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Author: Pelech, Petr ×

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    Gradient polyconvexity and modeling of shape memory alloys
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Horák, Martin; Kružík, Martin; Pelech, Petr; Schlömerkemper, Anja
    We show existence of an energetic solution to a model of shape memory alloys in which the elastic energy is described by means of a gradient-polyconvex functional. This allows us to show existence of a solution based on weak continuity of nonlinear minors of deformation gradients in Sobolev spaces. Admissible deformations do not necessarily have integrable second derivatives. Under suitable assumptions, our model allows for solutions which are orientation-preserving and globally injective everywhere in the domain representing the specimen. Theoretical results are supported by three-dimensional computational examples. This work is an extended version of [36].
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    On compatibility of the natural configuration framework with general equation for non-equilibrium reversible-irreversible coupling (GENERIC): Derivation of anisotropic rate-type models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Pelech, Petr; Tůma, Karel; Pavelka, Michal; Šípka, Martin; Sýkora, Martin
    Within the framework of natural configurations developed by Rajagopal and Srinivasa, evolution within continuum thermodynamics is formulated as evolution of a natural configuration linked with the current configuration. On the other hand, withing the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, the evolution is split into Hamiltonian mechanics and (generalized) gradient dynamics. These seemingly radically different approaches have actually a lot in common and we show their compatibility on a wide range of models. Both frameworks are illustrated on isotropic and anisotropic rate-type fluid models. We propose an interpretation of the natural configurations within GENERIC and vice versa (when possible).