Coupling thermal transfer with viscoelastic deformation using generalized Kelvin chains

Abstract

Coupling thermal transfer with deformation caused by predominantly mechanical loads belongs to important tasks of engineering computational mechanics. Simplifying assumptions working with purely elastic deformation cannot describe real energy dissipation, thus some more general computational models are needed, as viscoelastic or elastoplastic ones, with potential incorporation of microscopic and/or macroscopic damage, with the possibility of both their formal mathematical verification and practical validation based on laboratory experiments and observations in situ. All resulting models are then compromises between i) the complexity of considered physical processes, ii) some reasonable setting of material parameters, based on sufficiently simple experiments, iii) some formulation of a transparent mathematical model, using available results from (nearly) linear functional analysis, iv) the design of robust and effective computational algorithms. In this short paper we shall pay attention namely to so-called generalized viscoelastic Kelvin chains, consisting of parallel or serial viscous and elastic terms, with a three-component standard linear solid as a quasi-static model problem. Such detailed analysis will be followed by brief comments to several non-linear generalizations of this approach, including still unclosed problems, as the challenge for future research.