The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place next Monday (March 9, 2020) in the room K2 from 9:00 till 10:00. The talk will be given by Karel Tůma. Please see the details below.

Speaker: **Karel Tůma**

Title: **Thermomechanical viscoelastic rate-type models with temperature dependent material coefficients**

Abstract: Response of many real materials such as asphalt, melted glass or rubber changes significantly with temperature. A frequently used approach of dealing with a model with complicated rheology/response is to take the governing equations describing the mechanical part, make the material parameters temperature dependent and add a classical heat equation with Newtonian dissipation. However, such evolution equation for temperature is not consistent with the mechanical part. Since all above metioned material can be reasonably described by viscoelastic fluid/solid models, we derive thermodynamically compatible viscoelastic rate-type models with temperature dependent material coefficients and couple the system with a consistent evolution equation for temperature. The coupled thermomechanical models are tested in two simulations: oscilating deformation of a rectangular plate with a circular hole; and deformation of a cracked material. In both cases the growth of the temperature close to the hole in the material is observed.