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Theory and thermohyperelasticity for near-incompressible elastomers. (English) Zbl 0864.73014
Contrary to common practice which discards thermal effects by considering purely isothermal evolutions, the authors formulate a truly thermo-hyperelasticity for near-incompressible elastomers. The thermal strain “gradient” is a nonintegrable part of a multiplicative decomposition of the true gradient of finite deformation. Furthermore, shear and volume deformation aspects are naturally decoupled, and the thermomechanical coupling takes place essentially via the thermal expansion. Criteria for thermodynamic stability are thus derived in a rather compact form. A particular expression for Helmholtz’s free energy is given which represents the thermo-mechanical counterpart of the conventional two-term incompressible Mooney-Rivlin model. These considerations are applied in a short study to the slow isothermal extension of a rubber rod and to the rapid adiabatic extension of this rod.
Reviewer: G.A.Maugin (Paris)

74B20 Nonlinear elasticity
74A15 Thermodynamics in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
Full Text: DOI
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