Milan Toma

Publications (8) View all

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  Article: Strongly Coupled Fluid-Structure Interaction Cardiovascular Analysis with the Effect of Peripheral Network

  Milan Toma, Absei Krdey, Shu Takagi, Marie Oshima
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  ABSTRACT: Atherosclerosis often occurs in the carotid artery. The rupture of an atherosclerosis plaque can result in a stroke in the cerebral or coronary arteries. A cerebral aneurysm, defined as a focal dilatation of the arterial wall, occurs usually at the branching points of arteries supplying blood to the brain. Genetics and risk factors are partially responsible, but also hemodynamic factors, e.g. pressure, flowrate, shear stress, have been proved to play a significant role in forming these vascular diseases, namely the atherosclerosis 1, 2) and aneurysms 3, 4) , which are responsible for significant morbidity and mortality. FSI simulations, in addition to the hemodynamic factors, provide also data on the vessel wall dynamics in the patient-specific models, such as the deformations, principal strains and stresses. The traditional FSI techniques are based on the arbitrary Lagrangian-Eulerian (ALE) method. In this study, the strongly coupled ALE method is used to address the added-mass effect, which is typical for loosely coupled time-stepping algorithms 5, 6) . An example of strongly coupled ALE method used for the coupling of an elastic structure with an incompressible fluid can be found in 7) . There are many models to describe the outflow boundary conditions, such as Windkessel models or lumped parameter models. However, the problem with these models is that a previous knowledge of certain parameters, such as the resistance and compliance, is required to conduct the simulations, therefore, a multi scale model is used, developed based on 8) , which does not bear this limitation.
  SEISAN-KENKYU. 01/2011; 63(3):339-344.
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  Article: Hybrid-Trefftz stress elements for incompressible biphasic media

  J. A. Teixeira de Freitas, M. Toma
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  ABSTRACT: A wavelet-based, high-order time integration method is applied to replace the parabolic problem governing the response of incompressible biphasic media by a set of uncoupled Helmholtz problems. Their formal solutions are used to formulate the stress model of the hybrid-Trefftz finite element formulation. The stress, pressure and displacement fields are directly approximated and designed to satisfy locally the equilibrium condition in each phase of the mixture. This basis is used to enforce on average the compatibility conditions and the constitutive relations of the mixture. The displacements in the solid and the normal displacement in the fluid are approximated independently on the boundary of the element and the basis is used to enforce in weak form the boundary equilibrium conditions. The resulting solving system is sparse, well suited to adaptive refinement and parallel processing. The energy statements associated with the formulation are recovered and sufficient conditions for the uniqueness of the finite element solutions are stated. Testing problems reported in the literature are used to illustrate the quality of the pressure, stress, displacement and velocity estimates obtained with the hybrid-Trefftz stress element.
  International Journal for Numerical Methods in Engineering 01/2009; 79:205. · 2.01 Impact Factor
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  Thesis: MODELLING OF HYDRATED SOFT TISSUES USING HYBRID-TREFFTZ FINITE ELEMENTS

  Milan Toma
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  ABSTRACT: The hybrid-Trefftz formulation of the finite element method is applied to the transient, physically and geometrically linear analysis of incompressible saturated porous media. Two finite element models are developed, namely the stress model and the displacement model. The stress (displacement) model develops from the direct approximation of the stress and pressure fields (displacements in each phase of the mixture) in the domain of the element and of the solid and fluid displacements (forces and pressure) on its boundary. The domain approximation bases are extracted from the formal solution of the system of differential equations that govern the behaviour of incompressible saturated porous media. The finite element equations are derived directly from the local conditions on equilibrium, compatibility, elasticity and incompressibility. The structure of the resulting algebraic solving systems is symmetric, except for the velocity induced terms, sparse, naturally p-adaptive and well-suited to parallel processing. The associated variational statements are recovered and sufficient conditions for the existence and uniqueness of the finite element solutions are stated. A comprehensive set of validation tests is presented. The benchmark tests used in the literature are solved in the frequency domain to assess the convergence characteristics of the alternative stress and displacement elements. They are implemented also in the time domain to assess the quality of the estimates they produce for the stress, pressure, displacement and velocity fields at every instant of the analysis.
  01/2007, Degree: Ph.D., Supervisor: João António Teixeira de Freitas
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  Article: Use of Trefftz functions in non-linear BEM/FEM

  Milan Toma, Vladimir Kompis, Milan Zmindak, Marian Handrik
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  ABSTRACT: Simulation of many practical problems requires to use non-linear formulations with large displacements, large strains and large rotations. It is well known that the use of Trefftz (T -) functions (i. e. the functions satisfying the governing equations inside the domain) as weighting, or interpolation functions leads to more efficient formulations than those obtained by classical methods. In this paper we will show the use of T -functions and especially T -polyno-mials, Kelvin, or Kupradze and Boussinesq functions (Green functions with singularity points defined outside of the domain) and their combination in connection with the total Lagrangian formulation for multi-domain BEM (reci-procity based FEM) analysis of displacements and for the post-processing phase in the analysis (evaluation of both gradient of displacements and stress fields). The formulation results in non-singular boundary integrals which has numerical advantages over other formulations using singular boundary integral equations.
  Computers & Structures 01/2004; 82:2351-2360. · 1.87 Impact Factor
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  Conference Proceeding: Numerical simulation of lifted tribrachial n-heptane laminar flames in heated coflow

  M Toma, F Bisetti, S M Sarathy, S K Choi, S Al-Noman, S H Chung
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  ABSTRACT: This study presents a numerical analysis of lifted atmospheric tribrachial flames in heated coflow in a two-dimensional axisymmetric domain. A reduced mechanism for n-heptane/air combustion comprising 97 species is used together with a mixture-averaged transport model. The chemical mechanism is complemented with the chemiluminescent OH (OH*) and CH (CH*) reaction pathways. The mechanism is validated. A parametric study of lift-off height of the tribrachial flame is performed for a range of temperatures, jet velocities and fuel compositions. The lift-off height dependence on inlet temperature is compared with preliminary experimental data showing excellent agreement. A preliminary comparison of the line-of-sight integrated CH* fields from the simulations with narrow-band filtered photographs is presented.
  European Combustion Meeting 2013, Sweden; 06/2013