities are excluded in the unloading branch, whereas they remain possible in the loading bran ch of the elastoplastic constitutive operator. Therefore, the geometri cal terms of the constitutive equations (when small compared to the el astic shear modulus) provide examples of perturbations which induce fl utter and non-propagation instability in elastoplasticity, yet have no effect on infinitesimal, three-dimensional, isotropic elasticity (whe re two wave speeds always coincide).