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On flutter instability in elastoplastic constitutive models. (English) Zbl 0921.73137

Two conditions of non-propagation of wave modes are analyzed: futter instability and non-propagation due to different algebraic and geometric multiplicity in the eigenvalues of the acoustic tensor. Explicit reference is made to elastoplastic constitutive operators at finite strains. Both loading and unloading branches of the constitutive operator are analyzed, but they are treated independently (we disregard the interaction between loading and unloading). The spectral analysis is used to examine an unsymmetric acoustic tensor for the unloading branch of the constitutive operator. Two constitutive laws for finite-strain elastoplasticity are considered, in which the unloading of the material follows a specific grade 1-hypoelasticity, lacking in any stress-rate potential. For these materials, we show that instabilities are excluded in the unloading branch, whereas they remain possible in the loading branch of the elastoplastic constitutive operator. Therefore, the geometrical terms of the constitutive equations (when small compared to the elastic shear modulus) provide examples of perturbations which induce flutter and non-propagation instability in elastoplasticity, yet have no effect on infinitesimal, three-dimensional, isotropic elasticity (where two wave speeds always coincide).

MSC:

74H99 Dynamical problems in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
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