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Flutter Instability and Ill-Posedness in Solids and Fluid-Saturated Porous Media

  • Conference paper
Material Instabilities in Elastic and Plastic Solids

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 414))

Abstract

For elastoplasticity with locally smooth yield surface and plastic potential, the nature, real or complex, of the squares of the acceleration wave-speeds is analyzed. Emphasis is laid on the effect that some features of the constitutive equations have on that nature. Specifically, our reference problem contemplates an infinite elastic-plastic body endowed with elastic isotropy and deviatoric associativity. In a second step, individual or simultaneous deviations with respect to these reference properties are analyzed. The performed linearized analyses are essentially intended to detect, in the course of a loading process, the onset of wave-speeds whose squares are complex, a phenomenon called flutter. Finite element simulations show how perturbations evolve in such a situation, and, as expected, the plastic loading condition plays a crucial role.

The problem is reconsidered in the context of fluid-saturated porous media whose solid skeleton is elastic-plastic. Unlike for single phase solids, flutter is not excluded in the reference situation where elasticity is isotropic and deviatoric plasticity holds. The propagation of waves of different lengths leads to make a distinction between the two phenomena of flutter instability and flutter ill-posedness. The introdution of a characteristic length in the elastic-plastic behaviour of the solid skeleton may imply the existence of an infimum wavelength below which instability modes do not exist, and well-posedness of the dynamic problem is recovered.

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Authors and Affiliations

  1. Laboratoire Sols, Solides, Structures, Grenoble, France

    B. Loret

  2. Instituto Superior Técnico, Lisbon, Portogallo

    F. M. F. Simões & J. A. C. Martins

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  1. B. Loret
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  2. F. M. F. Simões
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  3. J. A. C. Martins
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  1. Polish Academy of Sciences, Poland

    Henryk Petryk

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Loret, B., Simões, F.M.F., Martins, J.A.C. (2000). Flutter Instability and Ill-Posedness in Solids and Fluid-Saturated Porous Media. In: Petryk, H. (eds) Material Instabilities in Elastic and Plastic Solids. CISM International Centre for Mechanical Sciences, vol 414. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2562-5_3

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