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Polish Academy of Sciences

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J. Hron

Charles University in Prague (CZ)

Recent publications
1.  Tůma K., Rezaee Hajidehi M., Hron J., Farrell P.E., Stupkiewicz S., Phase-field modeling of multivariant martensitic transformation at finite-strain: computational aspects and large-scale finite-element simulations, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 0045-7825, DOI: 10.1016/j.cma.2021.113705, Vol.377, pp.113705-1-23, 2021

Abstract:
Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic anisotropy of the phases, and incorporates Hencky-type elasticity, a penalty-regularized double-obstacle potential, and viscous dissipation. The finite-element discretization of the model is performed in Firedrake and relies on the PETSc solver library. The large systems of linear equations arising are efficiently solved using GMRES and a geometric multigrid preconditioner with a carefully chosen relaxation. The modeling capabilities are illustrated through a 3D simulation of the microstructure evolution in a pseudoelastic CuAlNi single crystal during nano-indentation, with all six orthorhombic martensite variants taken into account. Robustness and a good parallel scaling performance have been demonstrated, with the problem size reaching 150 million degrees of freedom.

Keywords:
phase-field method, finite-element method, large-scale simulations, shape memory alloys, nano-indentation

Affiliations:
Tůma K. - IPPT PAN
Rezaee Hajidehi M. - IPPT PAN
Hron J. - Charles University in Prague (CZ)
Farrell P.E. - other affiliation
Stupkiewicz S. - IPPT PAN
2.  Hron J., Miloš V., Průša V., Souček O., Tůma K., On thermodynamics of incompressible viscoelastic rate type fluids with temperature dependent material coefficients, INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, ISSN: 0020-7462, DOI: 10.1016/j.ijnonlinmec.2017.06.011, Vol.95, pp.193-208, 2017

Abstract:
We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type models for incompressible viscoelastic fluids. In particular, we study the models that allow one to consider temperature dependent material coefficients. This naturally calls for the formulation of a temperature evolution equation that would accompany the evolution equations for the mechanical quantities. The evolution equation for the temperature is explicitly formulated, and it is shown to be consistent with the laws of thermodynamics and the evolution equations for the mechanical quantities. The temperature evolution equation contains terms that are ignored or even not thought of in most of the practically oriented (computational) works dealing with this class of fluids. The impact of the additional terms in the temperature evolution equation on the flow dynamics is documented by the solution of simple initial/boundary value problems.

Keywords:
Maxwell fluid, Oldroyd-B fluid, Temperature dependent material coefficients, Thermodynamics, Cylindrical Couette flow, Biaxial extension, Numerical simulations

Affiliations:
Hron J. - Charles University in Prague (CZ)
Miloš V. - Charles University (CZ)
Průša V. - Charles University in Prague (CZ)
Souček O. - Charles University (CZ)
Tůma K. - IPPT PAN
3.  Hron J., Rajagopal K.R., Tůma K., Flow of a Burgers fluid due to time varying loads on deforming boundaries, Journal of Non-Newtonian Fluid Mechanics, ISSN: 0377-0257, DOI: 10.1016/j.jnnfm.2014.05.005, Vol.210, pp.66-77, 2014

Abstract:
In this paper we study three boundary-initial value problems within the context of four rate type viscoelastic constitutive models, the Maxwell model, the Oldroyd-B model, Burgers model and the generalized Burgers model. We consider challenging problems wherein the boundary is deforming with time. The flows lead to a complex system of partial differential equations that require the development of a robust numerical procedure based on the arbitrary Lagrangian–Eulerian method.

Keywords:
Rate type fluid, Maxwell, Oldroyd-B, Burgers, Finite element method, Monolithic ALE method

Affiliations:
Hron J. - Charles University in Prague (CZ)
Rajagopal K.R. - Texas A&M University (US)
Tůma K. - other affiliation
4.  Hron J., Kratochvil J., Malek J., Rajagopal K.R., Tůma K., A thermodynamically compatible rate type fluid to describe the response of asphalt, Mathematics and Computers in Simulation, ISSN: 0378-4754, DOI: 10.1016/j.matcom.2011.03.010, Vol.82, No.10, pp.1853-1873, 2012

Abstract:
In this paper, we consider two models that have been recently developed from a thermodynamic standpoint and that are capable of describing the response of nonlinear viscoelastic fluids. We test the efficacy of both models by comparing their predictions against torsion experiments conducted for asphalt, a material that is notoriously difficult to model. Both the models seem to describe the response adequately, though neither is really very accurate. This should not be surprising as asphalt is a heterogenous material comprising of many components which is being homogenized and modeled as a single constituent viscoelastic fluid.

Keywords:
Rate type fluid, Large deformation, Numerical simulation

Affiliations:
Hron J. - Charles University in Prague (CZ)
Kratochvil J. - other affiliation
Malek J. - Charles University (CZ)
Rajagopal K.R. - Texas A&M University (US)
Tůma K. - other affiliation

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