Martin Kružík

Martin Kružík, Jan Valdman

We study computational behavior of a mesoscopic model describing temperature/external magnetic field-driven evolution of magnetization. Due to nonconvex anisotropy energy describing magnetic properties of a body, magnetization can develop fast spatial oscillations creating complicated microstructures. These microstructures are encoded in Young measures, their first moments then identify macroscopic magnetization. Our model assumes that changes of magnetization can contribute to dissipation and, consequently, to variations of the body temperature affecting the length of magnetization vectors. In the ferromagnetic state, minima of the anisotropic energy density depend on temperature and they tend to zero as we approach the so-called Curie temperature. This brings the specimen to a paramagnetic state. Such a thermo-magnetic model is fully discretized and tested on two-dimensional examples. Computational results qualitatively agree with experimental observations. The own MATLAB code used in our simulations is available for download.

Miroslav Frost, Martin Kružík, Jan Valdman

A sharp-interface model describing static equilibrium configurations of shape mory alloys by means of interfacial polyconvex energy density introduced by Šilhavý in 2010 and extended to a quasistatic situation by Knüpfer and Kružík in 2016 is computationally tested. Elastic properties of variants of martensite and the austenite are described by polyconvex energy density functions. Volume fractions of particular variants are modeled by a map of bounded variation. Additionally, energy stored in martensite-martensite and austenite-martensite interfaces is measured by an interface-polyconvex function. It is assumed that transformations between material variants are accompanied by energy dissipation which, in our case, is positively and one-homogeneous giving rise to a rate-independent model. Various two-dimensional computational examples are presented and the used computer code is made available for downloads.

Rufat Badal, Manuel Friedrich, Martin Horák et al.

We consider a quasi-static nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations. We refine the discretization schemes in [Badal-Friedrich-Kružík '23, Mielke-Roub\'ıček '20] by imposing frame indifference already at a time-discrete level. This is justified both analytically and numerically.