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1 Bulletin of the Polish Academy of Sciences. Technical Sciences

1 1999

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Monotonicity of Operators of Viscoplastic Response: Application to the Model of Bodner-Partom

Chełmiński K., Gwiazda P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

1999

Vol. 47, nr 3

191-208

A class of viscoplastic constitutive models relating strain rate to stress and state variables (of the type proposed by S.R.Bodner and Y.Partom) is considered and the monotonicity of the related operator is studied. It was shown earlier (1) that the considered operator is not of monotone type but the extended class of the monotone constitutive equations is introduced (clas LM) and evolution of total energy of the viscoplastic body from this class is studied. It is shown that assuming vanishing external forces, homogeneous boundary conditions and non vanishing initial state in the dissipative system the total energy cannot blow up in finite time. The noncoercive model of Bodner-Partom is approximated (using the idea from (7) by a sequence of coercive nonelastic constitutive equations.