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Based on a continuum thermodynamics approach, new formulae extending to viscoelasticity in the time domain the classical Clapeyron formula of linear elasticity are introduced and their properties described. Symmetry and coercivity properties of associated multilinear forms are obtained. Auxiliary problems involving data continuations are defined. From this, general comparison theorems between appropriate history functionals of solution fields are directly derived in the time domain. They apply to any linearly viscoelastic body, possibly heterogeneous and anisotropic. The involved functionals are built on the time-dependent relaxation function tensor or its rate. Application to the derivation of order relationships in the time domain for the overall properties of viscoelastic heterogeneous or composite media is presented as illustrative example. The obtained results partly extend to the viscoelastic case the boundary-condition hierarchy previously obtained in the elastic case. |
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