On the wellposedness of constitutive laws involving dissipation potentials

Desch, Wolfgang; Grimmer, Ronald

doi:10.1090/S0002-9947-01-02847-1

On the wellposedness of constitutive laws involving dissipation potentials
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by Wolfgang Desch and Ronald Grimmer PDF

Trans. Amer. Math. Soc. 353 (2001), 5095-5120 Request permission

Abstract:

We consider a material with memory whose constitutive law is formulated in terms of internal state variables using convex potentials for the free energy and the dissipation. Given the stress at a material point depending on time, existence of a strain and a set of inner variables satisfying the constitutive law is proved. We require strong coercivity assumptions on the potentials, but none of the potentials need be quadratic.

As a technical tool we generalize the notion of an Orlicz space to a cone “normed” by a convex functional which is not necessarily balanced. Duality and reflexivity in such cones are investigated.

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