Smoothed-Particle Hydrodinamics simularions of viscoelastic integral fractional models

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 Oldroyd-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.

[1] P Yang, YC Lam,K Zhu, J. Non-Newtonian Fluid Mech. 165, 88 (2010).

[2] X-L Luo and RI Tanner, International J. Numerical Methods in Engineering 25, 9 (1988).

[3] A Vázquez-Quesada, P Espanol, RI Tanner and M Ellero, J. Fluid Mech. 880, 1070 (2019).

[4] A Jaishankar and GH McKinley, J. Rheo. 58, 1751 (2014).