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A thermoelastoplastic theory for special Cosserat rods. (English) Zbl 07225902
The authors develop a unified dynamic model for the coupled thermoelastoplastic motions of special Cosserat rods using a direct approach. The kinematics, dynamics and the first and second laws of thermodynamics are discussed. The one-dimensional form of the energy balance and the entropy balance are presented for the rods and their constitutive equations are given. The evolution equation of the temperature-like one-dimensional field variable is obtained. The yield function, flow rule and hardening law are introduced. The total strain measures of the rod are assumed to decompose additively into elastic and plastic parts. The stored thermoelastic energy of the rod is assumed to depend only on the elastic part of the total strain. Then, the most general quadratic form of the thermoelastic stored energy for hemitropic rods is obtained. The total material strains are postulated to be additively decomposed into elastic and plastic parts. The thermoelastoplastic constitutive relations are recorded by using a special form of the Helmholtz energy density. The yield function, the associative flow rule and the hardening law are obtained. The model is developed without any connection to the three dimensional basic equations of thermoelastoplasticity. The engineering applications remain to the determination of material constants. This paper may be of interest to mathematically minded engineers.
##### MSC:
 74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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##### References:
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