Discrete Lattice Element Approach for Rock Failure Modeling

Nikolić, Mijo; Ibrahimbegović, Adnan; Miščević, Predrag

doi:10.13167/2017.14.1

Cited by 1 publication

(1 citation statement)

References 12 publications

(17 reference statements)

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“…Here, we give the basic relations used in the formulation of the Composite Smeared Finite Element (CSFE) according to [16]. Formulation of the composite finite element has been present in the FE literature, as, for example in [17,18] where beam and continuum 3D are coupled. First, the diffusive transport in tissue can be described by a differential equation, based on Fick’s law and mass balance equation, [19]: −∂c∂t+∂∂xi(Dij∂c∂xj)+q=0,0.5emsum0.2emon0.2emi,j;0.5emi=1,2,3where D ij are diffusion tensor coefficients for the coordinate directions, c is concentration and q is a source term.…”

Section: Introductionmentioning

confidence: 99%

Correction function for accuracy improvement of the Composite Smeared Finite Element for diffusive transport in biological tissue systems

Milošević

Simić²,

Milićević³

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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Modeling of drug transport within capillaries and tissue remains a challenge, especially in tumors and cancers where the capillary network exhibits extremely irregular geometry. Recently introduced Composite Smeared Finite Element (CSFE) provides a new methodology of modeling complex convective and diffusive transport in the capillary-tissue system. The basic idea in the formulation of CSFE is in dividing the FE into capillary and tissue domain, coupled by 1D connectivity elements at each node. Mass transport in capillaries is smeared into continuous fields of pressure and concentration by introducing the corresponding Darcy and diffusion tensors. Despite theoretically correct foundation, there are still differences in the overall mass transport to (and from) tissue when comparing smeared model and a true 3D model. The differences arise from the fact that the smeared model cannot take into account the detailed non-uniform pressure and concentration distribution in the vicinity of capillaries. We introduced a field of correction function for diffusivity through the capillary walls of smeared models, in order to have the same mass accumulation in tissue as in case of true 3D models. The parameters of the numerically determined correction function are: ratio of thickness and diameter of capillary wall, ratio of diffusion coefficient in capillary wall and surrounding tissue; and volume fraction of capillaries within tissue domain. Partitioning at the capillary wall – blood interface can also be included. It was shown that the correction function is applicable to complex configurations of capillary networks, providing improved accuracy of our robust smeared models in computer simulations of real transport problems, such as in tumors or human organs.

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