Karel Tůma

Bio: Karel Tůma is an academic researcher from Charles University in Prague. The author has contributed to research in topics: Boundary value problem & Compressibility. The author has an hindex of 12, co-authored 27 publications receiving 310 citations. Previous affiliations of Karel Tůma include Polish Academy of Sciences & Texas A&M University.

On a variant of the Maxwell and Oldroyd-B models within the context of a thermodynamic basis

Abstract: In this paper we develop models within a thermodynamic standpoint that are very similar in form to the classical Maxwell and Oldroyd-B models but differ from them in one important aspect, the manner in which they unload instantaneously from the deformed configuration. As long as the response is not instantaneous, the models that are derived cannot be differentiated from the Maxwell and Oldroyd-B models, respectively. The models can be viewed within the context of materials whose natural configuration evolves, the evolution being determined by the maximization of the rate of entropy production of the material. However, the underpinnings to develop the model are quite different from an earlier development by Rajagopal and Srinivasa [8] in that while the total response of the viscoelastic fluid satisfies the constraint of an incompressible material, the energy storage mechanism associated with the elastic response is allowed to be that for a compressible elastic solid and the dissipative mechanism associated with the viscous response allowed to be that for a compressible fluid, the total deformation however being isochoric. The analysis calls for a careful evaluation of firmly held customs in viscoelasticity wherein it is assumed that it is possible to subject a material to a purely instantaneous elastic response without any dissipation whatsoever. Finally, while the model developed by Rajagopal and Srinivasa [8] arises from the linearization of the non-linear elastic response that they chose and leads to a model wherein the instantaneous elastic response is isochoric, here we develop the model within the context of a different non-linear elastic response that need not be linearized but the instantaneous elastic response not necessarily being isochoric.

Size effects in martensitic microstructures: Finite-strain phase field model versus sharp-interface approach

Abstract: A finite-strain phase field model for martensitic phase transformation and twinning in shape memory alloys is developed and confronted with the corresponding sharp-interface approach extended to interfacial energy effects. The model is set in the energy framework so that the kinetic equations and conditions of mechanical equilibrium are fully defined by specifying the free energy and dissipation potentials. The free energy density involves the bulk and interfacial energy contributions, the latter describing the energy of diffuse interfaces in a manner typical for phase-field approaches. To ensure volume preservation during martensite reorientation at finite deformation within a diffuse interface, it is proposed to apply linear mixing of the logarithmic transformation strains. The physically different nature of phase interfaces and twin boundaries in the martensitic phase is reflected by introducing two order-parameters in a hierarchical manner, one as the reference volume fraction of austenite, and thus of the whole martensite, and the second as the volume fraction of one variant of martensite in the martensitic phase only. The microstructure evolution problem is given a variational formulation in terms of incremental fields of displacement and order parameters, with unilateral constraints on volume fractions explicitly enforced by applying the augmented Lagrangian method. As an application, size-dependent microstructures with diffuse interfaces are calculated for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and compared with the sharp-interface microstructures with interfacial energy effects.

On thermodynamics of incompressible viscoelastic rate type fluids with temperature dependent material coefficients

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.

Solving Ordinary Differential Equations

Abstract: Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

The Non Linear Field Theories Of Mechanics

Abstract: Thank you for reading the non linear field theories of mechanics. Maybe you have knowledge that, people have search hundreds times for their favorite books like this the non linear field theories of mechanics, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they juggled with some malicious virus inside their computer. the non linear field theories of mechanics is available in our book collection an online access to it is set as public so you can get it instantly. Our digital library spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the the non linear field theories of mechanics is universally compatible with any devices to read.

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

Abstract: Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).