Thermodynamic restrictions on constitutive equations for second-deformation-gradient inelastic behavior. (English) Zbl 0876.73023
We examine the possibility of a model of non-local inelasticity on thermodynamic grounds in the absence of higher-order stresses or additional kinematic entities. By considering a material that cannot support higher-order stresses, it is found that thermodynamics does not allow an explicit nonlocal dependence in the free-energy, and hence the stress and entropy response, but allows it in the strength and internal variable rate response. Rate-independent plasticity presents its own peculiarities in the proof of this result, which are also inherent in deriving the constitutive restrictions for the local material. An account of the basic thermodynamic framework and the reasoning used in these proofs are provided in listing the result for the conventional rate-independent solid. This procedure represents the building blocks for the derivation of the constitutive restrictions of the non-local theory, in which second-deformation-gradient-dependent constitutive postulates for inelastic materials are introduced. The general considerations are utilized to illustrate the constitutive structure of a rate-independent metal single crystal deforming by multiple slip.
MSC:
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
| 74A15 | Thermodynamics in solid mechanics |
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