Smoothed-Particle Hydrodynamics simulations of viscoelastic integral fractional models

  • Santelli, Luca (BCAM)
  • Vázquez-Quesada, Adolfo (UNED)
  • Ellero, Marco (BCAM)

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In order to capture specific characteristics of non-Newtonian fluids, during the past years fractional constitutive models have become increasingly popular. Indeed, these models are able to capture in a simple and compact way the complex behaviour of viscoelastic materials, such as the change in power- law relaxation pattern during the relaxation process of some materials [1]. Classical integral viscoelastic models have been already proposed more than thirty years ago [2], however they required to perform complex tasks, such as reconstructing the flow history using Eulerian grid-based, e.g. finite element method, frameworks. Using the Lagrangian Smoothed-Particle Hydrodynamics (SPH) method [3] greatly ease the process, as the flow history is already available and the only passage needed is the computation of a convolution with a specific kernel. Hence, we develop here a SPH integral viscoelastic method which is first validated for simple Maxwell or Oldroid-B models under Small Amplitude Oscillatory Shear flows (SAOS). The method is then expanded to include fractional constitutive models [4], validating the approach by comparing results with theory and experimental results under SAOS. REFERENCES [1] Pan Yangb, Yee Cheong Lama, Ke-Qin Zhub, “Constitutive equation with fractional derivatives for the generalized UCM model”, J. Non-Newtonian Fluid Mech. 165, 88 (2010). [2] X.-L. Luo and R. I. Tanner, “Finite element simulation of long and short circular die extrusion experiments using integral models”, International J. Numerical Methods in Engineering 25, 9 (1988). [3] A. Vázquez-Quesada, P. Espanol, R. I. Tanner and M. Ellero, “Shear thickening of a non-colloidal suspension with a viscoelastic matrix”, J. Fluid Mech. 880, 1070 (2019). [4] A. Jaishankar and G. H. McKinley, “A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids”, J. Rheo. 58, 1751 (2014).