• DOI:10.1137/080729992
• Corpus ID: 17651064

Thermodynamics of Rate-independent Processes in Viscous Solids at Small Strains

@article{Roubek2010ThermodynamicsOR,
  title={Thermodynamics of Rate-independent Processes in Viscous Solids at Small Strains},
  author={Tom{\'a}{\vs} Roub{\'i}{\vc}ek},
  journal={SIAM J. Math. Anal.},
  year={2010},
  volume={42},
  pages={256-297}
}

• T. Roubíček
• Published 5 March 2010
• Engineering
• SIAM J. Math. Anal.

So-called generalized standard solids (of the Halphen–Nguyen type) involving also activated rate-independent processes such as plasticity, damage, or phase transformations are described as a system of a momentum equilibrium equation and a variational inequality for inelastic evolution of internal-parameter variables. The stored energy is considered as temperature dependent and then the thermodynamically consistent system is completed with the heat-transfer equation. Existence of a suitably defined “energetic” solution is proved by a nontrivial combination of theory of rate-independent processes by Mielke et al. [Handbook of Differential Equations, Elsevier, Amsterdam, 2005, pp. 461–559; Models of Continuum Mechanics in Analysis and Engineering, H.-D. Alber, R. Balean, and R. Farwig, eds., Shaker Ver., Aachen, 1999, pp. 117–129; Nonlinear Differ. Equ. Appl., 11 (2004), pp. 151–189; Arch. Ration. Mech. Anal., 162 (2002), pp. 137–177] adapted for coupling with viscous/inertial effects and of sophisticated es...